Robust integral sliding mode control for uncertain stochastic systems with time-varying delay

Niu, Yugang; Ho, Daniel W. C.; Lam, James

doi:10.1016/j.automatica.2004.11.035

Cited by 485 publications

(215 citation statements)

References 13 publications

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“…The trajectories of the system states under the SMC law in (14) is shown in Figure 1 (a) and the trajectories of the estimation error of the ASMO is shown in Figure 1 can be guaranteed and the overall closed-loop system is globally asymptotically stable in probability. And also, in Figure1 (b), the effectiveness of the adaptive observer is numerically verified.…”

Section: Tmentioning

confidence: 99%

Adaptive observer-based non-linear stochastic system control with sliding mode schemes

Qiao

Zhu

Liu

et al. 2008

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this paper, an adaptive sliding mode observer is designed to reconstruct the states of non-linear stochastic systems with uncertainties from the measurable system output and the reconstructed states are employed to construct a sliding mode controller for the stabilization control of complex non-linear systems. It takes the advantages of the sliding mode schemes to design both the observer and the controller. The convergence of the observer and the globally asymptotical stability of the controller are analysed in terms of stochastic Lyapunov stability, and the effectiveness of the control strategy is verified with numerical simulation studies.

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Section: Tmentioning

confidence: 99%

Adaptive observer-based non-linear stochastic system control with sliding mode schemes

Qiao

Zhu

Liu

et al. 2008

Proceedings of the Institution of Mechanical Engineers, Part I:

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“…A great number of results on this topic have been reported in the literature, see, e.g., [2,3,4], and the references therein. Very recently, the designs of sliding mode control (SMC) for uncertain stochastic systems were also developed in, e.g., [5,6]. Both the theoretical proof and numerical simulation in the aforementioned works show that SMC is an effective and promising approach for the stabilization of Itô stochastic systems.…”

Section: Introductionmentioning

confidence: 99%

“…Consider the uncertain stochastic state-delay system (1)- (3) In the work, the simulations are undergone by using the discretization approach as in [5,19] Figs. 4-6 show, respectively, the simulation results on x(t) along 10 individual paths (dotted lines) and the average over 10 paths (solid line).…”

Section: Simulation Examplementioning

confidence: 99%

Robust sliding mode design for uncertain stochastic systems based on H_∞ control method

Niu

Wang

2009

Optim Control Appl Methods

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SUMMARYIn this paper, the design of sliding mode control is addressed for uncertain stochastic systems modeled by Itô differential equations. There exist the parameter uncertainties in both the state and input matrices, and the unmatched external disturbance. The key feature of this work is the integration of sliding mode control method with H∞ technique such that the robustly stochastic stability with a prescribed disturbance attenuation level γ can be obtained. A sufficient condition for the existence of the desired sliding mode controller is obtained via linear matrix inequalities (LMIs). The reachability of the specified sliding surface is proven. Finally, a numerical simulation is presented to illustrate the proposed method.

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“…Furthermore, from the fact Eω(k) = 0 and (4)- (5), calculating the difference of the Lyapunov functional (12) according to (8) gives…”

Section: S)(12)mentioning

confidence: 99%

“…On the other hand, the robust filtering and control problems for stochastic systems with both time delays and parameter uncertainties have also received considerable research attention, see e.g. [5,9,10,12] for some sample publications.…”

Section: Introductionmentioning

confidence: 99%

Robust filtering with stochastic nonlinearities and multiple missing measurements

2009

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This paper is concerned with the filtering problem for a class of discrete-time uncertain stochastic nonlinear time-delay systems with both the probabilistic missing measurements and external stochastic disturbances. The measurement missing phenomenon is assumed to occur in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. Such a probabilistic distribution could be any commonly used discrete distribution over the interval [0 1]. The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. The purpose of the addressed filtering problem is to design a filter such that, for the admissible random measurement missing, stochastic disturbances, norm-bounded uncertainties as well as stochastic nonlinearities, the error dynamics of the filtering process is exponentially mean-square stable. By using the linear matrix inequality (LMI) method, sufficient conditions are established that ensure the exponential mean-square stability of the filtering error, and then the filter parameters are characterized by the solution to a set of LMIs. Illustrative examples are exploited to show the effectiveness of the proposed design procedures.

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Robust integral sliding mode control for uncertain stochastic systems with time-varying delay

Cited by 485 publications

References 13 publications

Adaptive observer-based non-linear stochastic system control with sliding mode schemes

Adaptive observer-based non-linear stochastic system control with sliding mode schemes

Robust sliding mode design for uncertain stochastic systems based on H_∞ control method

Robust filtering with stochastic nonlinearities and multiple missing measurements

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Robust integral sliding mode control for uncertain stochastic systems with time-varying delay

Cited by 485 publications

References 13 publications

Adaptive observer-based non-linear stochastic system control with sliding mode schemes

Adaptive observer-based non-linear stochastic system control with sliding mode schemes

Robust sliding mode design for uncertain stochastic systems based on H∞ control method

Robust filtering with stochastic nonlinearities and multiple missing measurements

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Robust sliding mode design for uncertain stochastic systems based on H_∞ control method