Linear Tracking MPC for Nonlinear Systems-Part II: The Data-Driven Case

• Published in: IEEE transactions on automatic control Vol. 67; no. 9; pp. 4406 - 4421
• Main Authors: Berberich, Julian, Kohler, Johannes, Muller, Matthias A., Allgower, Frank
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loops; Continuously stirred tank reactors; Data-driven control; Linear systems; Noise measurement; Nonlinear control; Nonlinear dynamical systems; Nonlinear systems; Numerical stability; Optimal control; Parameterization; Predictive control; predictive control for linear systems; Predictive models; Robustness (mathematics); Stability analysis; time varying systems; Trajectory
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3166851

In this article, 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 parameterization 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.