Model Predictive Control for Tracking Bounded References With Arbitrary Dynamics

TL;DR

This paper tackles constrained tracking of bounded references with arbitrary dynamics in discrete-time linear systems by augmenting the MPC design with an artificial reference as an additional decision variable. The authors derive error dynamics, construct a quadratic cost with weights $Q$, $P$, and $T$, and impose a terminal constraint on an augmented system to guarantee recursive feasibility and asymptotic stability, even when references switch. They provide constructive strategies for the terminal set $\\mathcal{Z}_f$ and weight matrices in both periodic and non-periodic reference scenarios, showing finite determination of $\\mathcal{Z}_f$ for periodic exosystems and a decomposition-based approach for non-periodic ones. The resulting QP-based controller maintains feasibility under reference changes and reduces online computational burden by limiting decision variables, with demonstrated effectiveness in simulations that include abrupt reference switches.

Abstract

In this article, a model predictive control (MPC) method is proposed for constrained linear systems to track bounded references with arbitrary dynamics. Besides control inputs to be determined, artificial reference is introduced as additional decision variable, which serves as an intermediate target to cope with sudden changes of reference and enlarges domain of attraction. Cost function penalizes both artificial state error and reference error, while terminal constraint is imposed on artificial state error and artificial reference. We specify the requirements for terminal constraint and cost function to guarantee recursive feasibility of the proposed method and asymptotic stability of tracking error. Then, periodic and non-periodic references are considered and the method to determine required cost function and terminal constraint is proposed. Finally, the efficiency of the proposed MPC controller is demonstrated with simulation examples.

Figures (2)

• Figure 1: Trajectory of output $y$ and desired output $y_r$.
• Figure 2: Trajectories of the norm of tracking error $\|e(t)\|$, control input $u(t)$, and cost $J(t)$.

Theorems & Definitions (7)

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