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Decentralized Fuzzy Observer-Based Output-Feedback Control for Nonlinear Large-Scale Systems: An LMI Approach
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This paper presents a decentralized fuzzy control problem for asymptotic stabilization of a class of nonlinear large-scale systems that use an observer-based output-feedback scheme. A Takagi–Sugeno (T–S) fuzzy model is adopted for the nonlinear large-scale system, which has unknown interconnection terms, and a fuzzy controller is separately considered for measurable and nonmeasurable premise variable cases. Sufficient conditions are derived for both asymptotic stabilization and optimization of a maximum bound of interconnection and are formulated in terms of linear matrix inequalities. Finally, numerical examples are provided to verify the effectiveness of the proposed techniques.
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... For the above third mission which will perform the output feedback controller design, numerous publications of SOSMC laws with output information have been investigated in the research [15]- [17]. Koo et al. [15] explored an output-feedback controller based on an observer to stabilize a class of nonlinear large-scale plants with an unknown interconnection by employing a Takagi-Sugeno fuzzy typical. ...
... For the above third mission which will perform the output feedback controller design, numerous publications of SOSMC laws with output information have been investigated in the research [15]- [17]. Koo et al. [15] explored an output-feedback controller based on an observer to stabilize a class of nonlinear large-scale plants with an unknown interconnection by employing a Takagi-Sugeno fuzzy typical. In [16], a new SMC methodology is stretched to a class of mismatched uncertain large-scale systems with the mismatching interconnections and unknown perturbations. ...
... Consequently, the first (4) can be modified as (17). . (17) By substituting the suggested controller (14), control gains (15), and (17) into (16), it is obvious that ̇≤ − ∑̃‖ ( )‖ =1 , where ̃> 0. Thus, the state trajectories of the plant (1) reach the sliding manifold (2) in finite time and stay on it. Theorem 2 is demonstrated completely. ...
p>Novel results on complex interconnected time-delay systems with single phase second order sliding mode control is investigated. First, a reaching phase in traditional sliding mode control (TSMC) is removed by using a novel single phase switching manifold function. Next, a novel reduced order sliding mode observer (ROSMO) with lower dimension is suggested to estimate the unmeasurable variables of the plant. Then, a new single phase second order sliding mode controller (SPSOSMC) is established based on ROSMO tool to drive the state variables into the specified switching manifold from beginning of the motion and reduce the chattering in control input. Then, a stability condition is suggested based on the well-known linear matrix inequality (LMI) method to ensure the asymptotical stability of the whole plant. Finally, an illustrated example is simulated to validate the feasible application of the suggested technique.</p
... SOSMC framework guarantees the alignment of active and reactive powers with their respective reference values. Extensive investigations have explored diverse SOSMC algorithms, particularly emphasizing output feedback [20]- [23]. Derived from the established sliding mode surface (20), the following expressions can be inferred: ...
... Extensive investigations have explored diverse SOSMC algorithms, particularly emphasizing output feedback [20]- [23]. Derived from the established sliding mode surface (20), the following expressions can be inferred: ...
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator(DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC).Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
... ranging from the modeling (e.g., Tensor-Product modeling approach in [6], [7]; sum-of-square approach in [8]) to the controller design with various uncertainties (e.g., with unmeasurable state as in [9]; with disturbance as in [10]; with varying steady-state target as in [11]). For all of the applicable control approaches, the model predictive control (MPC) approach is the most useful one due to its constraint handling ability. ...
This article considers the dynamic output feedback model predictive control (DOFMPC) for the constrained Takagi-Sugeno (T-S) model with bounded disturbance. Unlike the existing approach where the robust positively invariant set is characterized by a single ellipsoid, we characterize it by the intersection of multiple ellipsoids, each corresponds to a vertex sub-model of the T-S model realization. The previous single ellipsoid is then an inner approximation of the intersection of multiple ellipsoids in this article. Therefore, the performance can be improved. We also generalize the multi-ellipsoid approach to the previous multi-step approach and formulate the so-called multi-step multi-ellipsoid approach in this article, which can further enlarge the feasibility region and enhance the performance. The recursive feasibility and the convergence of the approach are guaranteed. The proposed approaches are compared through a numerical problem to show their effectiveness. Index Terms-Takagi-Sugeno model, output feedback, model predictive control, multi-step approach, multi-ellipsoid approach; stability.
... Besides the existence of nonlinearities, unmeasurable process state is another issue which needs to be considered in real industrial processes, so the design of the state estimator in combination with the feedback control law has received great attentions (see e.g, [15], [16], [17], [18], [19]). An output feedback MPC algorithm can be formulated by combining the state feedback control with a Luenberger state estimator (see e.g., [15], [20], [21], [22]), or by utilizing a dynamic output feedback controller (see e.g., [23], [24], [25], [26], [27]). In [27], it is shown that, as compared with the state feedback controller with Luenberger state estimator, applying the dynamic output feedback control law can result in better control performance due to the introduction of extra degrees of freedom. ...
This paper studies the output feedback model pre-dictive control (MPC) being suitable to a large operation range of the constrained system represented by a nonlinear model with a bounded disturbance. The model is further parameterized as a multiple linear parameter varying (LPV) state-space equation, each LPV representation being valid around an exclusive equilibrium. Off-line, for each equilibrium, a set of local control laws (in the dynamic output feedback), each having its region of attraction, are calculated. All the control laws for all the equilibriums constitute a lookup table, and all the corresponding regions of attraction take a union. On-line, the real-time control law is searched as one, as per its region of attraction, in the lookup table when the estimated system state moves inside of the union. Once the initial estimation error lies in a pre-specified set, the augmented state is guaranteed to converge to the neighborhood of the target equilibrium, and the constraints on input and output are consistently satisfied. An example is given to illustrate the effectiveness of the proposed algorithm.
... One of the main advantages of this approach stems from the fact that it can handle structural constraints on the gain matrix, as well as uncertain nonlinearities in the system. As a result, it can be used to produce decentralized control laws [6], [7], [8], [9], [10], [11], output feedback [12], [13], [14], [15], [16], and even gain matrices with arbitrary nonzero patterns [17]. This inherent versatility of LMI-based design explains why it remains an attractive option for solving control-related problems, and finds applications in diverse fields ranging from multiagent systems [18], [19], [20], [21] and aerospace engineering [22], [23], [24] to electric power systems [25], [26], [27], [28], [29], [30], [31], [32]. ...
This paper proposes a new LMI-based strategy for designing decentralized control, which is aimed at large-scale systems. A distinguishing feature of this approach is its ability to produce decentralized feedback laws without placing any structural constraints on the Lyapunov function. It also allows the user to control the number of LMI variables, which can significantly reduce the computational effort. The effectiveness of this method is illustrated through applications to interconnected microgrid clusters. Simulation results show that the proposed approach can be used to regulate energy exchanges between the clusters in a way that ensures robust stability.
... The authors of [38] presented an observer-based decentralized control scheme for stability analysis of networked systems. In [67], a decentralized fuzzy observer-based control for large systems was presented. The reduced-order observer-based decentralized control design problem was solved by using LMI approach in [74]. ...
The present thesis is the result of research conducted in Longwy, within the department Control, Identification, Diagnosis (CID) of Research Center for Automatic Control of Nancy (CRAN). This thesis investigates the problem of dynamic observer (full- and reduced-order) and observer-based control design and their applications to large-scale systems.Firstly, a new form of H∞ dynamic observer is designed for linear systems in the presence of unknown inputs and disturbances. The proposed observer generalizes the existing results on proportional observer and proportional integral observer. The observer design is based on the solution of linear matrix inequalities (LMI). Both continuous-time and discrete-time systems are considered.Thereafter, by inserting the proposed observer into a closed-loop, an observer-based control is presented for uncertain systems in the presence of disturbances. Based on the parameterization of algebraic constraints obtained from the analysis of the estimation error, the control design is derived from the solution of bilinear matrix inequality, by using a two-step algorithm.Finally, the obtained results have been extended to large-scale systems. A decentralized observer-based control is proposed for large-scale uncertain systems in the presence of disturbances. These systems are composed of several interconnected subsystems of low dimensions, where the interconnections are assumed to be nonlinear and satisfy quadratic constraints.
This paper develops a novel hybrid system approach to address the event-triggered stabilization problem of largescale T-S fuzzy systems subject to variable long transmission delays. Various changing behaviours of deviation errors caused by transmission delays, as well as the changes of some auxiliary variables are modeled by a hybrid dynamical system with flow dynamics and jump dynamics. Then, under the hybrid control framework, an observer based anti-disturbance controller and a delay-independent hybrid event-triggering mechanism (HETM) are proposed to stabilize the closed-loop system, while guaranteeing desired performance in disturbance attenuation and delay tolerance. Compared with the case that small transmission delays could naturally lead to delay-independent HETM, the long transmission delays pose many difficulties. Given this, we propose a more robust triggering condition with only using several memorized previous states to guarantee the HETM to be delay-independent even in case with long transmission delays. Moreover, the obtained stability conditions avoid involving lower and upper bounds of transmission delays in matrix inequalities, thus can be delay-independent and significantly simplified. Relationships between system stability and maximally allowable transmission delay are transformed to designing proper auxiliary functions offline. Finally, the effectiveness of proposed control protocol is demonstrated by a numerical example.
In this article, the decentralized repetitive tracking controller design for fractional‐order large‐scale Takagi–Sugeno fuzzy system with time delays is developed. We mainly focus on the design of a decentralized repetitive tracking controller based on the Lyapunov stability theory, by which the addressed large‐scale system asymptotically stabilized with performance index. Further, the repetitive control with quantized signal is developed to ensure the good tracking performance with the presence of interconnected model and external disturbances. Specifically, a logarithmic quantizer is used to quantify the control signal which can reduce the data transmission rate in the network. Finally, a numerical example is presented to verify the effectiveness of the proposed controller design technique.
This paper presents the problem of robustly stabilizing a class of nonlinear systems by using an H∞ fuzzy output feedback controller. Sufficient condition is derived to ensure the robust stability of the fuzzy observer based controller with guaranteed H∞ disturbance attenuation level. The observer and controller design problem is cast in the form of bilinear matrix inequalities (BMIs). Using two-step procedure, these BMIs are reduced to two sets of LMIs which can be solved very efficiently using convex optimization techniques. The design procedure proposed in this paper extends previous results in the literature by considering both the premise uncertainty and the consequent uncertainty simultaneously. Furthermore, a modified two-step procedure is suggested for the plants with linear output equation. Finally, a simulation example illustrates the validity and applicability of the given approach
In general, due to the interactions among subsystems, it is difficult to design an H-infinity decentralized controller for nonlinear Interconnected systems. In this study, the model reference tracking control problem of nonlinear Interconnected systems is studied via H-infinity decentralized fuzzy control method. First, the nonlinear interconnected system is represented by an equivalent Takagi-Sugeno type fuzzy model. A state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the H-infinity model reference tracking performance is achieved. Furthermore, the stability of the nonlinear Interconnected systems is also guaranteed. If states are not all available, a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control. Consequently, a fuzzy observer-based state feedback decentralized fuzzy controller is proposed to solve the H-infinity tracking control design problem for nonlinear interconnected systems. The problem of H-infinity decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem (EVP). The EVP can be solved very efficiently using convex optimization techniques. Finally, simulation examples are given to illustrate the tracking performance of the proposed methods.
This paper studies the finite-time H ∞ control problem for time-delay nonlinear jump systems via dynamic observer-based state feedback by the fuzzy Lyapunov-Krasovskii functional approach. The Takagi-Sugeno (T-S) fuzzy model is first employed to represent the presented nonlinear Markov jump systems (MJSs) with time delays. Based on the selected Lyapunov-Krasovskii functional, the observer-based state feedback controller is constructed to derive a sufficient condition such that the closed-loop fuzzy MJSs is finite-time bounded and satisfies a prescribed level of H ∞ disturbance attenuation in a finite time interval. Then, in terms of linear matrix inequality (LMIs) techniques, the sufficient condition on the existence of the finite-time H ∞ fuzzy observer-based controller is presented and proved. The controller and observer can be obtained directly by using the existing LMIs optimization techniques. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach.
This paper provides an improved result over that in Liu and Zhang [2003, New approaches to H"~ controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica, 39, 1571-1582] for the problem of observer-based H"~ control for nonlinear systems in Takagi-Sugeno (T-S) fuzzy model. It contributes in three aspects: (i) The present result is less conservative than that in Liu and Zhang [2003, New approaches to H"~ controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica, 39, 1571-1582]; (ii) The present strict LMI method is a single step approach which overcomes the drawback of a two-step approach in Liu and Zhang [2003, New approaches to H"~ controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica, 39, 1571-1582]; (iii) The matrix dimensions are largely reduced compared with the corresponding ones in Liu and Zhang [2003, New approaches to H"~ controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica, 39, 1571-1582].
This article further studies the observer-based H∞-control problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems. By using fuzzy Lyapunov functions and introducing slack variables, a sufficient condition, which can guarantee observer-based H∞-control performance for T-S fuzzy systems, is proposed in terms of a set of bilinear matrix inequalities. Moreover, in the so-called two-step procedure, results of the first step are allowed to select in order to reduce the conservatism of previous approaches. In comparison with the existing literature, the proposed approach not only provides more relaxed H∞-control conditions but also ensures better H∞-control performance. Finally, the validity and applicability of the proposed approach are successfully demonstrated through two numerical examples.
The robust control problem is studied for a class of large-scale networked control systems. The subsystems are in the nonlinear form, and they exchange information through the communication networks. The interconnections considered are nonlinear, and not the traditional linear form, which brings a challenging issue for the decentralized control design. We develop a new memoryless control scheme with the use of the decomposition for each subsystem that is based on the input matrix. By Takagi-Sugeno (T-S) fuzzyfication for each subsystem, the interconnected T-S fuzzy subsystems are obtained. When the upper bound functions of uncertain interconnections are known, we design a decentralized memoryless state feedback controller. When the parameters of bound functions are not available, the adaptive method is used, and the decentralized memoryless adaptive controller is developed. By the construction of a new Lyapunov-Krasovskii functional, we prove the stability of the resultant closed-loop system for the both cases. Finally, we apply the theoretic results to the decentralized controller design of networked interconnected chemical reactor systems. The simulations are performed, and the effectiveness of the proposed method is demonstrated.
This paper addresses the problem of robust H∞H∞ fuzzy observer-based controller design for the Takagi–Sugeno (T–S) fuzzy systems with unmeasurable premise variables. The proposed design method considers uncertainty for such a problem for the first time. Using some linear transformations for the output matrices of each local model of the T–S fuzzy system, and employing Finsler's lemma, the robust stability conditions in the form of linear matrix inequalities (LMIs) are derived. Two numerical simulations are provided to show the validity of the proposed method.
This paper considers decentralized Hinfin fuzzy filter design for fuzzy large-scale systems. The T-S fuzzy large-scale system consists of N T-S fuzzy subsystems. The decentralized Hinfin filter is designed such that the asymptotic stability and a prescribed Hinfin performance index is guaranteed for the overall filtering error system. A sufficient condition for the existence of such a filter is established by using linear matrix inequalities (LMIs) that are numerically feasible. Simulation example is given to show the effectiveness of the present approach.
The problems of relaxed quadratic stability conditions, fuzzy observer designs and H∞ controller designs for T-S fuzzy systems have been studied. First new stability conditions are obtained by relaxing the stability conditions derived in previous papers. Secondly, new fuzzy observers based on the relaxed stability conditions for the T-S fuzzy systems have been proposed. Thirdly two sufficient LMI conditions, which guarantee the existence of the H∞ controllers based on fuzzy observers for the T-S fuzzy systems have been proposed. The conditions are not only simple, but also consider the interactions among the fuzzy subsystems. Finally by some examples, using the LMI technique, we show that the regulators, the fuzzy observers and the H∞ controller designs based on new observers for the T-S fuzzy systems are very practical and efficient.