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研究了一类脉冲依赖于状态的混杂系统的最优控制问题.与传统的变分方法不同,通过将跳跃瞬间转化为一个新的待优化参数,得到了该混杂系统的必要最优性条件,从而将最优控制问题转化为一边界值问题,该边界值问题可由数值方法或解析方法解决.此外,利用广义微分的理论,将该必要最优性条件推广到Frechet微分形式.结论表明,在混杂动态系统运行的连续部分,最优解所满足的必要性条件和传统的连续系统相同.在混杂动态系统的脉冲点处,哈密尔顿函数满足连续性条件,协态变量则满足一定的跳跃条件.最后,通过两个实例分析,表明该方法是有效的.
The optimal control problem for a class of impulsive state-dependent hybrid systems is studied. Unlike traditional variational methods, the necessary optimality conditions for the hybrid system are obtained by translating the jumps into a new parameter to be optimized. So the optimal control problem can be transformed into a boundary value problem, which can be solved by numerical method or analytic method.In addition, the generalized differential theory is used to generalize the necessary optimality condition to the Frechet differential form. In the continuous part of the hybrid dynamic system, the necessary conditions of the optimal solution are the same as those of the traditional continuous system. At the pulse point of the hybrid dynamic system, the Hamiltonian function satisfies the continuity condition, and the co-variant variable satisfies certain jumping conditions. Finally, two case studies show that the method is effective.