一类非线性耗散系统的逆最优控制

Inverse Optimal Control of a Class of Nonlinear Dissipative Systems

首先研究一类单输入非仿射非线性系统的逆最优控制问题,其代价泛函为非线性-非二次型,设计出一族参数化的状态反馈逆最优控制器;然后讨论当该系统为耗散系统时,在供给率为二次型的耗散性理论框架下,给出使系统渐近稳定的李雅普诺夫函数和镇定控制律,并通过适当选取代价泛函中的参数,使得李雅普诺夫函数也是最优值函数,进而揭示出耗散系统在线性输出反馈意义下稳定性与最优性之间的等价关系.

The inverse optimal control problem of a class of single-input non-affine nonlinear systems with nonlinear- nonquadratic cost functional is addressed. A family of parameterized controllers are designed. When the system is dissipative, in the framework of dissipativity theory with quadratic supply rates, the Lyapunov function and the stabilizing control law that provide asymptotical stability of the closed-loop system are derived. The Lyapunov function is the optimal value function by choosing appropriate parameters of the cost functional. The equivalent relationship between stability and optimality of nonlinear dissipative systems is exposed in the sense of linear output feedback control.