On the horizons in constrained linear quadratic regulation

Authors:
Xiaodong Zhao;Zongli Lin
Affiliations:
Institude of Information and Control, Hangzhou Dianzi University, Hangzhou, Zhejiang, China;Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904-4743, USA
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

This paper revisits the problem of infinite horizon constrained linear quadratic regulation (LQR) for discrete-time systems. It is known that there exists a finite horizon such that the infinite horizon constrained LQR problem can be solved as a finite horizon constrained LQR problem. We first propose several algorithms to estimate the upper bound on the length of this finite horizon. Conservativeness and computational complexity of these algorithms are compared through numerical examples.