Learning-Based Modeling and Predictive Control for Unknown Nonlinear System With Stability Guarantees

Abstract

This work focuses on the safety of learning-based control for unknown nonlinear system, considering the stability of learned dynamics and modeling mismatch between the learned dynamics and the true one. A learning-based scheme imposing the stability constraint is proposed in this work for modeling and stable control of unknown nonlinear system. Specifically, a linear representation of unknown nonlinear dynamics is established using the Koopman theory. Then, a deep learning approach is utilized to approximate embedding functions of Koopman operator for unknown system. For the safe manipulation of proposed scheme in the real-world applications, a stable constraint of learned dynamics and Lipschitz constraint of embedding functions are considered for learning a stable model for prediction and control. Moreover, a robust predictive control scheme is adopted to eliminate the effect of modeling mismatch between the learned dynamics and the true one, such that the stabilization of unknown nonlinear system is achieved. Finally, the effectiveness of proposed scheme is demonstrated on the tethered space robot (TSR) with unknown nonlinear dynamics.