Physics

Nonlinear system

Pure mathematics

Parametrization (atmospheric modeling)

Mathematics

Gene

Mathematical optimization

Quadratic equation

Regular polygon

Convex optimization

Mathematical analysis

Model predictive control

Artificial intelligence

Control (management)

Chemistry

Geometry

Computer science

Quantum mechanics

Control theory (sociology)

Biochemistry

Robustness (evolution)

Linear system

Radiative transfer

Affine transformation

IEEE Transactions on Automatic Control

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.

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