Fast model predictive control based on linear input/output models and bounded-variable least squares

摘要

This paper introduces a fast and simple model predictive control (MPC) approach for multivariable discrete-time linear systems described by input/output models subject to bound constraints on inputs and outputs. The proposed method employs a relaxation of the dynamic equality constraints by means of a quadratic penalty function so that the resulting real-time optimization becomes a (sparse), always feasible, bounded-variable least-squares (BVLS) problem. Criteria for guaranteeing closed-loop stability in spite of relaxing the dynamic equality constraints are provided. The approach is not only very simple to formulate, but also leads to a fast way of both constructing and solving the MPC problem in real time, a feature that is especially attractive when the linear model changes on line, such as when the model is obtained by linearizing a nonlinear model, by evaluating a linear parameter-varying model, or by recursive system identification. A comparison with the conventional state-space based MPC approach is shown in an example, demonstrating the effectiveness of the proposed method.