No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
On robust control of uncertain chaotic systems: A sliding-mode synthesis via chaotic optimization
Abstract
This paper presents a novel Lyapunov-based control approach which utilizes a Lyapunov function of the nominal plant for robust tracking control of general multi-input uncertain nonlinear systems. The difficulty of constructing a control Lyapunov function is alleviated by means of predefining an optimal sliding mode. The conventional schemes for constructing sliding modes of nonlinear systems stipulate that the system of interest is canonical-transformable or feedback-linearizable. An innovative approach that exploits a chaotic optimizing algorithm is developed thereby obtaining the optimal sliding manifold for the control purpose. Simulations on the uncertain chaotic Chen’s system illustrate the effectiveness of the proposed approach.
... Recently, Sun et al. [20] adopted chaos search algorithm to implement the node repositioning for tetrahedral mesh in the computer-aided design. Lu et al. [21][22][23] utilized chaos optimization algorithm to search and construct optimal sliding mode for tracking control of the Chen's chaotic system. Ji and Tang [24] and Liu et al. [25] suggested a hybrid method of simulated annealing and particle swarm optimization combined with chaos search, and examined its efficiency with several nonlinear functions, respectively. ...
... In general, there are three main characteristics of the variation of the chaotic variable, i.e. pseudo-randomness, ergodicity and irregularity. By using these properties, the chaos optimization algorithm is proposed and developed to solve various kinds of global optimization problem [16][17][18][19][20][21][22][23][24][25]. ...
... Since we have cut the 'bad' part of chaotic variable interval (0, 1) during the generation of chaotic sequences, which is distinct from the conventional chaos optimization algorithms in the papers [15][16][17][18][19][20][21][22][23][24][25], the presented hybrid optimization algorithm enhances the computational efficiency significantly. This will be confirmed by the numerical examples later. ...
Chaos optimization algorithms as a novel method of global optimization have attracted much attention, which were all based on Logistic map. However, we have noticed that the probability density function of the chaotic sequences derived from Logistic map is a Chebyshev-type one, which may affect the global searching capacity and computational efficiency of chaos optimization algorithms considerably. Considering the statistical property of the chaotic sequences of Logistic map and Kent map, the improved hybrid chaos-BFGS optimization algorithm and the Kent map based hybrid chaos-BFGS algorithm are proposed. Five typical nonlinear functions with multimodal characteristic are tested to compare the performance of five hybrid optimization algorithms, which are the conventional Logistic map based chaos-BFGS algorithm, improved Logistic map based chaos-BFGS algorithm, Kent map based chaos-BFGS algorithm, Monte Carlo-BFGS algorithm, mesh-BFGS algorithm. The computational performance of the five algorithms is compared, and the numerical results make us question the high efficiency of the chaos optimization algorithms claimed in some references. It is concluded that the efficiency of the hybrid optimization algorithms is influenced by the statistical property of chaotic/stochastic sequences generated from chaotic/stochastic algorithms, and the location of the global optimum of nonlinear functions. In addition, it is inappropriate to advocate the high efficiency of the global optimization algorithms only depending on several numerical examples of low-dimensional functions.
... Although it appears to be stochastic, it occurs in a deterministic non-linear system under deterministic conditions. In recently years, growing interests from physics, chemistry, biology and engineering have stimulated the studies of chaos for control [1,2], synchronization [3] and optimization [4][5][6]. Due to the easy implementation and special ability to avoid being trapped in local optima, chaos has been a novel optimization technique and chaos-based searching algorithms have aroused intense interests [7]. ...
... Through the rich non-equilibrium dynamics with various concomitant attractors, chaotic neuron-dynamics can be used to continually search for the global optimum by following chaotic ergodic orbits. The other one is chaotic optimization algorithm (COA) [5,6] based on chaotic evolution of variables. The simple philosophy of the COA includes two main steps: firstly mapping from the chaotic space to the solution space, and then searching optimal regions using chaotic dynamics instead of random search. ...
As a novel optimization technique, chaos has gained much attention and some applications during the past decade. For a given energy or cost function, by following chaotic ergodic orbits, a chaotic dynamic system may eventually reach the global optimum or its good approximation with high probability. To enhance the performance of particle swarm optimization (PSO), which is an evolutionary computation technique through individual improvement plus population cooperation and competition, hybrid particle swarm optimization algorithm is proposed by incorporating chaos. Firstly, adaptive inertia weight factor (AIWF) is introduced in PSO to efficiently balance the exploration and exploitation abilities. Secondly, PSO with AIWF and chaos are hybridized to form a chaotic PSO (CPSO), which reasonably combines the population-based evolutionary searching ability of PSO and chaotic searching behavior. Simulation results and comparisons with the standard PSO and several meta-heuristics show that the CPSO can effectively enhance the searching efficiency and greatly improve the searching quality.
... In order to find a sliding mode control law, uðtÞ 2 R 2 , which can guide the system state xðtÞ to track the prespecified reference signal x r ðtÞ, a sliding surface needs to be defined for the nominal system beforehand. The desired sliding manifold can be obtained by using the method proposed in [16]: ...
... For the purpose of controlling the nonlinear uncertain systems (1) by sliding mode control, the desired sliding manifold was firstly constructed via the method proposed in [16]: ...
As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. In this paper, chaos-based optimization is exploited so as to develop a systematic approach to seeking the simplex control vectors; particularly, the flexibility of simplex control is enhanced by making the simplex control vectors dependent on the Euclidean norm of the sliding vector rather than being constant, which result in both reduction of the chattering and speedup of the convergence. Computer simulation on a nonlinear uncertain system is given to illustrate the effectiveness of the proposed control method.
... The paper by Lu et al. [2003] presents a Lyapunov-based control approach which utilizes a Lyapunov function of the nominal plant for robust tracking control of general multi-input uncertain nonlinear systems. They have developed a chaotic optimizing algorithm to obtain the optimal sliding manifold for control purposes. ...
Robust control of chaotic vibration in composite plate in the presence of noise using sliding mode control methodology is considered in this paper. The composite plate system has a combination of linear, quadratic and cubic stiffness terms. Robustness of the controller is analyzed with reference to the parametric variations of the system and external disturbances due to noise and compared with Pyragas control method. The composite plate considered is a six-layered rectangular antisymmetric cross-ply plate with immovable edges. The plate is assumed to be viscously damped and harmonically excited.
... Chaos theory was applied to various fields such as optimization (Alikhani et al. 2016;Jiang 1998;Aihara et al. 1990;Lu et al. 2003), synchronization (Pecora and Carroll 1990), machine vision (Firouznia et al. 2018;Abdechiri et al. 2017) and control (Ott et al. 1990;Kapitaniak 1995). In 1963, Edward Lorenz exhibited the first chaotic attractor by a toy model. ...
This paper presents a novel chaotic augmented Lagrange method for solving constrained optimization problems. The algorithm employs chaotic maps to reduce the search space and to get the best parameters for handling the problem constraints. Then, the first carrier wave method can be applied to obtain a solution as an initial point of simplex method to find optimal solution. To verify the efficiency of the proposed algorithm, an empirical study is conducted in three groups: mathematical, challenging, and structural optimization problems. The experimental results show that the proposed method can solve different kinds of constrained optimization problems with great precision.
... In addition, being deterministic and ergodic, chaos is combined with evolutionary heuristics and acts as a prominent role in solving optimization problems. There exist two chaotic ways to be applied to optimization areas [3][4][5]. The first way is to introduce chaos into a unified ensemble like neural network. ...
Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO), we herein propose a chaotic proportional integral derivative (PID) controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles’ search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles’ premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA) and PSO.
... Generating an ideal random sequence is of great importance in the fields of numerical analysis, sampling and heuristic optimization. Recently, a technique which employs chaotic sequences via the chaos approach (chaotic maps) has gained a lot of attention and been widely applied in different areas, such as the chaotic neural network (CNN) [8], chaotic optimization algorithms (COA) [9], [10], nonlinear circuits [11], DNA computing [12], and image processing [13]. All of the above-mentioned methods rely on the same pivotal operation, namely the adoption of a chaotic sequence instead of a random sequence, and thereby improve the results due to the unpredictability of the chaotic sequence [14]. ...
In this paper, an intelligent PID controller based on Chaotic Particle Swarm Optimization (CPSO) algorithm for Ball and Hoop system is designed. In this system, two goals are tracked; the first one implies on set-point tracking, and the second one includes both set-point tracking and disturbance rejection. The classical methods of PID tuning such as Ziegler-Nichols are based on trial and error, and generally, their responses have a high settling time and overshoot; however, the proposed CPSO-PID controller determines the parameters of PID controller automatically and intelligently by minimizing the integral absolute error (IAE). The simulation results on Ball and Hoop system show that the proposed CPSO-PID controller leads to superior performance compared to Ziegler-Nichols method in both set-point tracking and disturbance rejection in terms of rise time, settling time, maximum overshoot, and the integral of absolute error (IAE) performance criterion. Index Terms—Chaotic particle swarm optimization, PID controller, ball and hoop system, integral of absolute error (IAE).
... During the last decade, various techniques and approaches have been proposed for controlling chaos under different conditions and requirements, which include for instance methods of differential geometric control [6,7], sliding mode control [15,25], backstepping [17], linear state-feedback control [10], and so on. More recently, some adaptive control methods are also developed for classes of chaotic systems with uncertain parameters, based on the Lyapunov stability theory [3,9,16,23,24]. ...
In practice, most physical chaotic systems are inherently with urdmown nonlinearities, and conventional adaptive control for such chaotic systems typically faces with formidable technical challenges. As a better alternative, we propose using the recurrent high-order neural networks to identify and control the urdmown chaotic systems, in which the Lyapunov synthesis approach is utilized for tuning the neural network model parameters. The globally uniform boundedness of the parameters estimation errors and the asymptotical stability of the tracking errors are proved by Lyapunov stability theory and LaSalle-Yoshizawa theorem. This method, in a systematic way, enables stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory. Computer simulation on a complex chaotic system illustrates the effectiveness of the proposed control method.
... Generating an ideal random sequence is of great importance in the fields of numerical analysis, sampling and heuristic optimization. Recently, a technique which employs chaotic sequences via the chaos approach (chaotic maps) has gained a lot of attention and been widely applied in different areas, such as the chaotic neural network (CNN) [18], chaotic optimization algorithms (COA) [19], [20], nonlinear circuits [21], DNA computing [22], and image processing [23]. All of the above-mentioned methods rely on the same pivotal operation, namely the adoption of a chaotic sequence instead of a random sequence, and thereby improve the results due to the unpredictability of the chaotic sequence [24]. ...
In this paper, An Intelligent PID Controller has been tuned by minimizing the Integral of Time multiplied Absolute Error (ITAE) and squared control signal (ITAESCS) for a DC motor. The parameters of PID controller, automatically and intelligently are determined by Chaotic Particle Swarm Optimization (CPSO) Algorithm. The experimental results demonstrate that the performance of proposed Intelligent CPSO-PID controller is superior to the conventional Ziegler-Nichols method in terms of settling time, maximum overshoot and ITAESCS.
... The notion of species based PSO (SPSO) was proposed by Li (2004), for solving multimodal optimization problems. Chaos is a kind of characteristic of nonlinear systems and chaotic motion can traverse every state in a certain region by its own regularity, and nowadays, it has been applied in different fields (Jiang, Kwong, Chen, & Ysim, 2012;Lu, Shieh, & Chen, 2003;Wong, Kwok, & Law, 2008;Zhao, Sun, Sun, & Jiang, 2011). Due to the unique ergodicity and special ability in avoiding being trapped in local optima, chaos search is much higher than some other stochastic algorithms (Li & Jiang, 1998). ...
... Chaos is a kind of characteristic of nonlinear systems and chaotic motion can traverse every state in a certain region by its own regularity, and nowadays, has been applied in different fields [4,5]. The scheme of opposition-based learning (OBL) was introduced by Tizhoosh in 2005 [6]. ...
An evolutionary circle detection method based on a novel Chaotic Hybrid Algorithm (CHA) is proposed. The method combines the strengths of particle swarm optimization, genetic algorithms and chaotic dynamics, and involves the standard velocity and position update rules of PSOs, with the ideas of selection, crossover and mutation from GA. The opposition-based learning (OBL) is employed in CHA for population initialization. In addition, the notion of species is introduced into the proposed CHA to enhance its performance in solving multimodal problems. The effectiveness of the Species-based Chaotic Hybrid Algorithm (SCHA) is proven through simulations and benchmarking; finally it is successfully applied to solve circle detection problems. To make it more powerful in solving circle detection problems in complicated circumstances, the notion of ‘tolerant radius’ is proposed and incorporated into the SCHA-based method. Simulation tests were undertaken on several hand drawn sketches and natural photos, and the effectiveness of the proposed method was clearly shown in the test results.
... Although it appears to be stochastic, it occurs in a deterministic nonlinear system under deterministic conditions. In recent years, growing interests from physics, chemistry, biology and engineering have stimulated the studies of chaos for control [1][2][3][4], synchronization [5,6] and optimization [7][8][9][10][11]. ...
This paper applies a novel evolutionary algorithm named differential evolution (DE) to direct the orbits of discrete chaotic dynamical systems towards desired target region within a short time by adding only small bounded perturbations, which could be formulated as a multi-modal numerical optimization problem with high dimension. Moreover, the synchronization of chaotic systems is also studied, which can be dealt with as an online problem of directing orbits. Numerical simulations based on Hénon Map demonstrate the effectiveness and efficiency of DE, and the effects of some parameters are investigated as well.
... Currently, it has raised enormous interest in different fields of sciences, such as chaos control, synchronization, pattern recognition, optimization theory and so on. In random-based optimization algorithms, the methods using chaotic variables instead of random variables are called chaotic optimization algorithm (COA) [2][3][4][5][6][7]. Numerical results indicate that COA can more easily escape from local optima for comparing with other stochastic optimization algorithms although it is not mathematically proved yet [8]. ...
The goal of this paper is to present a novel chaotic particle swarm optimization (CPSO) algorithm and compares the efficiency of three one-dimensional chaotic maps within symmetrical region for long-term cascaded hydroelectric system scheduling. The introduced chaotic maps improve the global optimal capability of CPSO algorithm. Moreover, a piecewise linear interpolation function is employed to transform all constraints into restrict upriver water level for implementing the maximum of objective function. Numerical results and comparisons demonstrate the effect and speed of different algorithms on a practical hydro-system.
... Mathematically, chaos is random and unpredictable, yet it also possesses an element of regularity due to its deterministic dynamic behavior within a bounded nonlinear system. Since logistic maps are frequently used as chaotic behavior maps, the chaotic sequences can be quickly generated and easily stored; thus there is no need to record long sequences [10]. This function generates random seed processes and further improves the performance of PSO due to the logistic map's unpredictability. ...
... Although it appears to be stochastic, it occurs in a deterministic nonlinear system under deterministic conditions. In recently years, growing interests from physics, chemistry, biology and engineering have stimulated the studies of chaos for control [1][2][3], synchronization [4] and optimization [5][6][7][8][9]. ...
This paper applies a novel evolutionary computation algorithm named particle swarm optimization (PSO) to direct the orbits of discrete chaotic dynamical systems towards desired target region within a short time by adding only small bounded perturbations, which could be formulated as a multi-modal numerical optimization problem with high dimension. Moreover, the synchronization of chaotic systems is also studied, which can be dealt with as an online problem of directing orbits. Numerical simulations based on Hénon Map demonstrate the effectiveness and efficiency of PSO, and the effects of some parameters are also investigated.
... As a characteristic of non-linear systems, chaos is a bounded unstable dynamic behavior that exhibits sensitive dependence on initial conditions and includes infinite unstable periodic motions. Control and synchronization of chaotic systems have been investigated intensely in various fields during recent years [1][2][3][4][5][6]. Many of the proposed approaches only work under the assumption that the parameters of chaotic systems are known in advance. ...
Parameter estimation for chaotic systems is an important issue in nonlinear science and has attracted increasing interests from various research fields, which could be essentially formulated as a multi-dimensional optimization problem. As a novel evolutionary computation technique, particle swarm optimization (PSO) has attracted much attention and wide applications, owing to its simple concept, easy implementation and quick convergence. However, to the best of our knowledge, there is no published work on PSO for estimating parameters of chaotic systems. In this paper, a PSO approach is applied to estimate the parameters of Lorenz system. Numerical simulation and the comparisons demonstrate the effectiveness and robustness of PSO. Moreover, the effect of population size on the optimization performances is investigated as well.
... It needs to be re-tuned adequately to retain robust control performance over a wide range of operating conditions [4] . Alternatively, several approaches have been proposed in the literature for controlling nonlinear processes, such as model predictive control [5], neural control [6], fuzzy control78910, robust control [11], sliding mode control [12,13], and adaptive control141516. Adaptive control methods are able to cope with control problems involving internal process uncertainties as well as external environmental uncertainties. ...
It is well known that conventional control theories are widely suited for applications where the processes can be reasonably described in advance. However, when the plant’s dynamics are hard to characterize precisely or are subject to environmental uncertainties, one may encounter difficulties in applying the conventional controller design methodologies. Despite the difficulty in achieving high control performance, the fine tuning of controller parameters is a tedious task that always requires experts with knowledge in both control theory and process information. Nowadays, more and more studies have focused on the development of adaptive control algorithms that can be directly applied to complex processes whose dynamics are poorly modeled and/or have severe nonlinearities. In this context, the design of a Model-Free Learning Adaptive Control (MFLAC) based on pseudo-gradient concepts and optimization procedure by a Particle Swarm Optimization (PSO) approach using constriction coefficient and Hénon chaotic sequences (CPSOH) is presented in this paper. PSO is a stochastic global optimization technique inspired by social behavior of bird flocking. The PSO models the exploration of a problem space by a population of particles. Each particle in PSO has a randomized velocity associated to it, which moves through the space of the problem. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed CPSOH introduces chaos mapping which introduces some flexibility in particle movements in each iteration. The chaotic sequences allow also explorations at early stages and exploitations at later stages during the search procedure of CPSOH. Motivation for application of CPSOH approach is to overcome the limitation of the conventional MFLAC design, which cannot guarantee satisfactory control performance when the plant has different gains for the operational range when designed by trial-and-error by user. Numerical results of the MFLAC with CPSOH tuning for a nonlinear distillation column model are showed.
... In order to improve the whole performance and to enhance the GA's operations in terms of searching ability, the notion of chaos is introduced into the initialization and replaces the ordinary GA mutation. Chaos is a kind Chaotic Hybrid Algorithm and Its Application in Circle Detection 303 of characteristic of nonlinear systems and chaotic motion can traverse every state in a certain region by its own regularity, and nowadays has been applied in different fields [4,5]. Due to the unique ergodicity and special ability in avoiding being trapped in local optima, the performance of chaos search is much higher than some other sto-chastic algorithms [6]. ...
An evolutionary circle detection method based on a novel Chaotic Hybrid Algorithm (CHA) is proposed. The method combines the
strengths of particle swarm optimization, genetic algorithms and chaotic dynamics, and involves the standard velocity and
position updating rules of PSO with the ideas of GA selection, crossover and mutation. In addition, the notion of species
is introduced into the proposed CHA to enhance its performance in solving multimodal problems. The effectiveness of the Species
based Chaotic Hybrid Algorithm (SCHA) is proven through simulations and benchmarking, and finally, it is successfully applied
to solve circle detection problems.
This paper presents a novel multi-swarm competitive algorithm based on the dynamic task allocation particle swarm optimization (MSCPSO-DTA) to solve global optimization problems. The MSCPSO-DTA consists of three main steps. Firstly, we propose a multi-swarm competitive (MSC) schedule to help the stagnant sub-swarm to jump out of local optima. When a certain condition is matched, the stagnant sub-swarm will be reinitialized with a chaotic strategy to begin a new search process in a different part of the search space. Secondly, in order to serve the MSC strategy which will reinitialize the stagnant sub-swarms and need the inertia weight to be increased correspondingly, a novel adaptive inertia weight strategy is proposed based on the maximum distance between the particles. Thirdly, a modified dynamic task allocation (DTA) strategy is adopted to make a better control of the balance between exploitation and exploration; specifically, with the help of the cumulative distribution function of normal distribution, the swarm is automatically divided into two labors to serve different tasks according to the position diversity. A set of benchmark functions are employed to test the performance of the proposed algorithm, as well as the contribution of each strategy employed in improving the performance of the algorithms. Experimental results demonstrate that, compared with other seven well-established optimization algorithms, the MSCPSO-DTA significantly performs the greatest improvement in terms of searching reliability, searching efficiency, convergence speed, and searching accuracy on most of the problems.
Recognition of cattle based on muzzle point image pattern (nose print) is a well study problem in the field of animal biometrics, computer vision, pattern recognition and various application domains. Missed cattle, false insurance claims and relocation at slaughter houses are major problems throughout the world.Muzzle pattern of cattle is a suitable biometric trait to recognize them by extracted features from muzzle pattern by using computer vision and pattern recognition approaches. It is similar to human’s fingerprint recognition. However, the accuracy of animal biometric recognition systems is affected due to problems of low illumination condition, pose and recognition of animal at given distance. Feature selection is known to be a critical step in the design of pattern recognition and classifier for several reasons. It selects a discriminant feature vector set or pre-specified number of features from muzzle pattern database that leads to the best possible performance of the entire classifier in muzzle recognition of cattle. This book chapter presents a novel method of feature selection by using Hybrid Chaos Particle Swarm Optimization (PSO) and Bacterial Foraging Optimization (BFO) techniques. It has two parts: first, two types of chaotic mappings are introduced in different phase of hybrid algorithms which preserve the diversity of population and improve the global searching capability; (2) this book chapter exploited holistic feature approaches: Principal Component Analysis (PCA), Local Discriminant Analysis (LDA) and Discrete Cosine Transform (DCT) [28, 85] extract feature from the muzzle pattern images of cattle. Then, feature (eigenvector), fisher face and DCT feature vector are selected by applying hybrid PSO and BFO metaheuristic approach; it quickly find out the subspace of feature that is most beneficial to classification and recognition of muzzle pattern of cattle. This chapter provides with the stepping stone for future researches to unveil how swarm intelligence algorithms can solve the complex optimization problems and feature selection with helps to improve the cattle identification accuracy.
Parameter estimation of chaotic systems is essentially a multidimensional optimization problem. To estimate the unknown parameters of chaotic systems precisely, we present an effective hybrid quantum-inspired evolutionary algorithm (HQEA), in which the real-valued quantum angle is used to express the Q-bits of chromosome, and the probability of each Q-bit is considered the position information of the chromosome. Combining the quantum differential evolutionary algorithm (QDE) which uses differential evolution to update the state of Q-bits with the real-coded quantum evolutionary algorithm (RQEA) which employs quantum rotation gate to update the state of Q-bits, we make a balance between the global exploration and the local exploitation. In addition, the HQEA performs the quantum non-gate operation in which the Q-bits selected from the current best chromosome with a certain probability are transformed to get rid of the premature local optimum. The experimental results of benchmark function tests show that the HQEA algorithm greatly improves the global optimization performance as well as the reliability performance. Numerical simulation results of the Lorenz system also demonstrate its effectiveness.
In order to improve system stability and to increase the power factor, we put forward a new approach of design for a high-voltage static var compensator and parameter calculation, in which the system adopts a photoelectric trigger, and control commands are produced by upper computer and transferred to monitoring system in a low potential computer by ethernet. After analyzing and processing data, a monitoring system deduces the trigger and testing orders, which are sent to a trigger board in the high-voltage by fiber according to sync signal. To control the thyristor trigger and to detect the fault condition of the thyristor, the fault signals are returned to the monitoring system by fiber, too. The system control algorithm can not only achieve the power factor compensation, but also achieve unbalance compensation. We also present a description of the hardware architecture and the parameter calculation of loop inductance and average voltage circuit. Moreover, in order to optimize the parameters of passive filter, a Logistic mapping and its chaos feature are introduced and adopted to calculate a set of optimized parameters. At last, the simulation and experiment results show that the system has a good compensation effect and high reliability.
Parameter estimation for chaotic systems is an important issue in nonlinear science which could be essentially formulated as a multidimensional optimization problem. For the accurate estimation of the unknown parameters of chaotic systems, puts forward the quantum genetic algorithm (QGA) is used to solve the optimization problem. The formulation of the parameter estimation as a nonlinear optimization problem to minimize the synchronization error of the observed state of the actual system and its mathematical model, benchmark function test shows that QGA's global search ability and reliability are improved greatly. Through a typical chaotic systems for numerical simulation of Lorenz equation and compared with QA and PSO show that whether it is in the speed and accuracy of identification of optimization have shown superiority. Quantum genetic algorithm is an efficient intelligent algorithm; the simulation results demonstrate the effectiveness of the proposed method.
In this paper, we present an efficient algorithm for the prediction of sunspotrelated time series, namely the Chaotic Dynamic Adaptive Local Search (CDALS) algorithm. This algorithm is based on exploiting partially recurrent Elman Neural Network (ENN) and it can be divided into two main steps: the first one is the basic model of the Adaptive Local Search (ALS) proposed in our previous work. After that, a hybrid local search method is proposed by introducing the chaos signals into ALS. Thus, ALS and chaos are hybridized to form a powerful CDALS algorithm, which reasonably combines the searching ability of ALS and chaotic searching behavior. Simulation results show that the CDALS algorithm can eventually reach the global optimum or its good approximation with high probability, effectively enhance the searching efficiency and quality within reasonable number of iterations. ICIC International
The flowshop scheduling problem has been widely studied in the literature and many techniques have been applied to it, but few algorithms have been proposed to solve it using particle swarm optimization algorithm (PSO) based algorithm. In this paper, an improved PSO algorithm (IPSO) based on the ldquoall differentrdquo constraint is proposed to solve the flowshop scheduling problem with the objective of minimizing makespan. It combines the particle swarm optimization algorithm with genetic operators together effectively. When a particle is going to stagnates, the mutation operator is used to search its neighborhood. The proposed algorithm is tested on different scale benchmarks and compared with the recently proposed efficient algorithms. The results show that both the solution quality and the convergent speed of the IPSO algorithm precede the other two recently proposed algorithms. It can be used to solve large scale flowshop scheduling problem effectively.
This study is devoted to schedule a three-stage manufacturing system including machining, assembly and batch processing stages. The system is supposed to be capable of manufacturing a variation of products. At the first stage, the need for machining raw parts causes the manufacturer to deal with a flow shop scheduling problem. In the next stage, processed parts should be assembled together in order to form desired products. It is noteworthy that several operations are not allowed to be executed simultaneously on the same machine. Second stage should be considered as a single-assembly line or a single team of operators, and finally the manufacturing processing stage. The considered objectives are to minimize completion time of all products (makespan) and sum of the earliness and tardiness costs, simultaneously. First, the proposed scheduling problem is formulated into a mixed-integer mathematical model, and then owing to the NP-hardness of the concluded model a meta-heuristic approach is applied. A hybrid algorithm is modified to create a powerful method in searching the discrete solution space of this problem by taking advantage of superiorities of both Genetic Algorithm and Particle Swarm Optimization methods. Numerical experiments are designed to evaluate the performance of the proposed algorithm.
Contemporary design in engineering and industry relies heavily on computer simulation and efficient algorithms to reduce the cost and to maximize the performance and sustainability as well as profits and energy efficiency. Solving an optimization problem correctly and efficiently requires not only the right choice of optimization algorithms and simulation methods, but also the proper implementation and insight into the problem of interest. This book consists of ten self-contained, detailed case studies of real-world optimization problems, selected from a wide range of applications and contributed from worldwide experts who are working in these exciting areas.
Optimization topics and applications include gas and water supply networks, oil field production optimization, microwave engineering, aerodynamic shape design, environmental emergence modelling, structural engineering, waveform design for radar and communication systems, parameter estimation in laser experiment and measurement, engineering materials and network scheduling. These case studies have been solved using a wide range of optimization techniques, including particle swarm optimization, genetic algorithms, artificial bee colony, harmony search, adaptive error control, derivative-free pattern search, surrogate-based optimization, variable-fidelity modelling, as well as various other methods and approaches. This book is a practical guide to help graduates and researchers to carry out optimization for real-world applications. More advanced readers will also find it a helpful reference and aide memoire.
The chaos phenomenon has been observed in many natural and manmade systems. It can potentially direct a system to unstable condition, undesirable performance, and terrible situations. In many practical applications, in order to improve performance of a system and avoid undesirable situations caused by chaos, the system must be controlled in way which makes it able to remove the chaos. Moreover, the control signal must be smooth, since high frequency switching caused by chattering effect can be destructive for some control devices. This paper presents a finite time sliding mode control strategy to control chaotic systems. The main objective is controlling chaos smoothly without chattering phenomenon. The sliding manifold is constructed using Lyapunov function and is attained in finite time. It is proved that if the states are confined to the sliding surface, then the chaotic trajectory will slide toward the origin. A controller is designed, based on smooth second order sliding mode control, so that there is no chattering in the states of the system, and the control input is a smooth signal, also finite time convergence is attained. An illustrative example is given to demonstrate the effectiveness of the proposed sliding mode controller.
This study mainly focuses on the development of a total sliding-mode control (TSMC) strategy for a Chua's chaotic circuit. The TSMC scheme, which is insensitive to uncertainties including parameter variations and external disturbance in the whole control process, comprises the baseline model design and the curbing controller design. In the baseline model design, a computed torque controller is designed to cancel the non-linearity of the nominal plant. In the curbing controller design, an additional controller is designed using a new sliding surface to ensure the sliding motion through the entire state trajectory. Therefore the controlled system has a total sliding motion without a reaching phase in the TSMC system. The effectiveness of the proposed TSMC scheme is verified by experimental results, and the advantages of good transient response and robustness to uncertainties are indicated in comparison with a conventional sliding-mode control system.
Robust control of chaotic vibration in composite plate in the presence of noise using sliding mode control methodology is considered in this paper. The composite plate system has a combination of linear, quadratic and cubic stiffness terms. Robustness of the controller is analyzed with reference to the parametric variations of the system and external disturbances due to noise and compared with Pyragas control method. The composite plate considered is a six-layered rectangular antisymmetric cross-ply plate with immovable edges. The plate is assumed to be viscously damped and harmonically excited.
Chaos theory studies the behavior of dynamical systems that are highly sensitive to their initial conditions. This effect is popularly referred to as the butterfly effect. Small differences in the initial conditions yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general. In mathematics, a chaotic map is a map (i.e., an evolution function) that exhibits some sort of chaotic behavior. Chaotic maps occur in the study of dynamical systems and often generate fractals. In this paper, an improved logistic map, namely a double-bottom map, with particle swarm optimization was applied to the test function. Simple PSO adopts a random sequence with a random starting point as a parameter, and relies on this parameter to update the positions and velocities of the particles. However, PSO often leads to premature convergence, especially in complex multi-peak search problems. In recent years, the use of chaotic sequences in optimization techniques rather than random sequences with random seeds has been growing steadily. Chaotic sequences, which are created by means of chaotic maps, have been proven easy and fast to generate and are more easily stored then random seed processes. They can improve the performance of PSO due to their unpredictability. Double-bottom maps are designed by the updating equation of PSO in order to balance the exploration and exploitation capability. We embedded many commonly used chaotic maps as well as our double-bottom map into PSO to improve performance, and compared these versions to each other to demonstrate the effectiveness of the PSO with the double-bottom map. We call this improved PSO method Double-Bottom Map PSO (DBMPSO). In the conducted experiments, PSO, DBMPSO and other chaotic PSOs were extensively compared on 22 benchmark test functions. The experimental results indicate that the performance of DBMPSO is significantly better than the performance of other PSOs tested.
Particle swarm optimization (PSO) is a population based statistical optimization technique which inspired by social behavior of bird flocking or fish schooling. PSO algorithm has been developing rapidly and has been applied widely since it was introduced, as it is easily understood and realized. The main weakness of PSO especially in multi modal problems is trapping in local optimums. This paper presents an improved particle swarm optimization algorithm (CLAPSO) to improve the performance of standard PSO, which uses the dynamic inertia weight. Experimental results indicate that the CLAPSO improves the search performance on the benchmark functions significantly.
This letter studies the robust synchronization and parameter identification problems on a class of uncertain chaotic systems with bounded time-varying unknown parameters. Based on Lyapunov stability theory, a novel robust controller and a parameter identification scheme are proposed. The proposed scheme can successfully synchronize some typical chaotic systems, such as Rössler and Lorenz chaotic systems, with their parameters also convergence to the nominal value despite the noise of the parameters. Simulation results verify the proposed scheme’s effectiveness.
It is well known that the flow-shop scheduling problem (FSSP) is a branch of production scheduling and is NP-hard. Now, many different approaches have been applied for permutation flow-shop scheduling to minimize makespan, but current algorithms even for moderate size problems cannot be solved to guarantee optimality. Some literatures searching PSO for continuous optimization problems are reported, but papers searching PSO for discrete scheduling problems are few. In this paper, according to the discrete characteristic of FSSP, a novel particle swarm optimization (NPSO) algorithm is presented and successfully applied to permutation flow-shop scheduling to minimize makespan. Computation experiments of seven representative instances (Taillard) based on practical data were made, and comparing the NPSO with standard GA, we obtain that the NPSO is clearly more efficacious than standard GA for FSSP to minimize makespan.
In this paper, a chattering-free sliding mode controller design for uncertain chaotic systems is presented. Since the implementation of the sliding mode control may cause a significant problem of chattering, many modified methodologies have been developed to overcome this drawback. However, each of them has own problems such as lack of robustness against disturbance variations, steady-state error, large convergence time and effect on transient performance. This paper proposes an improved sliding mode control strategy in which a modified sliding condition in a continuous function in control signal is taken into account instead of discontinuous part and also it adds an auxiliary continuous control to the control input. Then, the stability of controlled system is proved by using Lyapunov’s direct method. The usefulness of this proposed method for eliminating the chattering phenomenon in transient and steady states, in the face of uncertain chaotic systems with disturbances, is well appeared. For this purpose, the Lorenz system is studied and its simulation results are presented to demonstrate the effectiveness of the proposed control scheme.
In this paper, a novel robust controller based on Lyapunov stability theory is introduced. This controller can achieve the tracking control of a class of chaotic systems with time-varying unknown parameters. Without complex algorithms, this robust controller is achieved by adjusting the robust factor. By adjusting the robust factor, the controller can be applied to different chaotic systems with different uncertainties. By increasing or decreasing the robust factor’s weight, the controller can perform different robustness. Increasing the robust factor, the proposed controller can stand larger uncertainties of the parameters, and can track the desired orbit more quickly. So the structure of the controller is flexible, it can be easily adjusted for different applications. Simulation results with R
This study is concerned with the identical synchronization problem for a class of chaotic systems. A dynamic compensator is proposed to achieve the synchronization between master and slave chaotic systems using only the accessible output variables. A sufficient condition is also proposed to ensure the global synchronization. Furthermore, the strictly positive real (SPR) restriction, which is normally required in most of the observer-based synchronization schemes, is released in our approach. Two numerical examples are included to illustrate the proposed scheme.
In this paper, an improved differential evolution algorithm, named the Taguchi-sliding-based differential evolution algorithm
(TSBDEA), is proposed to solve the problem of parameter identification for Chen, Lü and Rossler chaotic systems. The TSBDEA,
a powerful global numerical optimization method, combines the differential evolution algorithm (DEA) with the Taguchi-sliding-level
method (TSLM). The TSLM is used as the crossover operation of the DEA. Then, the systematic reasoning ability of the TSLM
is provided to select the better offspring to achieve the crossover, and consequently enhance the DEA. Therefore, the TSBDEA
can be more robust, statistically sound, and quickly convergent. Three illustrative examples of parameter identification for
Chen, Lü and Rossler chaotic systems are given to demonstrate the applicability of the proposed TSBDEA, and the computational
experimental results show that the proposed TSBDEA not only can find optimal or close-to-optimal solutions but also can obtain
both better and more robust results than the DEA.
Differential evolution algorithm-Taguchi sliding level method-Chaotic systems
An important issue in nonlinear science is parameter estimation for Lorenz chaotic systems. There has been increasing interest
in this issue in various research fields, and it could essentially be formulated as a multidimensional optimization problem.
A novel evolutionary computation algorithm, nonlinear time-varying evolution particle swarm optimization (NTVEPSO), is employed
to estimate these parameters. In the NTVEPSO method, the nonlinear time-varying evolution functions are determined by using
matrix experiments with an orthogonal array, in which a minimal number of experiments would have an effect that approximates
tothe full factorial experiments. The NTVEPSO method and other PSO methods are then applied to identify the Lorenz chaotic
system. Simulation results demonstrate the feasibility and superiority of the proposed NTVEPSO method.
Key wordsParticle swarm optimization-Nonlinear timevarying evolution-Orthogonal array-Lorenz chaotic system
Genetic Algorithms (GAs) have been widely used to solve network optimization problems with varying degrees of success. Part
of the problem with GAs lies in the premature convergence when dealing with large-scale and complex problems; Caught in local
optima, the algorithm might fail to reach the global optimum even after a large number of iterations. In order to overcome
the problems with traditional GAs, a method is proposed to integrate Chaos Optimization Algorithms (COAs) with GA to fully
exploit their respective searching advantages. The basic idea of COA is to transform the problem variables, by way of a map,
from the solution space to a chaos space and to perform a search that benefits from the randomness, orderliness and ergodicity
of chaos variable. In this chapter, we will first discuss network optimization in general, and then focus on how chaos theory
can be incorporated into the GA in order to enhance its optimization capacities. We will also examine the efficiency of the
proposed Chaos-Genetic algorithm in the context of two different types of network optimization problems, Grid scheduling and
Network-on-Chip mapping problem.
Keywordsnetwork optimization–Genetic Algorithm–Chaos theory–Grid scheduling–Network-on-Chip mapping problem
A new hybrid particle swarm optimization (PSO) algorithm with adaptive inertia weight factor (AIWF) is proposed. By incorporating chaotic local research method, it proposed the PSO which combined with chaos (CPSO), and applied it in evolving the artificial neural network (ANN). Then, based on the actual load data provided by a regional power grid in the south of China, the proposed method is used in the load forecasting. Results and comparisons with the PSO-ANN and the GA-ANN algorithms show that the CPSO can effectively enhance the searching efficiency and greatly improve the searching quality. While being used in the short-term load forecasting, the CPSO-ANN is better than the other algorithms in both forecasting effect and network function, such as PSO-ANN, GA-ANN and so on
This paper presents the tuning of the structure and parameters of a wavelet neural network (WNN) using a improved chaotic particle swarm optimization (ICPSO), the ICPSO approach is a method of combining the improved particle swarm optimization (IPSO), which has a powerful global exploration capability, with the chaotic strategy , which can exploit the local optima. By introduced a new strategy to the ICPSO, it will also be shown that the ICPSO performs better than the traditional PSO and GA based on some benchmark test functions. A WNN with switches introduce to links is proposed. By tuning the structure and improving the connection weights of WNN simultaneously, a partially connected WNN can be obtained. By doing this, it eliminates some ill effects introduced by redundant in features of WNN. An application example on Iris forecasting is given to show the merits of the ICPSO and the improved WNN.
This paper investigates the control of chaos for several classical chaotic Rössler type systems using the sliding mode control strategy. For an arbitrarily given equilibrium point of a Rössler system, we achieve global stabilizing for the equilibrium points. Particularly, a class of proportional–integral (PI) switching surface is introduced for determining the convergence rate. Six typical Rössler systems are studied and their simulation results are presented to demonstrate the effectiveness of the proposed control scheme.
In this paper, we analyze the dynamics of a system consisting of two coupled nonlinearly Duffing oscillators, obtained from a nonlinear electrostatic device which is a prototype of emitters and receivers in communication engineering. Inverse or backward period doubling cascades and sudden transition to chaos are observed. A sliding mode controller is applied to control the electrostatic transducers system. The sliding surface used is one dimension higher than the traditional surface and guarantees its passage through the initial states of the controlled system. By means of the design of sliding mode dynamics characteristics, the controlled system performance is arbitrarily determined by assigning the switching gain of the sliding mode dynamics. Therefore, using the characteristic of this sliding mode we aim to design a controller that can meet the desired specification and use less control energy by comparing with the result in the current literature. The results show that the proposed controller can steer electrostatic transducers to the desired reference trajectory without chattering phenomenon and abrupt state change.
Particle swarm optimization (PSO) algorithm has been developing rapidly and has been applied widely since it was introduced, as it is easily understood and realized. This paper presents an improved particle swarm optimization algorithm (IPSO) to improve the performance of standard PSO, which uses the dynamic inertia weight that decreases according to iterative generation increasing. It is tested with a set of 6 benchmark functions with 30, 50 and 150 different dimensions and compared with standard PSO. Experimental results indicate that the IPSO improves the search performance on the benchmark functions significantly.
Parameter estimation for chaotic systems is an important issue in nonlinear science and has attracted increasing interests from various research fields, which could be essentially formulated as a multidimensional optimization problem. As a novel evolutionary computation technique, differential evolution algorithm (DE) has attracted much attention and wide applications, owing to its simple concept, easy implementation and quick convergence. However, to the best of our knowledge, there is no published work on DE for estimating parameters of chaotic systems. In this paper, a DE approach is applied to estimate the parameters of Lorenz system. Numerical simulation and the comparisons demonstrate the effectiveness and robustness of DE. Moreover, the effect of population size on the optimization performances is investigated as well.
Control of chaotic systems is an important issue in nonlinear science, which could be formulated as a multi-modal numerical optimization problem with high dimension. As a novel evolutionary computation technique, chaotic particle swarm optimization (CPSO) has attracted much attention and wide applications, owing to its simple concept and easy implementation. This investigation elucidates the feasibility of applying CPSO to direct the orbits of discrete chaotic dynamical systems towards desired target region within a short time by adding only small bounded perturbations. Numerical simulations based on Hénon Map demonstrate the effectiveness and efficiency of CPSO, and the effects of some parameters are also investigated.
As a kind of correlated time-dependent behavior between different processes when they interact with each other, synchronization for finite-dimension chaotic dynamical systems is an important and active research issue in nonlinear dynamics science. Due to its potential applications in explaining natural systems, designing engineering systems, and so on, researches are focused on proposing effective and efficient approaches for synchronization of chaotic systems. As a novel evolutionary computation technique, chaotic particle swarm optimization (CPSO) (B. Liu, L. Wang, Y. Jin, F. Tang, and D. Huang, “Improved particle swarm optimization combined with chaos,” Chaos, Solitons & Fractals, vol. 25, pp. 1261-1271, 2005) has attracted much attention and wide applications, owing to its simple concept and easy implementation. In this study, an attempt is made to propose an optimization-based approach, i.e., CPSO based approach for chaotic synchronization, which could be formulated as an on-line multi-modal numerical optimization problem with high dimension. Numerical simulations based on Hénon map elucidate the feasibility of CPSO for synchronization of finite dimensional Hénon dynamical system.
Chaotic catfish particle swarm optimization (C-CatfishPSO) is a novel optimization algorithm proposed in this paper. C-CatfishPSO introduces chaotic maps into catfish particle swarm optimization (CatfishPSO), which increase the search capability of CatfishPSO via the chaos approach. Simple CatfishPSO relies on the incorporation of catfish particles into particle swarm optimization (PSO). The introduced catfish particles improve the performance of PSO considerably. Unlike other ordinary particles, catfish particles initialize a new search from extreme points of the search space when the gbest fitness value (the best previously encountered value) has not changed for a certain number of consecutive iterations. This results in further opportunities of finding better solutions for the swarm by guiding the entire swarm to promising new regions of the search space, and by accelerating search efficiency. In this study, we adopted chaotic maps to strengthen the solution quality of PSO and CatfishPSO. After the introduction of chaotic maps into the process, the improved PSO and CatfishPSO are called chaotic PSO (C-PSO) and chaotic CatfishPSO (C-CatfishPSO), respectively. PSO, C-PSO, CatfishPSO and C-CatfishPSO were extensively compared on six benchmark functions. Statistical analysis of the experimental results indicates that the performance of C-CatfishPSO is better than the performance of PSO, C-PSO, and CatfishPSO.
This Letter reports the finding of a new chaotic at tractor in a simple three-dimensional autonomous system, which resembles some familiar features from both the Lorenz and Rossler at tractors.
In this Letter backstepping design is proposed for controlling chaotic systems. The tool consists in a recursive procedure that combines the choice of a Lyapunov function with the design of feedback control. The advantages of the method are the following: (i) it represents a systematic procedure for controlling chaotic or hyperchaotic dynamics; (ii) it can be applied to several circuits and systems reported in literature; (iii) stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory can be achieved. In order to illustrate the general applicability of backstepping design, the tool is utilized for controlling the chaotic dynamics of the Lorenz system and Chua's circuit. Finally, numerical simulations are carried out to show the effectiveness of the technique.
There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom
in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given
function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization
of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and
provides an unfamiliar perspective on traditional optimization problems and methods.
A class of dynamical systems in the presence of uncertainty is formulated by contingent differential equations. Asymptotic stability (in the sense of Lyapunov) is then developed via generalized dynamical systems (GDS's). The uncertainty is deterministic; the only assumption is that its value belongs to a known compact set. Application to variable structure and model reference control systems are discussed.
The globally stable robust output tracking for a class of
nonlinear systems is considered. Based only on the knowledge of the
bounds on the uncertainties, a variable structure control (VSC) law is
developed under the structure matching assumption. It is shown that the
outputs of the closed-loop system asymptotically track given output
trajectories despite the uncertainties while maintaining the boundedness
of all signals inside the loop. All signals inside the loop are shown to
be bounded for all time. To illustrate the efficiency of the controller,
the approach is applied to the case of a two degree-of-freedom (DOF)
robotic manipulator with variable payload. Numerical simulation results
are also provided
Approaches to robust nonlinear control.- Dynamical sliding mode control via adaptive input-output linearization: A backstepping approach.- A generic Lyapunov procedure to design robust control for nonlinear uncertain systems: Introducing interlacing into recursive design.- Nonlinear tracking via discontinuous feedback under uncertainty.- Implementation of variable structure control for sampled-data systems.- Higher order sliding modes as a natural phenomenon in control theory.- An adaptive servomechanism for a class of uncertain nonlinear systems encompassing actuator hysteresis.- A new class of identifiers for robust parameter identification and control in uncertain systems.- Exponential convergence for uncertain systems with component-wise bounded controllers.- Quadratic stabilization of uncertain linear systems.- Piecewise-linear functions in robust control.- A lie-backlund approach to dynamic feedback equivalence and flatness.- Asymptotic stability and periodic motions of selector-linear differential inclusions.- Structured dissipativity and absolute stability of nonlinear systems.
A sliding mode hyperplane design for a class of chaotic systems with uncertainties is considered in this paper. The concept of extended systems is used such that continuous control input is obtained using a sliding mode design scheme. It is guaranteed that under the proposed control law, uncertain chaotic systems can asymptotically track target orbits. The converging speed of error states can be arbitrarily set by assigning the corresponding dynamics to the sliding surfaces. Illustrative examples of a controlled uncertain Duffing–Holmes system are presented.
Anticontrol of chaos by making a nonchaotic system chaotic has led to the discovery of some new chaotic systems, particularly the continuous-time three-dimensional autonomous Chen equation with only two quadratic terms. This paper further investigates some basic dynamical properties and various bifurcations of Chen’s equation, thereby revealing its different features from some other chaotic models such as its origin, the Lorenz system.
Properties of min-max controllers (previously obtained) for uncertain dynamical systems are discussed. In particular, new model for switching action is presented, and asymptotic stability is reexamined. The attractiveness of switching surfaces is demonstrated, and the insensitivity of solutions in those surfaces to the uncertainty is pointed out.
Asymptotic stability in the sense of min–max theory is developed for a class of uncertain variable structure systems. Based on this unification between the theories, a min–max controller with predescribed sliding motion is designed. The proposed design method simplifies the one previously obtained for this purpose.
Sliding control has been well developed for single-input single-output (SISO) systems, or quasi-SISO systems, in which the sliding condition is a single inequality, or a set of decoupled inequalities. It is also well understood for multiple-input multiple-output (MIMO) systems when certain types of structural information on the dynamics, such as conservation of energy, are available. This paper analyzes, in the general MIMO case, conditions on the system's parametric uncertainties for the existence of control inputs which keep sliding conditions satisfied. The development is illustrated with a simple example.
The problem of constructing discontinuity planes in variable structure systems is studied from a Lyapunov point of view. A switching surface determined by the control coefficient matrix and the associated Lyapunov function is able to ensure asymptotic stability for the system in sliding mode. The proposed method may also be used for systems with nonlinear dynamics which are not feedback linearizable and for linear systems with delays.
The problem of constructing discontinuity surfaces in variable structure systems is studied from a Lyapunov point of view. A switching surface determined by the control coefficient matrix and the associated Lyapunov function is able to ensure asymptotic stability for the system in sliding mode. The proposed method may also be used for systems with nonlinear dynamics and for linear systems with delays.
The aim of this paper is to study both the theoretical and experimental properties of chaotic neural network (CNN) models for solving combinatorial optimization problems. Previously we have proposed a unifying framework which encompasses the three main model types, namely, Chen and Aihara's chaotic simulated annealing (CSA) with decaying self-coupling, Wang and Smith's CSA with decaying timestep, and the Hopfield network with chaotic noise. Each of these models can be represented as a special case under the framework for certain conditions. This paper combines the framework with experimental results to provide new insights into the effect of the chaotic neurodynamics of each model. By solving the N-queen problem of various sizes with computer simulations, the CNN models are compared in different parameter spaces, with optimization performance measured in terms of feasibility, efficiency, robustness and scalability. Furthermore, characteristic chaotic neurodynamics crucial to effective optimization are identified, together with a guide to choosing the corresponding model parameters.
We propose a novel approach for solving large scale traveling salesman problems (TSPs) by chaotic dynamics. First, we realize the tabu search on a neural network, by utilizing the refractory effects as the tabu effects. Then, we extend it to a chaotic neural network version. We propose two types of chaotic searching methods, which are based on two different tabu searches. While the first one requires neurons of the order of n2 for an n-city TSP, the second one requires only n neurons. Moreover, an automatic parameter tuning method of our chaotic neural network is presented for easy application to various problems. Last, we show that our method with n neurons is applicable to large TSPs such as an 85,900-city problem and exhibits better performance than the conventional stochastic searches and the tabu searches.
Presents a guide to sliding mode control for practicing control
engineers. It offers an accurate assessment of the so-called chattering
phenomenon, catalogs implementable sliding mode control design
solutions, and provides a frame of reference for future sliding mode
control research
This paper presents a new approach for the design of variable structure control (VSC) of nonlinear systems. The approach is based on a new method called the reaching law method, and is complemented by a sliding mode equivalence technique. They facilitate the design of the system dynamics in all three modes of a VSC system including the sliding, reaching, and steady-state modes. Invariance and robustness properties are discussed. The approach is applied to a robot manipulator to demonstrate its effectiveness.
Robust flight control laws based on variable structure control (VSC) theory and Lyapunov V-function method are designed for a simplified aircraft model F-18. A min-max control (MMC) and VSC laws are derived, for multi-input multi-output (MIMO) systems with plant uncertainties and input disturbance. Two types of robust feedback controllers MMC and VSC for uncertain MIMO systems are considered. For both cases the existence conditions of a stable sliding mode and the robust asymptotic stability in uncertain MIMO systems by MMC and VSC are investigated. For the design of an MMC and VSC, measurable states and sliding surface are chosen so that the zero dynamics of the system are stable. An application of tracking and positioning of VSC of longitudinal dynamics is presented. Finally, simulation results are presented to show the effectiveness of the design methods.
The design of variable-structure control (VSC) systems for a class
of multivariable, nonlinear, time-varying systems is presented. Using
the Utkin-Drazenovic method of equivalent control and generalized
Lyapunov stability concepts, the VSC design is described in a unified
manner. Complications that arise due to multiple inputs are examined,
and several approaches useful in overcoming them are developed. Recent
developments are investigated, as is the kinship of VSC and the
deterministic approach to the control of uncertain systems. All points
are illustrated by numerical examples. The recent literature on VSC
applications is surveyed
Methods for constructing discontinuity planes in multidimensional variable structure systems
- V I Utkin
- K D Young
Utkin VI, Young KD. Methods for constructing discontinuity planes in multidimensional variable structure systems. Automat
Remote Control 1979;39:1466-70.
Chaotic optimization method and its application (in Chinese)
- Li