Finite Receding Horizon Linear Quadratic Control: A Unifying Theory for Stability and Performance Analysis

We consider a finite horizon based formulation of receding horizon control for linear discrete-time plants with quadratic costs. A framework is developed for analyzing stability and performance of finite receding horizon control for arbitrary terminal weights. Previous stability and performance results, including end constraints, infinite horizon formulations, and the fake algebraic Riccati equation, arc all shown to be special cases of the derived results. The unconstrained case is presented, where conditions for finite receding horizon control to be stabilizing and within specified bounds of the optimal infinite horizon performance can be computed from the solution to the Riccati difference equations. Nevertheless, the framework presented is general in that it lays the groundwork for extension to constrained systems.