Efficient suboptimal solutions of switched LQR problems

Authors:
Wei Zhang;Alessandro Abate;Jianghai Hu
Affiliations:
School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN;Department of Aeronautics and Astronautics, Stanford University, CA;School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

Citing 4
Cited 2

Neuro-Dynamic Programming

Neuro-Dynamic Programming
Convex Optimization

Convex Optimization
Dynamic Programming and Optimal Control, Vol. II

Dynamic Programming and Optimal Control, Vol. II
Dynamic programming for constrained optimal control of discrete-time linear hybrid systems

Automatica (Journal of IFAC)

Exponential stabilization of discrete-time switched linear systems

Automatica (Journal of IFAC)
Brief paper: Linear-quadratic switching control with switching cost

Automatica (Journal of IFAC)

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Abstract

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.