A Computable Plant-Optimizer Region of Attraction Estimate for Time-distributed Linear Model Predictive Control

Abstract

Time-distributed optimization is a suboptimal implementation strategy for reducing the computational effort required to implement Model Predictive Control (MPC). Time-distributed MPC (TDMPC) methods maintain a running estimate of the solution to an Optimal Control Problem and improve this estimate using a limited number of optimizer iterations during each sampling period. This paper studies closed-loop stability properties of a constrained linear system controlled using TDMPC. A sufficient bound on the number of iterations per sampling period required to enforce asymptotic stability is derived in closed-form with a computable region of attraction estimate in the plant-optimizer space. Conditions under which a user-provided optimizer initialization yields asymptotically stable trajectories are also established. The results of numerical experiments are reported to illustrate theoretical concepts and demonstrate the computation of the plant-optimizer region of attraction estimate.