Two approximate solutions for optimal control of switched systems with autonomous subsystems and continuous-time dynamics are developed. The proposed solutions consist of online training algorithms with recursive least squares training laws. The first solution is the classic policy iteration algorithm which imposes heavy computational burden (full back-up). In order to relax the computational burden in the policy iteration algorithm, the second algorithm is presented. The convergence of the proposed algorithms to the optimal solution in online training is investigated. Simulation results are presented to illustrate the effectiveness of the discussed algorithms.

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