非线性时滞系统次优控制的逐次逼近法

对状态变量含有时滞的非线性系统的次优控制问题进行了研究，提出了一种次优控制的逐次逼近设计方法．针对由最优控制理论导出的既含有时滞项又含有超前项的非线性两点边值问题，构造了其解序列一致收敛于原问题最优解的非齐次线性两点边值问题序列．从而将两点边值问题解序列的有限次迭代结果作为系统的次优控制律．仿真结果表明了所提出方法的有效性．

Successive approximation approach of suboptimal control for nonlinear time-delay systems

The suboptimal control for nonlinear systems with time-delay in state variables is considered, and a successive approximation approach is proposed. For the nonlinear two-point boundary value problem with both time-delay terms and time-advanced terms driven by the optimal control theory, a sequence of nonhomogeneous linear two-point boundary value problems are constructed, the solution sequence of which uniformly converges to the optimal solution of the original problem. Some finite iterative result of the two-point boundary value problem sequence is taken as a suboptimal control law of the system. The simulation results show the effectiveness of the presented algorithm.