Observer-based Finite-time Control of Stochastic Non-strict-feedback Nonlinear Systems
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Observer-based Finite-time Control of Stochastic Non-strict-feedback Nonlinear Systems Yan Zhang and Fang Wang* Abstract: This paper investigates the observer-based adaptive finite-time neural control issue of stochastic nonstrict-feedback nonlinear systems. By establishing a state observer and utilizing the approximation property of the neural network, an adaptive neural network output-feedback controller is constructed. The controller solves the issue that the states of stochastic nonlinear system cannot be measured, and assures that all signals in the closed-loop system are bounded. Different from the existing adaptive control researches of stochastic nonlinear systems with unmeasured states, the proposed control scheme can guarantee the finite-time stability of the stochastic nonlinear systems. Furthermore, the effectiveness of the proposed control approach is verified by the simulation results. Keywords: Adaptive neural control, finite-time control, non-strict-feedback form, state observer, stochastic nonlinear systems.
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INTRODUCTION
In the past few decades, the adaptive control of the nonlinear systems has been paid considerable attention, and some significant results have been published in references [1–6]. The main idea of such control schemes is to model the unknown nonlinear functions by utilizing the function approximation ability of the fuzzy logic systems or neural networks. It should be pointed out that all the control results in [1–6] are applicable to the deterministic systems, but the stability of practical systems is influenced by uncertainties and random disturbances. Because the random differential of stochastic nonlinear systems designed by Lyapunov includes higher order Hessian terms, the control of stochastic nonlinear systems is more difficult than that of deterministic nonlinear systems. Therefore, the study on the control design for the stochastic nonlinear systems has important theoretical and practical significance, and more and more scholars pay attention to it. In particular, for deterministic nonlinear systems [1–6], the control design approaches have been successfully extended to stochastic nonlinear systems [7–10]. Among them, references [7,8] concerned the control design for stochastic nonlinear systems with strict-feedback form, Namadchian et al. [9] addressed the issue of adaptive fuzzy control for a kind of stochastic pure-feedback nonlinear systems, and Zhao et al. [10] developed the adaptive neural control scheme for a category of stochastic non-strict-feedback nonlinear systems. However, for a
class of stochastic nonlinear systems with unmeasurable state variables, the above control strategies [1–10] may not be available. In practical systems, the state variables are usually unmeasurable or just partly measurable, and some control plans may not be well implemented. The observer can estimate those unmeasurable state variables, it overcomes the difficulties caused by lack of accurate state information. In parti
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