一类非线性系统的鲁棒H_∞控制

Robust H_∞ Control for a Class of Nonlinear Systems

研究一类可部分反馈线性化且具扰动三角结构的非线性参数不确定系统的鲁棒H∞控制问题,不确定参数属于已知紧集并以非线性形式进入系统.在输入到状态稳定的理论框架下,基于李雅谱诺夫函数和反演法构造出状态反馈控制器,使得闭环系统对所有允许的参数不确定性是内稳定的,且从扰动输入到输出有有界的L2-增益.控制器的设计不需解任何H am ilton-Jacob i方程,并给出仿真算例说明了该结论的可行性和有效性.

The problem of robust H∞ control is considered for a class of nonlinear systems with parameter uncertainties. The uncertain parameter belongs to a known compact set and enters the system nonlinearly. The systems are assumed to admit partially feedback linearization and satisfy disturbance strict triangularity conditions, In the framework of the input-to-state stable theory, based on Lyapunov argument and backstepping design technique a state feedback controller is constructed which renders the closed-loop system internally stable with bounded L2-gains from exogenous input to output for all admissible parameter uncertainties. No Hamilton-Jacobi equation is needed for the controller design. A simulation example shows the feasibility and effectiveness of the conclusion.