Controller design for stochastic nonlinear systems and performance analysis of the closed-loop systems

doi:10.7523/j.issn.2095-6134.2010.5.020

Abstract

Abstract:

For several classes of important stochastic nonlinear systems we develop new concepts and basic analysis tools, based on which some problems of controller design are investigated and solved. The main contents are the following. (1) For a class of stochastic nonlinear systems with unmeasurable dynamics, the concept of stochastic input-to-state stability (SISS) is introduced. By using the probability theory, a method of changing supply functions is developed in the stochastic framework, and a small-gain condition on the SISS is given for cascaded stochastic nonlinear systems. (2) For a class of large-scale stochastic nonlinear systems with SISS stochastic inverse dynamics, a decentralized adaptive stabilization controller based on output feedback is constructively designed. Both practical stabilization and asymptotical stabilization are solved. A method dealing with the stochastic nonlinear inverse dynamics is given in the framework of decentralized control. (3) For a class of stochastic nonlinear systems with unstable zero dynamics, the concept of stochastic input-to-state stabilization is introduced, and by using this concept a global stabilization controller based on output feedback is constructively designed. (4) For a class of stochastic nonlinear systems with linearly bounded unmeasurable states, the concept of generalized stochastic input-to-state stability is introduced with respect to the noises with unknown covariance and the general stochastic inputs, and by using this concept, output-feedback controllers are constructively designed for stochastic disturbance attenuation and asymptotically global stabilization, respectively. (5) For general stochastic nonlinear systems with time delays, some conditions on the existence and uniqueness of the solution are provided, global (asymptotical) stability in probability is introduced, and the corresponding criterion is obtained. Besides, for a class of uncertain stochastic nonlinear systems with time-varying time delays, an adaptive output-feedback stabilization controller is constructed.

Key words: stochastic nonlinear systems, zero dynamic, inverse dynamic, output feedback, integrator backstepping method, stabilization controller, strict-feedback, stochastic input-to-state stability

CLC Number:

O231
TP13

LIU Shu-Jun, ZHANG Ji-Feng. Controller design for stochastic nonlinear systems and performance analysis of the closed-loop systems[J]. , 2010, 27(5): 711-719.

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