针对切换系统中子系统最优且稳定与系统总体最优与稳定之间的关系问题,研究了一类由任意多子系统组成的切换总次数、切换次序、切换时刻均为系统变量的切换系统,指出设计最优的切换序列是切换系统最优控制的关键.在切换总次数和切换次序没有事先确定的情况下,给出了包括切换总次数、切换次序、切换时刻3组变量的代价函数,然后利用遗传算法求解代价函数,得到使得代价函数最小的一组切换总次数、切换次序、切换时刻.通过算例仿真验证了所提方法可以解决这一优化问题.%Referring to the relation between optimization and stabilization of sun-systems and whole-system, a kind of switched system with arbitrary number of sub-systems are investigated, in which, the switching number, switching sequence and switching instants are variable. It is indicated that the optimal switching sequence is the key of switched system optimal control. A kind of cost function which contains the switching number, switching sequence and switching instants is proposed. The cast function can be solved by using genetic algorithms and a group of switching number, switching sequence and switching instants, which make the cost function to be minimum, is obtained. A numerical example is provided to demonstrate the effectiveness of the proposed method.
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