不确定性非线性系统借助量测反馈的鲁棒控制

On Ensuring Robustness of Controller for Nonlinear System with Uncertainties

主要讨论不确定非线性系统通过借助测量反馈实现内部稳定的干扰衰减问题。借助求解Hamiltonian- Jacobi不等式 ,给出一种控制器和观测器设计方法 ,然后利用配方方法 ,分析由所设计的动态控制器所构成闭环系统对模型不确定性具有较强的鲁棒性。

Isidori's method in Ref.[2] cannot, in our opinion, guarantee the robustness of controller for nonlinear system with uncertainties. We propose a method that can ensure its robustness. We considered nonlinear system with uncertainties described by the three equations in eq.(1). We made assumptions 1, 2, 3 and 4 as listed in section one. We used completion of square argument to prove two theorems in section one, which form the theoretical basis of our design method. We used the Hamilton-Jacobi inequality as given in expression (5), and we used eq.(7) and eqs.(9) through (14) to design the controller. Eq.(8) was the final form of the controller and eq.(6) showed the robustness scope of our controller. Simulation results given in Figs.1a and 1b show preliminarily that our design method can ensure the robustness of the controller for nonlinear system with uncertainties. Fig.1a is for the standard uncertain system and Fig.1b for the perturbed system.