Infinite-Horizon Switched LQR Problems in Discrete Time: A Suboptimal Algorithm With
Wei Zhang, Jianghai Hu, and Alessandro Abate
Abstract-- This paper studies the quadratic regulation problem
for discrete-time switched linear systems (DSLQR problem) on
an infinite time horizon. A general relaxation framework is
developed to simplify the computation of the value iterations.
Based on this framework, an efficient algorithm is developed
to solve the infinite-horizon DSLQR problem with guaranteed
closed-loop stability and suboptimal performance. Due to its
stability and suboptimal performance guarantees, the proposed
algorithm can be used as a general controller synthesis tool for
switched linear systems.
This paper studies an extension of the classical LQR prob-
lem to switched linear systems (SLS), which will be referred
to as the Discrete-Time Switched LQR (DSLQR) Problem.
The goal is to find both the continuous-control and switching-
control strategies to minimize a quadratic cost functional over
an infinite time horizon. The problem is expected to play a