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

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.

Automated summary

In this article, a novel data-driven model predictive control (MPC) approach is presented for controlling unknown nonlinear systems using measured input-output data with closed-loop stability guarantees. The proposed scheme utilizes the data-driven system parameterization provided by the fundamental lemma of Willems et al. By updating the data with new input-output measurements online and exploiting local linear approximations of the underlying system, the MPC scheme ensures that the closed loop converges to the optimal reachable equilibrium while satisfying input constraints. The study also extends the fundamental lemma to affine systems and derives robustness bounds for the open-loop optimal control problem under noisy data, which can be applied to other data-driven MPC schemes.