Data-Driven Tracking MPC for Changing Setpoints

TL;DR

This paper introduces a data-driven model predictive control scheme for tracking changing setpoints in unknown linear systems, ensuring stability and extending existing results to cases with only positive semidefinite stage costs.

Contribution

It develops a purely data-driven MPC approach for setpoint tracking in unknown systems, providing stability guarantees and extending model-based results to broader cost functions.

Findings

Proves exponential stability for reachable setpoints.

Guarantees stability for unreachable but reachable equilibria.

Demonstrates effectiveness through a practical example.

Abstract

We propose a data-driven tracking model predictive control (MPC) scheme to control unknown discrete-time linear time-invariant systems. The scheme uses a purely data-driven system parametrization to predict future trajectories based on behavioral systems theory. The control objective is tracking of a given input-output setpoint. We prove that this setpoint is exponentially stable for the closed loop of the proposed MPC, if it is reachable by the system dynamics and constraints. For an unreachable setpoint, our scheme guarantees closed-loop exponential stability of the optimal reachable equilibrium. Moreover, in case the system dynamics are known, the presented results extend the existing results for model-based setpoint tracking to the case where the stage cost is only positive semidefinite in the state. The effectiveness of the proposed approach is illustrated by means of a practical example.