A Survey on the Stabilization Control for Stochastic Nonlinear Systems

摘要

The stabilization control of stochastic nonlinear systems is an important problem in control theory. Since its emergence in the 1960's, much progress has been obtained from stabilization to optimization, including the risk-sensitive control problem and other problems. The research of stochastic stabilization was renewed by Florchinger in 1990's in [11, 12], where the control Lyapunov method in control design of stochastic affine nonlinear systems was studied. Then the design of the controls for strict-feedback stochastic nonlinear systems was considered by means of state-feedback and output-feedback Under the assumption (A): "the disturbance vector field vanishes at the origin", [7], [8] and [12] studied the problem of designing a control to asymptotically stabilize the closed-loop systems in the large. While and considered the control design to achieve the boundedness in probability of the closed-loop system without using the assumption (A). Specifically, considered the disturbance attenuation problem; [6] and [27] considered the stabilization problem of systems with stable zero-dynamics; [1], [18], [21] and [24] considered the design of satisfaction control under a quadratic, a quartic regulation and quadratic tracking risk-sensitive cost criterion, respectively. [1] used the assumption (B): "the gain functions of stochastic noise are uniformly bounded", while and did not; considered the reduced-order observer-based stabilization control design of the single-input multi-output stochastic nonlinear systems.