Brief paper: Linear-quadratic switching control with switching cost

Authors:
Jianjun Gao;Duan Li
Affiliations:
Department of Automation, School of Electronic, Information, and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

We study in this paper the linear-quadratic (LQ) optimal control problem of discrete-time switched systems with a constant switching cost for both finite and infinite time horizons. We reduce these problems into an auxiliary problem, which is an LQ optimal switching control problem with a cardinality constraint on the total number of switchings. Based on the solution structure derived from the dynamic programming (DP) procedure, we develop a lower bounding scheme by exploiting the monotonicity of the Riccati difference equation. Integrating such a lower bounding scheme into a branch and bound (BnB) framework, we offer an efficient numerical solution scheme for the LQ switching control problem with switching cost.