Linear Data-Driven Economic MPC with Generalized Terminal Constraint

TL;DR

This paper introduces a data-driven economic MPC method for unknown linear systems that uses a generalized terminal constraint and the Fundamental Lemma to optimize economic performance without prior equilibrium knowledge.

Contribution

It presents a novel data-driven EMPC scheme with a generalized terminal constraint that does not require prior equilibrium knowledge and extends to unknown stage costs.

Findings

Asymptotic average performance approaches optimal equilibrium

Effective control of unknown linear systems demonstrated

Method extends to unknown stage cost functions

Abstract

In this paper, we propose a data-driven economic model predictive control (EMPC) scheme with generalized terminal constraint to control an unknown linear time-invariant system. Our scheme is based on the Fundamental Lemma to predict future system trajectories using a persistently exciting input-output trajectory. The control objective is to minimize an economic cost objective. By employing a generalized terminal constraint with artificial equilibrium, the scheme does not require prior knowledge of the optimal equilibrium. We prove that the asymptotic average performance of the closed-loop system can be made arbitrarily close to that of the optimal equilibrium. Moreover, we extend our results to the case of an unknown linear stage cost function, where the Fundamental lemma is used to predict the stage cost directly. The effectiveness of the proposed scheme is shown by a numerical example.