Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees
<|reference_start|>Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees: In this paper, we consider the design of data-driven predictive controllers for nonlinear systems from input-output data via linear-in-control input Koopman lifted models. Instead of identifying and simulating a Koopman model to predict future outputs, we design a subspace predictive controller in the Koopman space. This allows us to learn the observables minimizing the multi-step output prediction error of the Koopman subspace predictor, preventing the propagation of prediction errors. To avoid losing feasibility of our predictive control scheme due to prediction errors, we compute a terminal cost and terminal set in the Koopman space and we obtain recursive feasibility guarantees through an interpolated initial state. As a third contribution, we introduce a novel regularization cost yielding input-to-state stability guarantees with respect to the prediction error for the resulting closed-loop system. The performance of the developed Koopman data-driven predictive control methodology is illustrated on a nonlinear benchmark example from the literature.<|reference_end|>
@article{de jong2024koopman,
    title={Koopman Data-Driven Predictive Control with Robust Stability and
  Recursive Feasibility Guarantees},
    author={Thomas de Jong, Valentina Breschi, Maarten Schoukens and Mircea Lazar},
    journal={arXiv preprint arXiv:2405.01292},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.01292},
    primaryClass={math.OC cs.LG cs.SY eess.SY}
}