Data-Based Adaptive Model Predictive Control for Stochastic Sampled-Data Nonlinear Systems

Sampled-data systems (SDSs) have received extensive attention due to their wide application in industrial processes. However, for SDSs characterized by complex nonlinear dynamics, it is still a great challenge to achieve stable tracking control when they are affected by stochastic sampling. To deal with this situation, a data-based adaptive model predictive control (DAMPC) method is developed to stabilize the stochastic sampled-data complex nonlinear systems (SSDCNSs). First, an equivalent system with stochastic time-varying delay is constructed to describe SSDCNS. Then, the sampling interval variation of SSDCNS is equivalently converted into the stochastic time-varying delay, whose transfer probability can be gained by the activation frequencies of stochastic sampling intervals. Second, a fuzzy neural network (FNN)-based multistep predictive model with an adaptive prediction horizon (APH) is established. Then, APH is adaptively adjusted according to the stochastic time-varying delay and its transfer probability, and the necessary predictive information can be provided for the controller. Third, an optimal control problem (OCP) is solved to stabilize the SSDCNS. Especially, an attenuation learning rate (ALR) is designed for the controller to reduce excessive control increments. Then, the control action can be calculated to realize stable tracking control. Finally, the stability of the proposed scheme is analyzed in theory, and the effectiveness of the designed method is assessed by a numerical simulation system and an industrial application in the wastewater treatment process (WWTP).