Optimization-based Control Strategy with Deep Koopman Model for Constrained Complex Nonlinear Systems

It is well known that a nonlinear system can be represented in a linear lifted feature space according to the Koopman operator theory. However, the approximation errors are always ignored, which may damage the control performance. Therefore, this paper presents a deep Koopman-based two loop control structure, where nonlinearities, uncertainties, and constraints can be handled simultaneously. Namely, a deep Koopman linear model is trained off-line to approximate the dynamic of nonlinear system. Accordingly, an optimization problem is introduced in the outer loop to replan the desired trajectory such that state and input constraints can be satisfied. Considering the model uncertainties introduced by the Koopman linear model, an adaptive robust controller is synthesized in the inner loop to ensure that the optimization result of the outer loop can be strictly tracked. In this way, fast transient response can be reached by the outer loop and the high motion tracking accuracy can be promised by the inner loop. The proposed framework’s advantages and efficacy are evidenced through comparative simulations conducted on a 2-DoF robotic manipulator.