Learning Nonlinear Model Predictive Controllers and Virtual Sensors with Koopman Operators

Abstract

Model Predictive Control is an industry-standard technique used to drive systems based on their internal dynamics. When not all states are available for feedback, a state estimator, such as an Extended Kalman Filter, is employed to achieve control over the complete system state. Nevertheless, when the system under control is nonlinear, these two combined methods can result in a computationally heavy control strategy, raising significantly the cost of implementing it online. In this paper, a data-driven strategy based on the Koopman Operator theory is presented to identify and replicate the dynamics of the Kalman Filter plus Model Predictive Controller pair in a resource-efficient scheme. First, a closed-loop operation data-set is generated from a pre-calibrated reference controller; then, a finite-dimensional approximation is derived for the Koopman Operator of the filter plus controller dynamics in the lifted space of observables; finally, the stability of the identified controller is evaluated through closed-loop simulations; in case the desired response has not been achieved, the identification process is performed iteratively with a progressively increasing regularization coefficient. A simulated example applied to the Van der Pol oscillator is presented to illustrate the effectiveness of the approach.