Robust learning‐based iterative model predictive control for unknown non‐linear systems

Abstract This study presents a learning‐based iterative model predictive control (MPC) scheme for unknown (Lipschitz continuous) nonlinear dynamical systems. The proposed method begins by learning the unknown part of the controlled system using a Gaussian process (GP), which helps derive multi‐step reachable sets that are guaranteed to encompass the actual system states. At each time step in each iteration, the MPC controller calculates a sequence of control inputs that robustly satisfy state and control constraints, as well as terminal constraints based on the GP‐based reachable sets. Then only the first control input is applied to the system. After the iteration, the initial state is reset, and the same procedure is executed with the MPC optimization problem defined by the updated terminal set and cost. As iteration goes on, improvement of the control performance is expected since more data is obtained and the environment is progressively explored. The proposed method provides properties such as recursive feasibility and input to state stability of the goal region under certain assumptions. Moreover, bound on the performance cost in each iteration associated with the implementation of the proposed MPC scheme is also analyzed. The results of the simulation study show that the proposed control scheme can iteratively improve the control performance.