一类混杂系统的最优控制(英文)

Optimal control of a class of hybrid systems

中文关键词  最优控制  混杂系统  必要最优性条件  Frechet微分

英文关键词  optimal control  hybrid system  necessary optimality condition  Frechet differential

中文摘要

      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.

英文摘要

      An optimal control problem is investigated for a class of hybrid systems, where the impulsive instants are state-dependent. Instead of relying on the usual technique of variational approach, necessary optimality conditions of this hybrid system are obtained by parameterizing the impulsive instants. Then, the optimal control problem is transformed to a boundary value problem, which can be solved by numerical method or analytic method. Moreover, taking advantage of the theory of generalized differential, necessary optimality conditions are extended to Frechet differential form. It is shown that, at the continuous part of this hybrid dynamic system, the necessary optimality conditions have the same form as traditional continuous system. At the impulsive points of this system, the Hamiltonian function is continuous and the adjoint variable satisfies certain condition. Finally, two examples are presented to illustrate validity of the methods.