Global Output‐Feedback Stabilization for Stochastic Nonlinear Systems with Function Control Coefficients

Abstract

This paper investigates the global output‐feedback stabilization for a class of stochastic nonlinear systems with function control coefficients. Notably, the systems in question possess control coefficients that are functions of output, rather than constants; hence, they are different from the existing literature on stochastic stabilization. To solve the control problem, an appropriate reduced‐order observer is introduced to reconstruct the unmeasured system states before a smooth output‐feedback controller is designed using the backstepping method, which guarantees that the closed‐loop system is globally asymptotically stable in probability. This paper combines the related results in the deterministic and stochastic setting and gives the first treatment on the global output‐feedback stabilization for the stochastic nonlinear systems with function control coefficients. A simulation example is given also to illustrate the effectiveness of the proposed approach.

Output‐feedback stabilization of a class of stochastic nonlinear systems with time‐varying powers

“…It should be stressed that other studies in References 14‐21 have failed to consider the effect of time‐varying powers in the model. There has been less previous research for stochastic nonlinear systems.…”

“…References 19,20 proved output‐feedback stabilization problem for a general class of high‐order stochastic nonlinear systems. Reference 21 studied the global output‐feedback stabilization with functional control coefficients.…”

Continuous simultaneous stabilization of single‐input nonlinear stochastic systems

“…Many real systems are nonlinear and are also prone to stochastic phenomena. These features have naturally attracted attention in the control literature with studies examining stabilization problems for stochastic nonlinear systems, and some interesting results obtained during the past few decades, see [1][2][3][4][5][6][7] and references therein. These results were obtained using classical stochastic theory as found, for instance, in [8] and [9].…”

State‐feedback stabilization and inverse optimal control for stochastic high‐order nonlinear systems with time‐varying powers

“…When p ( t )=1, system () reduces to the well‐known normal form, controller design and stability analysis problems arise, which have been investigated in many works [1–11]. Specifically, [1]–[2] give the basic definitions and stability results for stochastic systems.…”

“…Specifically, [1]–[2] give the basic definitions and stability results for stochastic systems. For the Lyapunov‐based controller design, there are mainly two methods: quartic Lyapunov functions [3]‐[4] and quadratic Lyapunov functions multiplied by different weighting functions [5], which are further developed by [6–11]. When the power p ( t )>1, system () is called stochastic high‐order nonlinear system.…”