Deep Koopman-based reachability analysis for data-driven predictive control of unknown nonlinear systems

This paper proposes a deep Koopman-based reachability analysis technique for a data-driven control of unknown nonlinear systems subject to process and measurement noises. An intelligent approach combining a neural network and Q-learning algorithm is employed. In particular, the power of the Long Short-Term Memory (LSTM) neural network is leveraged to lift the original nonlinear system into a higher-dimensional space, where the nonlinear dynamics can be approximated linearly, relying solely on the input–output data. The LSTM is set to draw learning insights from Extended Dynamic Mode Decomposition (EDMD) and Information-Theoretic Metric Function (ITMF) results. The Q-learning algorithm is employed to compute adaptive input–output references in the implementation of an adaptive nonlinear zonotopic predictive control technique to compute a robust control input of the system. We also introduced controllability and observability criteria in the presence of noisy data. Finally, a numerical example is given to verify the proposed approach.