On the horizons in constrained linear quadratic regulation

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.