Data-Driven Model Predictive Control for Aperiodic Sampled-Data Nonlinear Systems

The study of aperiodic sampling has witnessed enormous interest due to the ubiquitous presence of digital controllers in relevant application domains. Most existing aperiodic sampled-data control methods assume that the model of the system is known or obtainable, though it is unknown and unavailable in reality. The idealized assumption will limit the application of these methods. To address this problem, a data-driven model predictive control (DMPC) strategy is designed to stabilize the aperiodic sampled-data unknown nonlinear systems (ASUNSs). The main contributions of the proposed DMPC are threefold. First, a linearized polytopic approximation dynamic (LPAD), based on the local linear approximation, is constructed to approximate the dynamics of ASUNSs. Then, the aperiodic sampling information of ASUNS is able to be contained. Second, a data-driven model predictive controller is designed to solve the optimal steady-state problem and the optimal control problem (OCP) successively. Then, the desired output reference can be tracked online. Third, the stability of DMPC is analyzed in theory. Then, the corresponding stability conditions are given to ensure its successful applications. Finally, some experimental studies have been performed on the online control of a general unknown nonlinear system (GUNS) with aperiodic sampling and wastewater treatment process (WWTP) with aperiodic sampling to verify its effectiveness.