Deep bilinear Koopman realization for dynamics modeling and predictive control

The data-driven approaches based on the Koopman operator theory have promoted the analysis and control of the nonlinear dynamics by providing an equivalent Koopman-based linear system associated with nonlinear systems. To facilitate the use of the Koopman framework for nonlinear systems with control inputs and to improve the prediction accuracy of the Koopman approximation, this work proposes a deep learning-based bilinear Koopman modeling framework. In this framework, we first deploy a deep neural network structure consisting of a lifting network, a control network, a linear layer, and a recovery network to fulfill the identification of the bilinear Koopman realization. During the neural network training process, the model uncertainty naturally arises from the data-driven setting variation. Then, to represent the impact of this implicit uncertainty, we integrate a variable parameter into the output of the control network to identify a relatively accurate model, thereby enhancing the prediction ability of the learned model. The non-convex property caused by the bilinear term is resolved using a linear approximation. After that, we apply a Koopman-based model predictive control scheme to the identified bilinear model with the parameter estimation to realize the control of the nonlinear dynamical system.