一类脉冲切换系统的最优控制

Optimal control for a class of impulsive and switching systems

研究一类脉冲依赖于状态的脉冲切换系统的最优控制问题.考虑了目标函数的两种情况:当目标函数光滑时,通过将跳跃瞬间转化为一个新的待优化参数,得到了该脉冲切换系统的必要最优性条件;当目标函数不光滑时,利用非光滑分析的知识,得到了广义微分形式的必要最优性条件.算例分析验证了所提出方法的有效性.

Optimal control problems are investigated for a class of impulsive and switching systems, where the transitions are state-dependent. Two kinds of situations for the cost function are considered. When the cost function is smooth, by parameterizing the jumping instants as a new parameter to be optimized, the necessary optimality conditions of the hybrid systems are obtained. When the cost functional is nonsmooth, necessary optimality conditions of the generalized differential form are presented by the knowledge of nonsmooth analysis. An example is given to illustrate the effectiveness of the proposed method.