Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization

• 成果类型: Article
• 署名作者: Tsukamoto, Hiroyasu; Chung, Soon-Jo
• 署名单位: California Institute of Technology; California Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3038402
• 发表日期: 2021
• 页码: 4731-4746
• 关键词: LMIs; Nonlinear systems; optimization algorithms; Robust control; stochastic optimal control

摘要

This article presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Ito stochastic nonlinear systems and Lagrangian systems. Its innovation lies in computing the control input by an optimal contraction metric, which greedily minimizes an upper bound of the steady-state mean squared tracking error of the system trajectories. Although the problem of minimizing the bound is nonconvex, its equivalent convex formulation is proposed utilizing SDC parameterizations of the nonlinear system equation. It is shown using stochastic incremental contraction analysis that the CV-STEM provides a sufficient guarantee for exponential boundedness of the error for all time with L-2-robustness properties. For the sake of its sampling-based implementation, we present discrete-time stochastic contraction analysis with respect to a state- and time-dependent metric along with its explicit connection to continuous-time cases. We validate the superiority of the CV-STEM to PID, H-infinity, and baseline nonlinear controllers for spacecraft attitude control and synchronization problems.