Linear tracking MPC for nonlinear systems Part II: The data-driven case

TL;DR

This paper introduces a data-driven model predictive control method for unknown nonlinear systems that guarantees stability and convergence using only input-output data and local linear approximations.

Contribution

It extends the Fundamental Lemma to affine systems, provides robustness bounds for noisy data, and offers a practical MPC scheme with stability guarantees for nonlinear systems.

Findings

Ensures convergence to the optimal equilibrium while satisfying input constraints.

Provides robustness bounds for noisy data in data-driven control.

Demonstrates effectiveness on a continuous stirred tank reactor.

Abstract

We present a novel data-driven model predictive control (MPC) approach to control unknown nonlinear systems using only measured input-output data with closed-loop stability guarantees. Our scheme relies on the data-driven system parametrization provided by the Fundamental Lemma of Willems et al. We use new input-output measurements online to update the data, exploiting local linear approximations of the underlying system. We prove that our MPC scheme, which only requires solving strictly convex quadratic programs online, ensures that the closed loop (practically) converges to the (unknown) optimal reachable equilibrium that tracks a desired output reference while satisfying polytopic input constraints. As intermediate results of independent interest, we extend the Fundamental Lemma to affine systems and we derive novel robustness bounds w.r.t. noisy data for the open-loop optimal control problem, which are directly transferable to other data-driven MPC schemes in the literature. The applicability of our approach is illustrated with a numerical application to a continuous stirred tank reactor.