Learning and Predictive Control of Nonlinear Systems with Multi-Modal Uncertainties Using Koopman Operator and Gaussian Mixture Model

In this paper, we consider learning-based modeling and predictive control of nonlinear systems subject to multimodal uncertainties. A Gaussian mixture Koopman operator, which learns the evolution of the observable distribution in a higher-dimensional space, is proposed to characterize the dynamics of the underlying nonlinear systems. Based on the learned probabilistic Koopman model, a stochastic model predictive control method with chance constraints is introduced for the nonlinear systems with state constraints. Finally, a simulated chemical process is used to illustrate the effectiveness of the proposed method.