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Fast Algorithm for Estimating Control Horizon of Input Constrained Linear Quadratic Regulation

A fast algorithm for estimating the control horizon of the input constrained linear quadratic regulation (LQR) problem is presented. 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. An efficient algorithm to estimate the upper bound of the horizon is presented based on the linear programming. It only needs to solve a linear programming problem for on line application. Finally, the comparison among some methods is shown by an example. The proposed algorithm has less conservative than those of other algorithms.