具非线性控制变量的非自治松驰系统时间最优追踪控制问题中的若干结果

本文讨论了一类广义非自治离散松驰系统的时间最优控制问题，将R^n中点曲线的目标约束推广为凸集值函数的超曲线约束．在证明了松驰系统与原系统可达集相等的基础上，得到了最优控制的存在性．由凸集分离定理及终端时间闺值函数方程，我们获得了最大值原理及最优控制时间的确定方法．较之Hamilton方法，本文的条件更一般．离散松驰系统的相关结论可以用于分散控制．

Some Results in Time Optimal Tracing Control Problem of Non-autonomous Relaxed System with Nonlinear Control Variables

The paper discusses a generalized non-autonomous discrete relaxed system in time optimal control with generalizing the target constraint from the point curve to convex set hyper curve. Based on the equivalence of the reachable sets from an original system to its relaxed system, the existence of time optimal control is proved. Using separation theorem of convex set and the time terminal value function equation, we obtain the determining method of optimal terminal time as well as the Maximum principle. Compared with the Hamilton method, conditions involved in the paper are more general. And concerning results of the discrete relaxed control system in finite dimension can be used in the decentralized control.