Efficient suboptimal solutions of switched LQR problems

This paper studies the discrete-time switched LQR (DSLQR) problem using a dynamic programming approach. Efficient algorithms are proposed to solve both the finite-horizon and the infinite-horizon suboptimal DSLQR problems. More importantly, we establish analytical conditions under which the strategies generated by the algorithms are stabilizing and suboptimal. These conditions are derived explicitly in terms of subsystem matrices and are thus easy to verify. The proposed algorithms and the analysis provide a systematical way of solving the DSLQR problem with guaranteed closed-loop stability and suboptimal performance. Simulation results indicate that the proposed algorithms can efficiently solve not only specific but also randomly generated DSLQR problems, making NP-hard problems numerically tractable.