Koopman fault-tolerant model predictive control

Abstract

This paper introduces a novel data-driven approach to develop a fault-tolerant model predictive controller (MPC) for non-linear systems. By adopting a Koopman operator-theoretic perspective, the proposed method leverages historical data from the system to construct a data-driven model that captures the non-linear behaviour and fault characteristics. The fault influence is addressed through an online estimation of a time-varying Koopman predictor, which allows for adjusting the MPC control law to counteract the fault effects. This estimation is performed in a higher dimensional Koopman feature space, where the dynamics behave linearly. As a result, the non-linear fault-tolerant MPC optimization problem can be replaced with a more practical and feasible linear time-varying one using the approximated Koopman predictor. Moreover, by incorporating the online update procedure, the time-varying Koopman predictor can represent the dynamics of the faulty system. Hence, the controller can adapt and compensate for the faults in real-time, integrating the fault diagnosis module in the MPC framework and eliminating the need for a separate fault detection unit. Finally, the efficacy of the proposed approach is demonstrated through case study results, which highlight the ability of the controller to mitigate faults and maintain desired system behaviour.