A Dual Adaptation-Based Spatial Model Predictive Control for Nonlinear Distributed Parameter Systems

Due to its spatiotemporal property and time-varying complexity, it is difficult to obtain the accurate model of the actual distributed parameter system (DPS), posing a significant obstacle to control. In this article, a spatial model predictive control (MPC) is proposed for the nonlinear DPS. A data-driven modeling method is first constructed for the performance prediction using the input–output data measured by sensors. In order to capture the most recent dynamics, a dual adaptation approach is devised. This includes updates to the spatial basis functions (SBFs) utilizing recursive techniques, as well as temporal updates employing sliding windows to enable online model updates. Based on the spatiotemporal model, a spatial MPC methodology with a novel objective function is designed for global space tracking. Theoretical analysis demonstrates that the stability of the proposed controller is guaranteed. The simulations and experiments conducted demonstrate that the proposed method satisfactorily achieves global tracking of targets and maintains robustness against time-varying input disturbances.