Data‐Driven Modeling With Polytopic Uncertainty and Nonlinear Robust Model Predictive Control Design Using Koopman Operator

ABSTRACT Model predictive control (MPC) based on the Koopman operator is an effective data‐driven control method for nonlinear systems. However, modeling errors are almost inevitable when applying the Koopman operator to model the nonlinear systems and influence the control performance. It is an important problem to guarantee the robustness of Koopman MPC under modeling approximation errors. Aiming at the above problem, this paper proposes a data‐driven approach to handle modeling errors and develops robust min–max MPC solutions with the Koopman operator for nonlinear discrete‐time dynamical systems. The data‐driven method is proposed to identify the modeling error as the polytopic uncertainty within the Koopman operator framework, and its effectiveness analysis is given. Based on the identified modeling error, the paper presents two design schemes for min‐max robust predictive controllers. The first scheme is formulated as the feedback control computed by minimizing the upper bound of the worst‐case value of an infinite‐horizon quadratic objective function at each sampling time. To formulate the other scheme, two algorithms are presented to estimate the current model based on the identified polytope. With the help of the estimated model, the scheme allows the inclusion of the first control move separately from the rest of the control sequence governed by the feedback law, which can achieve better performance, which is an improved version of the first one. Recursive feasibility and closed‐loop stability guarantees are provided. Numerical simulations verify the modeling and control effectiveness of the proposed algorithms.