Stochastic Nonlinear Prescribed-Time Stabilization and Inverse Optimality

• 成果类型: Article
• 署名作者: Li, Wuquan; Krstic, Miroslav
• 署名单位: Ludong University; University of California System; University of California San Diego
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3061646
• 发表日期: 2022
• 页码: 1179-1193
• 关键词: STOCHASTIC PROCESSES; Nonlinear systems; Time-varying systems; asymptotic stability; Stability criteria; optimal control; Mathematical model; inverse optimality; nonscaling design; prescribed-time stabilization; stochastic nonlinear systems

摘要

We solve the prescribed-time mean-square stabilization and inverse optimality control problems for stochastic strict-feedback nonlinear systems by developing a new nonscaling backstepping design scheme. A key novel design ingredient is that the time-varying function is not used to scale the coordinate transformations and is only suitably introduced into the virtual controllers. The advantage of this approach is that a simpler controller results and the control effort is reduced. By using this method, we design a new controller to guarantee that the equilibrium at the origin of the closed-loop system is prescribed-time mean-square stable. Then, we redesign the controller and solve the prescribed-time inverse optimal mean-square stabilization problem, with an infinite gain margin. Specifically, the designed controller is not only optimal with respect to a meaningful cost functional but also globally stabilizes the closed-loop system in the prescribed-time. Finally, two simulation examples are given to illustrate the stochastic nonlinear prescribed-time control design.