Abstract: In this paper,the optimal control problem of the switched system which subsystem is discrete linear system is investigated.At the condition of the given switched number,and the quadratic performance function,the multi-periods decision-making problem can be transformed into single decision-making problem to resolve,then the analytic solution of the switched discrete system optimal control problem can be obtained in global.Searching of the switched instant and sequence to minimum the performance function by genetic algorithm,the searching procedure is presented.A numerical example illustrates the effectiveness of the design approach.The simulation shows that the approach can resolve a kind of switched discrete optimal control problem.

Key words: switched system, optimal control, linear quadratic, dynamical programming principle；genetic algorithm