一类非线性不确定系统的最优自适应控制

研究了一类含有系统扰动，并且状态项与控制项中同时含有未知参数的非线性系统的反馈稳定问题.在控制器的设计中，将原系统的自适应稳定问题转化为扩展系统的非自适应稳定问题，并利用扩展系统的鲁棒控制Lyapunov函数，设计出使原系统自适应稳定的控制律.进一步，利用逆最优的方法，证明了该控制律同时也是满足某种性能指标的最优控制。

Optimal Adaptive Control of a Class of Nonlinear Uncertain Systems

In this paper, the problem of adaptive stabilization of a class of nonlinear systems with unknown parameters both in state and control vectors has been considered. The problem of adaptive stabilization of nonlinear systems is reduced to the problem of nonadaptive stabilization of an extended system. An adaptive controller is designed to complete the stabilization by employing the robust control Lyapunov function of the extended system. Furthermore, the controller is also verified to possess the optimality by applying the inverse optimal method.