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Zidong Wang - One of the best experts on this subject based on the ideXlab platform.
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a novel framework for backstepping based control of discrete time strict feedback nonlinear systems with Multiplicative Noises
IEEE Transactions on Automatic Control, 2021Co-Authors: Min Wang, Hongli Dong, Zidong Wang, Qinglong HanAbstract:This article is concerned with the exponential mean-square stabilization problem for a class of discrete-time strict-feedback nonlinear systems subject to Multiplicative Noises. The state-dependent Multiplicative noise is assumed to occur randomly based on a stochastic variable obeying the Gaussian white distribution. To tackle the difficulties caused by the Multiplicative noise, a novel backstepping-based control framework is developed to design both the virtual control laws and the actual control law for the original nonlinear system, and such a framework is fundamentally different from the traditional $n$ -step predictor strategy. The proposed design scheme provides an effective way in establishing the relationship between the system states and the controlled errors, by which a noise-intensity-dependant stability condition is derived to ensure that the closed-loop system is exponentially mean-square stable for exactly known systems. To further cope with nonlinear modeling uncertainties, the radial basis function neural network (NN) is employed as a function approximator. In virtue of the proposed backstepping-based control framework, the ideal controller is characterized as a function of all system states, which is independent of the virtual control laws. Therefore, only one NN is employed in the final step of the backstepping procedure and, subsequently, a novel adaptive neural controller (with modified weight updating laws) is presented to ensure that both the neural weight estimates and the system states are uniformly bounded in the mean-square sense under certain stability conditions. The control performance of the proposed scheme is illustrated through simulation results.
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dynamic event based state estimation for delayed artificial neural networks with Multiplicative Noises a gain scheduled approach
Neural Networks, 2020Co-Authors: Shuai Liu, Zidong Wang, Yun Chen, Guoliang WeiAbstract:Abstract This study is concerned with the state estimation issue for a kind of delayed artificial neural networks with Multiplicative Noises. The occurrence of the time delay is in a random way that is modeled by a Bernoulli distributed stochastic variable whose occurrence probability is time-varying and confined within a given interval. A gain-scheduled approach is proposed for the estimator design to accommodate the time-varying nature of the occurrence probability. For the sake of utilizing the communication resource as efficiently as possible, a dynamic event triggering mechanism is put forward to orchestrate the data delivery from the sensor to the estimator. Sufficient conditions are established to ensure that, in the simultaneous presence of the external Noises, the randomly occurring time delays with time-varying occurrence probability as well as the dynamic event triggering communication protocol, the estimation error is exponentially ultimately bounded in the mean square. Moreover, the estimator gain matrices are explicitly calculated in terms of the solution to certain easy-to-solve matrix inequalities. Simulation examples are provided to show the validity of the proposed state estimation method.
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quadratic estimation for discrete time varying non gaussian systems with Multiplicative Noises and quantization effects
Automatica, 2020Co-Authors: Qinyuan Liu, Zidong Wang, Qinglong Han, Changjun JiangAbstract:Abstract This paper is concerned with the remote state estimation problem for a class of linear discrete time-varying non-Gaussian systems with Multiplicative Noises. Due to bandwidth constraints in digital communication networks, the measured outputs are quantized before transmission by a probabilistic uniform quantizer. Our attention is focused on the design of a recursive quadratic estimator that exploits the quadratic functions of the measurements. By introducing a proper augmented system which aggregates the original state vector and its second-order Kronecker power, we are able to transfer the quadratic estimation problem into a corresponding linear estimation problem of the augmented state vector. An upper bound is first established for the covariance of the estimation error that is expressed in terms of the solutions to certain matrix difference equations, and such an upper bound is then minimized by designing the filter parameters in an iterative manner. Subsequently, we discuss the monotonicity of the optimized upper bound with respect to the quantization accuracy. A numerical example is provided to verify the effectiveness of the proposed filtering algorithm.
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recursive state estimation for linear systems with lossy measurements under time correlated Multiplicative Noises
Journal of The Franklin Institute-engineering and Applied Mathematics, 2020Co-Authors: Hongli Dong, Zidong Wang, Shaoying Wang, Fuad E AlsaadiAbstract:Abstract This paper is concerned with the recursive state estimation problem for a class of linear discrete-time systems with lossy measurements and time-correlated Multiplicative Noises (TCMNs). The lossy measurements result from one-step transmission delays and packet dropouts. Different from the traditional white Multiplicative Noises, TCMNs are included in the measurement model in order to reflect engineering practice. Utilizing the state augmentation approach, the system under investigation is first converted into a stochastic parameter system, and some new recursive terms (including the estimation for the product of state and Multiplicative Noises) are introduced to handle the difficulties caused by the TCMNs. Then, by the well-known projection theorem, recursive state estimation algorithms are developed in the sense of minimum mean-square error, which facilitate the design of the filter, the multi-step predictor and the smoothers. The proposed algorithms are explicitly dependant on the key system parameters including the covariances of the TCMNs, the occurrence probabilities of the transmission delays and the packet losses. Finally, simulation results illustrate the effectiveness of the presented estimation algorithms.
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robust kalman filtering for two dimensional systems with Multiplicative Noises and measurement degradations the finite horizon case
Automatica, 2018Co-Authors: Jinling Liang, Zidong Wang, Fan Wang, Xiaohui LiuAbstract:Abstract In this paper, robust Kalman filtering problem is investigated for a class of two-dimensional (2-D) shift-varying uncertain systems with both additive and Multiplicative Noises over a finite horizon. The measurement outputs suffer from randomly occurring degradations obeying certain probabilistic distributions, and the norm-bounded parameter uncertainties enter into both the state and the output matrices. The main aim of this paper is to design a robust Kalman filter such that, in the presence of parameter uncertainties and degraded measurements, certain upper bound of the generalized estimation error variance is locally minimized in the trace sense at each shift step. Recursion of the generalized estimation error variances for the addressed 2-D system is first established via the introduction of a 2-D identity quadratic filter, based on which an upper bound of the generalized estimation error variance is obtained. Subsequently, such an upper bound is minimized in the trace sense by properly designing the filter parameters. The design scheme of the robust Kalman filter is presented in terms of two Riccati-like difference equations which can be recursively computed for programmed applications. Finally, a numerical example is provided to demonstrate effectiveness of the proposed filter design method.
Wen-jer Chang - One of the best experts on this subject based on the ideXlab platform.
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Actuator Saturation Constrained Fuzzy Control for Discrete Stochastic Fuzzy Systems with Multiplicative Noises
2020Co-Authors: Wen-jer Chang, Hao-jie LiangAbstract:This paper deals with the fuzzy controller design problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with Multiplicative Noises. Using the Lyapunov stability theory and Itô formula, the sufficient conditions are derived to guarantee the stability of the closed-loop nonlinear stochastic systems subject to actuator saturation. Based on the Parallel Distributed Compensation (PDC) concept, the fuzzy controller can be obtained to stabilize the T-S fuzzy models with Multiplicative Noises by combining the same membership functions of plants and desired state feedback gains. In order to illustrate the availability and practicability of proposed fuzzy controller design approach, the numerical simulations for the nonlinear truck-trailer system are given to demonstrate the applications of this paper
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robust fuzzy control subject to state variance and passivity constraints for perturbed nonlinear systems with Multiplicative Noises
Isa Transactions, 2014Co-Authors: Wen-jer Chang, Bojyun HuangAbstract:The multi-constrained robust fuzzy control problem is investigated in this paper for perturbed continuous-time nonlinear stochastic systems. The nonlinear system considered in this paper is represented by a Takagi-Sugeno fuzzy model with perturbations and state Multiplicative Noises. The multiple performance constraints considered in this paper include stability, passivity and individual state variance constraints. The Lyapunov stability theory is employed to derive sufficient conditions to achieve the above performance constraints. By solving these sufficient conditions, the contribution of this paper is to develop a parallel distributed compensation based robust fuzzy control approach to satisfy multiple performance constraints for perturbed nonlinear systems with Multiplicative Noises. At last, a numerical example for the control of perturbed inverted pendulum system is provided to illustrate the applicability and effectiveness of the proposed multi-constrained robust fuzzy control method.
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passive estimated state feedback fuzzy controller design for discrete perturbed fuzzy systems with Multiplicative Noises
Journal of The Chinese Institute of Engineers, 2013Co-Authors: Wen-jer Chang, Sinsian JhengAbstract:This article presents an estimated state feedback fuzzy controller design method for uncertain passive discrete-time nonlinear stochastic systems with Multiplicative Noises. The nonlinear stochastic systems considered in this article are represented by Takagi–Sugeno (T–S) fuzzy models. For describing stochastic behaviors, stochastic differential equations are used to structure the stochastic T–S fuzzy model for representing nonlinear stochastic systems. Besides, the uncertainties of the controlled system are considered for dealing with molding errors and varying parameters. The concept of parallel distributed compensation is employed in this article to construct the estimated state feedback fuzzy controllers. Applying the Lyapunov and passivity theories, the sufficient stability conditions are derived in terms of linear matrix inequality. Finally, a numerical example is provided to show the effectiveness and applicability of the proposed fuzzy controller design approach.
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passive fuzzy controller design for discrete ship steering systems via takagi sugeno fuzzy model with Multiplicative Noises
Journal of Marine Science and Technology, 2013Co-Authors: Wen-jer Chang, Minwei ChenAbstract:This paper proposes a passive fuzzy controller design for the discrete ship steering system that is represented by the Takagi-Sugeno (T-S) fuzzy model with Multiplicative Noises. Applying the Lyapunov theory for guaranteeing mean square stability, the sufficient conditions are developed to design the fuzzy controller for the T-S fuzzy model with Multiplicative Noises. The sufficient conditions derived in this paper belong to the Linear Matrix Inequality (LMI) forms which can be solved by the convex optimal programming algorithm. Besides, the fuzzy controller is carried out by the concept of Parallel Distribution Compensator (PDC). Finally, the simulation results are proposed to show that the strictly input passivity and mean square stability of the closed-loop system can be achieved via the designed fuzzy controller.
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variance and passivity constrained fuzzy control for nonlinear ship steering systems with state Multiplicative Noises
Mathematical Problems in Engineering, 2013Co-Authors: Wen-jer Chang, Bojyun HuangAbstract:The variance and passivity constrained fuzzy control problem for the nonlinear ship steering systems with state Multiplicative Noises is investigated. The continuous-time Takagi-Sugeno fuzzy model is used to represent the nonlinear ship steering systems with state Multiplicative Noises. In order to simultaneously achieve variance, passivity, and stability performances, some sufficient conditions are derived based on the Lyapunov theory. Employing the matrix transformation technique, these sufficient conditions can be expressed in terms of linear matrix inequalities. By solving the corresponding linear matrix inequality conditions, a parallel distributed compensation based fuzzy controller can be obtained to guarantee the stability of the closed-loop nonlinear ship steering systems subject to variance and passivity performance constraints. Finally, a numerical simulation example is provided to illustrate the usefulness and applicability of the proposed multiple performance constrained fuzzy control method.
O L V Costa - One of the best experts on this subject based on the ideXlab platform.
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optimal control with constrained total variance for markov jump linear systems with Multiplicative Noises
International Journal of Systems Science, 2018Co-Authors: Fabio Augusto Barbieri, O L V CostaAbstract:We consider in this paper the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and Multiplicative Noises (MJLS-mn for short). Our objective is to present a...
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quadratic and h switching control for discrete time linear systems with Multiplicative Noises
International Journal of Control, 2014Co-Authors: O L V Costa, Carlos Alberto Cavichioli GonzagaAbstract:The goal of this paper is to study the switched stochastic control problem of discrete-time linear systems with Multiplicative Noises. We consider both the quadratic and the H∞ criteria for the performance evaluation. Initially we present a sufficient condition based on some Lyapunov–Metzler inequalities to guarantee the stochastic stability of the switching system. Moreover, we derive a sufficient condition for obtaining a Metzler matrix that will satisfy the Lyapunov–Metzler inequalities by directly solving a set of linear matrix inequalities, and not bilinear matrix inequalities as usual in the literature of switched systems. We believe that this result is an interesting contribution on its own. In the sequel we present sufficient conditions, again based on Lyapunov–Metzler inequalities, to obtain the state feedback gains and the switching rule so that the closed loop system is stochastically stable and the quadratic and H∞ performance costs are bounded above by a constant value. These results are illu...
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robust mode independent filtering for discrete time markov jump linear systems with Multiplicative Noises
International Journal of Control, 2013Co-Authors: O L V Costa, Guilherme R A M BenitesAbstract:This paper deals with the robust mode-independent linear filtering problem for discrete-time Markov jump linear systems with Multiplicative Noises. It is assumed that the values of the Markov chain are not available and that the parameters of the systems are subject to convex polytopic uncertainties. The goal is to design a mode-independent (that is, one that doesn’t depend on the Markov jump parameter) dynamic linear filter such that the closed loop system is mean square stable and minimises an upper bound for the stationary expected value of the square error. A Linear Matrix Inequalities (LMI) formulation, based on a parameter dependent Lyapunov procedure, is proposed to solve the problem. The paper concludes with an illustrative example.
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optimal mean variance control for discrete time linear systems with markovian jumps and Multiplicative Noises
Automatica, 2012Co-Authors: O L V Costa, Alexandre Adalardo De OliveiraAbstract:In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and Multiplicative Noises under two criteria. The first one is an unconstrained mean-variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor.
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linear minimum mean square filter for discrete time linear systems with markov jumps and Multiplicative Noises
Automatica, 2011Co-Authors: O L V Costa, Guilherme R A M BenitesAbstract:In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement Multiplicative Noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline.
Tingwen Huang - One of the best experts on this subject based on the ideXlab platform.
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observer based h fuzzy control for discrete time takagi sugeno fuzzy mixed delay systems with random packet losses and Multiplicative Noises
International Journal of Systems Science, 2015Co-Authors: Shiping Wen, Zhigang Zeng, Tingwen HuangAbstract:This paper investigates the observer-based H∞ fuzzy control problem for a class of discrete-time fuzzy mixed delay systems with random communication packet losses and Multiplicative Noises, where the mixed delays comprise both discrete time-varying and distributed delays. The random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the Multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and Multiplicative Noises, sufficient conditions for the existence of an observer-based fuzzy feedback controller are derived, such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H∞ performance. Then a linear matrix inequality approach for designing such an observer-based H∞ fuzzy controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theore...
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reliable h filtering for neutral systems with mixed delays and Multiplicative Noises
Signal Processing, 2014Co-Authors: Shiping Wen, Zhigang Zeng, Tingwen HuangAbstract:This paper investigates the reliable H"~ filtering problem for a class of neutral systems with mixed delays and Multiplicative Noises. The mixed delays comprise both discrete and distributed delays. And the Multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. Furthermore, the failures of sensors are quantified by a variable varying in a given interval. In the presence of mixed delays and Multiplicative Noises, sufficient conditions for the existence of a reliable H"~ filter are derived, such that the filtering error dynamics is asymptotically mean-square stable and also achieve a guaranteed H"~ performance level. Then a linear matrix inequality (LMI) approach for designing such a reliable H"~ filter is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.
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observer based h control of discrete markovian jump delay systems with random packet losses and Multiplicative Noises
Optimal Control Applications & Methods, 2013Co-Authors: Shiping Wen, Zhigang Zeng, Tingwen Huang, Gang BaoAbstract:SUMMARY This paper investigates the observer-based H ∞ control problem for a class of mixed-delay Markovian jump systems with random communication packet losses and Multiplicative Noises. The mixed delays comprise both discrete time-varying delays and distributed delays, the random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the Multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and Multiplicative Noises, sufficient conditions for the existence of an observer-based feedback controller are derived such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H ∞ performance. Then, a linear matrix inequality approach for designing such an observer-based H ∞ controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.
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robust probabilistic sampling h output tracking control for a class of nonlinear networked systems with Multiplicative Noises
Journal of The Franklin Institute-engineering and Applied Mathematics, 2013Co-Authors: Shiping Wen, Zhigang Zeng, Tingwen HuangAbstract:Abstract In this paper, the problem of robust sampled-data H ∞ output tracking control is investigated for a class of nonlinear networked systems with probabilistic sampling, Multiplicative Noises and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and can be extended to the case with multiple stochastic sampling periods. By the way of an input delay, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality (LMI)-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H ∞ . Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H ∞ output tracking design.
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reliable h filtering for mixed time delay systems with stochastic nonlinearities and Multiplicative Noises
Asian Journal of Control, 2013Co-Authors: Shiping Wen, Zhigang Zeng, Tingwen HuangAbstract:This paper investigates the reliable H∞ filtering problem for a class of mixed time-delay systems with stochastic nonlinearities and Multiplicative Noises. The mixed delays comprise both discrete time-varying and distributed delays. The stochastic nonlinearities in the form of statistical means cover several well-studied nonlinear functions. The Multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. Furthermore, the failures of sensors are quantified by a variable varying in a given interval. In the presence of mixed delays, stochastic nonlinearities, and Multiplicative Noises, sufficient conditions for the existence of a reliable H ∞ filter are derived, such that the filtering error dynamics is asymptotically mean-square stable and also achieves a guaranteed H ∞ performance level. Then, a linear matrix inequality (LMI) approach for designing such a reliable H ∞ filter is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.
Shiping Wen - One of the best experts on this subject based on the ideXlab platform.
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observer based h fuzzy control for discrete time takagi sugeno fuzzy mixed delay systems with random packet losses and Multiplicative Noises
International Journal of Systems Science, 2015Co-Authors: Shiping Wen, Zhigang Zeng, Tingwen HuangAbstract:This paper investigates the observer-based H∞ fuzzy control problem for a class of discrete-time fuzzy mixed delay systems with random communication packet losses and Multiplicative Noises, where the mixed delays comprise both discrete time-varying and distributed delays. The random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the Multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and Multiplicative Noises, sufficient conditions for the existence of an observer-based fuzzy feedback controller are derived, such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H∞ performance. Then a linear matrix inequality approach for designing such an observer-based H∞ fuzzy controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theore...
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reliable h filtering for neutral systems with mixed delays and Multiplicative Noises
Signal Processing, 2014Co-Authors: Shiping Wen, Zhigang Zeng, Tingwen HuangAbstract:This paper investigates the reliable H"~ filtering problem for a class of neutral systems with mixed delays and Multiplicative Noises. The mixed delays comprise both discrete and distributed delays. And the Multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. Furthermore, the failures of sensors are quantified by a variable varying in a given interval. In the presence of mixed delays and Multiplicative Noises, sufficient conditions for the existence of a reliable H"~ filter are derived, such that the filtering error dynamics is asymptotically mean-square stable and also achieve a guaranteed H"~ performance level. Then a linear matrix inequality (LMI) approach for designing such a reliable H"~ filter is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.
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observer based h control of discrete markovian jump delay systems with random packet losses and Multiplicative Noises
Optimal Control Applications & Methods, 2013Co-Authors: Shiping Wen, Zhigang Zeng, Tingwen Huang, Gang BaoAbstract:SUMMARY This paper investigates the observer-based H ∞ control problem for a class of mixed-delay Markovian jump systems with random communication packet losses and Multiplicative Noises. The mixed delays comprise both discrete time-varying delays and distributed delays, the random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the Multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and Multiplicative Noises, sufficient conditions for the existence of an observer-based feedback controller are derived such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H ∞ performance. Then, a linear matrix inequality approach for designing such an observer-based H ∞ controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.
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robust probabilistic sampling h output tracking control for a class of nonlinear networked systems with Multiplicative Noises
Journal of The Franklin Institute-engineering and Applied Mathematics, 2013Co-Authors: Shiping Wen, Zhigang Zeng, Tingwen HuangAbstract:Abstract In this paper, the problem of robust sampled-data H ∞ output tracking control is investigated for a class of nonlinear networked systems with probabilistic sampling, Multiplicative Noises and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and can be extended to the case with multiple stochastic sampling periods. By the way of an input delay, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality (LMI)-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H ∞ . Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H ∞ output tracking design.
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reliable h filtering for mixed time delay systems with stochastic nonlinearities and Multiplicative Noises
Asian Journal of Control, 2013Co-Authors: Shiping Wen, Zhigang Zeng, Tingwen HuangAbstract:This paper investigates the reliable H∞ filtering problem for a class of mixed time-delay systems with stochastic nonlinearities and Multiplicative Noises. The mixed delays comprise both discrete time-varying and distributed delays. The stochastic nonlinearities in the form of statistical means cover several well-studied nonlinear functions. The Multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. Furthermore, the failures of sensors are quantified by a variable varying in a given interval. In the presence of mixed delays, stochastic nonlinearities, and Multiplicative Noises, sufficient conditions for the existence of a reliable H ∞ filter are derived, such that the filtering error dynamics is asymptotically mean-square stable and also achieves a guaranteed H ∞ performance level. Then, a linear matrix inequality (LMI) approach for designing such a reliable H ∞ filter is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.
