期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 55, 期 2, 页码 304-320出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2009.2034924
关键词
Almost sure boundedness; output feedback; stochastic integral input-to-state stability (SiISS); stochastic inverse dynamics; stochastic nonlinear systems
资金
- National Natural Science Foundation of China [60774010, 10971256, 60674027, 60974127, 60974028]
- Shandong Provincial Natural Science Foundation of China [ZR2009GM008]
This paper develops a unifying framework for output feedback regulation of stochastic nonlinear systems with more general stochastic inverse dynamics. The contributions of this work are characterized by the following novel features: 1) Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) using Lyapunov function in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov function is first introduced, two important properties of SiISS are obtained: (i) SiISS is strictly weaker than SISS using Lyapunov function; (ii) SiISS is stronger than the minimum-phase property. However, only under the minimum-phase assumption, there is no dynamic output feedback control law for global stabilization in probability. 2) Almost sure boundedness, a reasonable and stronger concept than boundedness in probability, is introduced. The purpose of introducing the concept is to prove the boundedness and convergence of some signals in the closed-loop control system. 3) Some important mathematical tools which play an essential role in the boundedness and convergence analysis of the closed-loop system are established. 4) A unifying framework is proposed to design a dynamic output feedback control law, which drives the states to the origin almost surely while maintaining all the closed-loop signals bounded almost surely.
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