Computationally Efficient Model Predictive Control with Explicit Disturbance Mitigation and Constraint Enforcement

Making model predictive control (MPC) practical for systems with fast dynamics and limited on-board computing power has motivated researchers to propose various implementation or approximation methods that can alleviate the on-line computational demands. In this paper, we investigate one predictive control scheme (Wilson et al., 1999; You et al., 2005) which allows efficient utilization of processor idling time, between samples and control updates, to pre-compute the optimization solution. Two aspects of the MPC scheme are addressed, namely, the explicit mitigation of disturbances and the active enforcement of constraints. We first propose a novel method that provides estimation and compensation of the state-dependent disturbance for the perturbed system. In case the disturbance is known or measured, the stability of the closed-loop system is established. In dealing with input and state constraints, we propose to solve on-line a single step low-dimensional optimization problem to complement the scheme of Wilson et al. and You et al., thereby providing local compensation and avoiding constraint violation. A numerical example is provided to illustrate different computational aspects of the proposed scheme