Deep Bilinear Koopman Model Predictive Control for Nonlinear Dynamical Systems

This article presents a deep bilinear Koopman model predictive control (DBKMPC) approach for modelling and control of unknown nonlinear systems. The bilinear model, which has the computational speed of a linear model and the predictive accuracy of a nonlinear model, can accurately characterize a large class of airborne and ground-based robotic systems. Specifically, a bilinear Koopman dynamic deep neural network (BKDDNN) is developed to learn the finite-dimensional bilinear Koopman operator in the lifting space without prior knowledge or system parameters. Moreover, the bilinear model is integrated into the standard model predictive control (MPC) optimization problem, facilitating the solution of the bilinear optimization problem. In such a way, the proposed DBKMPC avoids the problems of excessive inductive bias and selection difficulty of dictionary functions encountered by the existing methods, so that it enables a more effective solution to the problem of modeling and control of nonlinear robotic systems. The experimental results show that the proposed DBKMPC method surpasses the existing representative methods in terms of prediction and control performance.