Receding horizon quadratic optimal control: Performance bounds for a finite horizon strategy

Stability results for receding horizon control (RHC) have generally been restricted to two cases: a finite horizon formulation with end (terminal) constraints, and an infinite horizon formulation. In this paper, we prove that stability can be guaranteed for finite receding horizon control applied to linear systems with quadratic costs, without the imposition of end constraints. In addition, conditions which guarantee that the receding horizon control will perform within specified bounds of the optimal infinite horizon performance are derived. The unconstrained case is presented, with extensions to constrained and nonlinear systems being possible. In the unconstrained case, computations involve iterations of the Riccati difference equation, and are demonstrated on a simple example.