Koopman-Based Economic Model Predictive Control for Nonlinear Systems

In this note, an economically optimal and stabilizing feedback control paradigm for nonlinear systems is introduced. Specifically, an Economic Model Predictive Control (EMPC) that utilizes an equivalent bilinear prediction model derived from Koopman operator theory is developed. Such control strategy is very useful for real-time implementation of the EMPC due to the potential computation time reduction caused by replacing the underlying nonlinear prediction model with a bilinear model. To attain this control objective, we utilize the Lyapunov theory as well as the Koopman eignefunctions to design the proposed predictive controller. Unlike the Koopman-based tracking MPC, we generalize the steady-state operation of nonlinear systems using the Koopman operator to a time-varying operation regime where the closed-loop state can perpetually transition from any point within a predefined stability region to another. In addition, we utilize the Lyapunov theory to construct a stability region that is fully structured from the Koopman-based bilinear model. Finally, we demonstrate the efficacy of the proposed Koopman-based Economic MPC through a chemical process example.