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In this paper, an adaptive neural network tracking control approach is proposed for a class of switched stochastic pure-feedback nonlinear systems with backlash-like hysteresis. In the design procedure, an affine variable is constructed, which avoids the use of the mean value theorem, and the additional first-order low-pass filter is employed to de...
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This paper addresses the master-slave synchronization problem for a class of continuous-time switched nonlinear systems. The sampled-data of system output and mode is utilized to design the quantized synchronizing controller. Based on the input delay approach, the synchronization error system is modeled as a switched system with state delay and asy...
Citations
... Consider the continuous stirred tank reactor with two modes feed stream [45], and an unknown Bouc-Wen hysteresis u defined in (5). Therefore, the following switched stochastic nonlinear system is considered: ...
The adaptive fuzzy backstepping control problem is studied for Itô-type nonlinear switched systems subject to unknown hysteresis input. Compared with existing works, the unknown hysteresis and stochastic disturbances are considered in the pure-feedback switched systems. The mean value theorem tackles the non-affine functions. The backstepping technique introduces an auxiliary virtual controller. In addition, the Nussbaum function is employed to solve the difficulty caused by the unknown hysteresis under arbitrary switching. Based on a fuzzy logic system and backstepping technique, a new adaptive control proposal is obtained, which ensures that the system states satisfy semiglobally uniformly ultimately bounded (SGUUB) in probability and that the tracking error converges to a region of the origin. Finally, we provide two examples to show the validity of the presented scheme.
... Later, intelligent control methods, e.g. neural network (NN) control [9], fuzzy control [10], iterative learning [11], and other artificial intelligence (AI) algorithms, are https://doi.org/10.1016/j.isatra.2021. 10.017 0019-0578/© 2021 ISA. ...
To handle the tracking control problem of the magnetic wheeled mobile robot (MWMR), this paper developed an online robust tracking control scheme by adaptive dynamic programming (ADP). The problem, that how to achieve optimal tracking control of continuous-time (CT) MWMR system with the time-varying unknown uncertainty, can be solved indirectly through matching the optimal tracking control of the associated nominal system . A single critic NN-based actor-critic structure is tailored for simpler controller architecture. By minimizing the Bellman error with gradient descending and least-squares updating laws, the critic NN weights can be optimized online. Thus the optimal cost function and the optimal control signal can be approximated with high precision. Using the Lyapunov stability theorem, the convergence of the critic NN weights, and the stability of the closed-loop system is provided. Simulations, in comparison with robust PD control and adaptive control, are presented to illustrate the effectiveness of the proposed tracking control method for the MWMR.
... Switched systems consist of a family of subsystems and a switching rule that orchestrates the switching among them; a large number of practical systems belong to this category due to changing environmental factors and various jumping parameters [1,2], such as circuit and power systems [3], hypersonic flight vehicles [4], and chemical processes [5]. Since their vital engineering applications and the development of intelligent control theories, for instance, neural networks (NNs) and fuzzy logical systems (FLSs), significant results have been obtained for nonlinear switched systems in the literature [1,[6][7][8][9][10][11][12]. Specifically, the back-stepping technology was employed to develop controllers for nonlinear switched systems with NNs [1,4,8,10,15] or FLSs [7][8][9][11][12][13] being introduced to approximate the unknown nonlinearities. ...
... Since their vital engineering applications and the development of intelligent control theories, for instance, neural networks (NNs) and fuzzy logical systems (FLSs), significant results have been obtained for nonlinear switched systems in the literature [1,[6][7][8][9][10][11][12]. Specifically, the back-stepping technology was employed to develop controllers for nonlinear switched systems with NNs [1,4,8,10,15] or FLSs [7][8][9][11][12][13] being introduced to approximate the unknown nonlinearities. On the other hand, a switched system does not inherit the characteristics of the subsystems, which makes stability analysis very complicated. ...
... Since their vital engineering applications and the development of intelligent control theories, for instance, neural networks (NNs) and fuzzy logical systems (FLSs), significant results have been obtained for nonlinear switched systems in the literature [1,[6][7][8][9][10][11][12]. Specifically, the back-stepping technology was employed to develop controllers for nonlinear switched systems with NNs [1,4,8,10,15] or FLSs [7][8][9][11][12][13] being introduced to approximate the unknown nonlinearities. On the other hand, a switched system does not inherit the characteristics of the subsystems, which makes stability analysis very complicated. ...
In this study, an adaptive anti-disturbance control scheme is investigated for a class of unknown pure feedback switched nonlinear systems subjected to immeasurable states and external disturbances. Radial basis function neural networks (RBFNNs) are employed to identify the switched unknown nonlinearities, and a Butterworth low-pass filter is adopted to remove the algebraic loop problem. Subsequently, a novel switched neural state observer and a novel switched disturbance are presented via the coupled design method to estimate the immeasurable states and compounded disturbances. Then, an improved adaptive control strategy for the studied problem is designed with the help of a filtering method to eliminate the “explosion of complexity” problem, and certain compensating signals are set up to compensate for the filter errors, where switched updated laws are constructed to lessen the conservativeness caused by adoption of a common updated law for all subsystems. By utilizing the Lyapunov stability theorem, the developed control scheme can guarantee that all signals in the closed-loop system are bounded under a class of switching signals with the average dwell time (ADT), while the tracking error can converge to a small neighbourhood of origin. Finally, simulation results are provided to demonstrate the effectiveness of the presented approach.
... Furthermore, the controller design for a class of stochastic nonlinear systems with switching is considered in [26]. An adaptive neural tracking control strategy is proposed for a class of stochastic pure-feedback nonlinear switched systems in [28]. Besides, [30] shows the problem of decentralized adaptive output-feedback control for more general large-scale stochastic nonlinear systems with uncertainties. ...
This paper addresses the adaptive neural fault-tolerant control (FTC) problem for a class of stochastic switched nonstrict-feedback nonlinear systems, which have actuator faults that incorporate loss of effectiveness, stuck and outage. Based on the character of Gaussian function, the problem of nonstrict-feedback form is solved well. In the process of designing the controller, neural networks (NNs) are utilized to estimate the unknown functions. The problem of actuator faults is handled by designing the FTC method who is obtained by introducing a smooth function and backstepping technique. Then, the control effect satisfies all the signals in the resulting closed-loop system are bounded and the tracking error converges to a small neighborhood around the origin. To illustrate the high efficiency of the proposed control method, a vivid simulation example is given in the end.
... On the other hand, stochastic disturbances often exist in practical systems, which may lead to severe performance deterioration or even instability of closed-loop systems [22]- [24]. Many significant control strategies have been proposed for stochastic nonlinear systems [25]- [34]. ...
This paper studies the problem of adaptive fault estimation and accommodation for a class of stochastic nonlinear systems with unknown time-varying faults. Different from existing fault estimation methods, a novel adaptive prescribed performance fault estimator (APPFE) is designed which guarantees that the fault estimation error is confined within a pre-set region, and better estimation accuracy is obtained. The designed faulttolerant tracking controller is capable of attenuating the effect of faults through using back-stepping techniques. Furthermore, the proposed method guarantees that all the error signals of closedloop system be bounded in probability, the fault estimation error and output tracking error both converge to desired neighborhoods of origin in the sense of quadratic mean value. Finally, simulation results are provided to verify the method proposed in this paper.
... An adaptive output feedback control method based on the fuzzy logic system (Li et al., 2012;Shahnazi et al., 2010) has been proposed, which makes the non-linear system with unknown hysteresis of the actuator stable. In the work of Cui et al. (2017), Wang et al. (2017) and Niu et al. (2016), the authors proposed an adaptive state feedback control algorithm based on neural networks for a class of switched systems with hysteresis of the actuator, in which the neural network is used to approximate the non-linear unknown function in the switched system. However, in practical applications, many system states are not measurable. ...
... Inspired by the above research, this article combines the DSC method and the adaptive neural network control method to construct an output feedback controller to solve the tracking problem of a switched system with input hysteresis. First, this article can achieve a similar control effect Cui et al. (2017), Wang et al. (2017) and Niu et al. (2016), but the system states must be measurable in these works. Second, compared with Li and Tong (2016), we consider a class of switched systems with input hysteresis and further avoid the issue of the explosion of complexity caused by the traditional backstepping technique. ...
This paper investigates the problem of adaptive neural output feedback control for a class of switched non-linear systems, and the unknown backlash-like hysteresis of the actuator is also taken into consideration. First, neural networks are used to approximate the uncertain functions in the studied system. Second, a state-observer is proposed to estimate the system states. Finally, an adaptive neural output feedback control algorithm based on a backstepping technique is constructed; in addition, dynamic surface control is applied to eliminate the explosion in complexity caused by the backstepping technique. By using Lyapunov stability theory, it is proved that all the signals of the switched system are bounded under the proposed control scheme. The effectiveness of the proposed approach is further confirmed by simulation experiments.
... For the first family, two approximating tools are widely used to approximate the uncertain nonlinear systems via adaptive laws, which are fuzzy membership functions (Zhao, Zheng, Niu, & Liu, 2015;Niu, Karimi, Wang, & Liu, 2016;Long & Zhao, 2016;Y. Li, Sui, & Tong, 2017), and neural networks (Han, Ge, & Lee, 2009;Jiang, Shen, & Shi, 2015;Zhao, Shi, Zheng, & Zhang, 2015;Niu, Qin, & Fan, 2016). However, at least one of the following problems typically arises for control designs in this family: the performance cannot be prescribed a priori, being dependent on the actual parameters which are unknown Niu, Karimi, et al., 2016;Long & Zhao, 2016;Y. ...
... However, at least one of the following problems typically arises for control designs in this family: the performance cannot be prescribed a priori, being dependent on the actual parameters which are unknown Niu, Karimi, et al., 2016;Long & Zhao, 2016;Y. Li et al., 2017;Han et al., 2009;Jiang et al., 2015;Zhao, Shi, et al., 2015;Niu, Qin, & Fan, 2016); stability cannot be guaranteed for arbitrarily fast switching (typically, average dwell time switching constraint is necessary to guarantee stability) (Niu, Karimi, et al., 2016;Long & Zhao, 2016;Han et al., 2009;. For the second family, the main design tools are: a reparametrization lemma, that overcomes the need for different estimators for different subsystems and can handle arbitrarily fast switching (Chiang & Fu, 2014); or a parameter separation technique, that requires slow-switching signals (Long, Wang, & Zhao, 2015). ...
In this paper, adaptive tracking control of switched nonlinear systems in the parametric strict-feedback form is investigated. After defining a reparametrization lemma in the presence of a non-zero reference signal, we propose a new adaptive backstepping design of the virtual controllers that can handle the extra terms arising from the reparametrization (and that the state-of-the-art backstepping designs cannot dominate). The proposed adaptive design guarantees, under arbitrarily fast switching, an a priori bound for the steady-state performance of the tracking error and a tunable bound for the transient error. Finally, the proposed method, by overcoming the need for subsystems with common sign of the input vector field, enlarges the class of uncertain switched nonlinear systems for which the adaptive tracking problem can be solved. A numerical example is provided to illustrate the proposed control scheme.
... At the same time, the ANNC method has been many successful applications for some unknown nonlinear systems, such as adaptive output-feedback control [31][32][33], pure-feedback [34][35][36][37] and so on. In ANNC, the neural network is often used to online approximate unknown nonlinearity owning to their inherent approximation capabilities. ...
In this paper, adaptive neural control (ANC) is investigated for a class of strict-feedback nonlinear stochastic systems with unknown parameters, unknown nonlinear functions and stochastic disturbances. The new controller of adaptive neural network with state feedback is presented by using a universal approximation of radial basis function neural network and backstepping. An adaptive neural network state-feedback controller is designed by constructing a suitable Lyapunov function. Adaptive bounding design technique is used to deal with the unknown nonlinear functions and unknown parameters. It is shown that, the global asymptotically stable in probability can be achieved for the closed-loop system. The simulation results are presented to demonstrate the effectiveness of the proposed control strategy in the presence of unknown parameters, unknown nonlinear functions and stochastic disturbances.
... In some works, several control approaches have been developed for the chaotic synchronization phenomena, such as linear and nonlinear feedback control, active control, adaptive (direct or indirect) control, time delay feedback approach, Sampled-data feedback control, adaptive open-plus-closed-loop control, fractional PID control, robust control, sliding mode control, Backstepping control, datadriven control, among others [1][2][3][4][5][6][7][8][9][10]. It is also well known that the singularity problem and chattering phenomena can appear while implementing some control approaches [87][88][89][90][91][92][93][94]. ...
... On the other hand, it has been found that the Grünwald-Letnikov, Hadamard, Weyl, Riesz, Riemann-Liouville, and Caputo's definitions are the most popular definitions for fractional-order integrals and derivatives [59,[63][64][65][66][69][70][71][72][73]76,[94][95][96][97][98][99]. As stated in 76,77,81,82,[87][88][89][90][91][92][93], the most classical stability tools of integer order systems cannot be extended or applied directly to that of the fractional-order differential systems. Recently, stability conditions for a class of fractional-order nonlinear systems has been developed based on Mittag-Leffler function, Laplace transform, Caputo derivatives and the generalized Gronwall inequality [8,[63][64][65]88]. ...
... Based on the previous research works [39,[52][53][54][55][56][57][58][59][60]67,74,84,86,88,[90][91][92] and by utilizing smooth functions, the unknown nonlinear input (3) can be approximated as follows ...
This research is concerned with the problem of generalized function projective synchronization of nonlinear uncertain time-delay incommensurate fractional-order chaotic systems with input nonlinearities. The considered problem is challenging owing to the presence of unmeasured master-slave system states, external dynamical disturbances, unknown nonlinear system functions, unknown time-varying delays, quantized outputs, unknown control direction, unknown actuator nonlinearities (backlash-like hysteresis, dead-zone and asymmetric saturation actuators) and distinct fractional-orders. Under some mild assumptions and using Caputo's definitions for fractional-order integrals and derivatives, the design procedure of the proposed neural adaptive controller consists of a number of steps to solve the generalized function projective synchronization problem. First, smooth functions and the mean value theorem are utilized to overcome the difficulties from actuator nonlinearities and distributed time-varying delays, respectively. Then, a simple linear observer is established to estimate the unknown synchronization error variables. In addition, a Nussbaum function is incorporated to cope with the unknown control direction and a neural network is adopted to tackle the unknown nonlinear functions. The combination of the frequency distributed model, the Razumikhin Lemma, the neural network parameterization, the Lyapunov method and the Barbalat's lemma is employed to perform the stability proof of the closed-loop system and to derive the adaption laws. The major advantages of this research are that: (1) the Strictly Positive Real (SPR) condition on the estimation error dynamics is not required, (2) the considered class of master-slave systems is relatively large, (3) all signals in the resulting closed-loop systems are semi-globally uniformly ultimately bounded and the synchronization errors semi-globally converge to zero. Finally, numerical examples are presented to illustrate the performance of the proposed synchronization scheme.
In this study, a neural network (NN) composite adaptive antidisturbance control scheme is investigated for a class of unknown pure-feedback switched nonlinear systems. First, radial basis function NNs are employed to identify unknown nonlinearities by employing a Butterworth low-pass filter to eliminate the algebraic loop problem. Subsequently, an NN composite switched state observer and an NN composite switched disturbance observer are presented by coupled design to estimate immeasurable states and compounded disturbances. Next, an improved composite control strategy is developed for the investigated problem with the help of a filtering method to avoid the “explosion of complexity” problem, and compensating signals are set up to alleviate the filter errors. By utilizing the Lyapunov stability theorem, the proposed control scheme can guarantee that all signals in the closed-loop system are bounded under a class of switching signals with the average dwell time, while the tracking error can converge to within a small neighbourhood of the origin. Simulation results are provided to demonstrate the effectiveness of the presented approach.
