Mixed Constrained Infinite Horizon Linear Quadratic Optimal Control

For a given initial state, a constrained infinite horizon linear quadratic optimal control problem can be reduced to a finite dimensional problem [12]. To find a conservative estimate of the size of the reduced problem, the existing algorithms require the on-line solutions of quadratic programs [10] or a linear program [2]. In this paper, we first show based on the Lyapunov theorem that the closed-loop system with a mixed constrained infinite horizon linear quadratic optimal control is exponentially stable on proper sets. Then the exponentially converging envelop of the closed-loop trajectory that can be computed off-line is employed to obtain a finite dimensional quadratic program equivalent to the mixed constrained infinite horizon linear quadratic optimal control problem without any on-line optimization. The example considered in [2] showed that the proposed algorithm identifies less conservative size estimate of the reduced problem with much less computation.