Model predictive control with linear models

TLDR

The paper unifies linear model predictive control concepts within a stabilizing infinite‑horizon linear quadratic regulator framework, including output‑feedback via linear‑quadratic state estimation. It aims to eliminate the need for tuning nominal stability by incorporating a nominally stabilizing constrained regulator. The approach models multivariable systems with a standard state‑space formulation, implements the controller as a standard quadratic program, and integrates the stabilizing constrained regulator. The resulting framework flexibly handles nonsquare systems, noisy inputs/outputs, and disturbances, and subsumes existing integral control schemes that remove steady‑state offset.

Abstract

Abstract This article discusses the existing linear model predictive control concepts in a unified theoretical framework based on a stabilizing, infinite horizon, linear quadratic regulator. In order to represent unstable as well as stable multivariable systems, the standard state‐space formulation is used for the plant model. The incorporation of a nominally stabilizing constrained regulator eliminates the current requirement of tuning for nominal stability. Output feedback is addressed in the well‐established framework of the linear quadratic state‐estimation problem. This framework allows the flexibility to handle nonsquare systems, noisy inputs and outputs, and nonzero input, output, and state disturbances. This formulation subsumes the integral control schemes designed to remove steady‐state offset currently in industrial use. The online implementation of the controller requires the solution of a standard quadratic program that is no more computationally intensive than existing algorithms.