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

For stochastic sampled-data systems characterized by unknown nonlinear dynamics (SSDUNSs), it is a great challenge to design an appropriate controller to achieve stable tracking control. In this article, a perceptron-based adaptive model predictive control (PAMPC) scheme is developed for SSDUNSs with multiple discrete stochastic sampling intervals. The activation frequency of each sampling interval can be statistically obtained, which can be described by the categorical distribution. First, a PAMPC structure is developed for the tracking control of SSDUNS. A perceptron with a cost function is designed to incorporate the exploration of the environmental state, encompassing the sampling interval, predictive error, and tracking error. Second, an adaptive predictive horizon (APH) is incorporated into the predictive model to provide the necessary predicting information for the controller. APH is adjusted based on the activation frequency of stochastic sampling intervals. Third, an optimal control problem (OCP) combined with the penalty of the perceptron is designed to stabilize SSDUNS. Then, the control law can be computed to achieve the stable tracking control of SSDUNSs. Finally, the stability of the proposed method is analyzed theoretically to ensure its reliability and robustness. In addition, the effectiveness of the designed method is verified by numerical simulations and real-world applications in the context of wastewater treatment processes (WWTPs).