Stochastic Sampled-Data Model Predictive Control for T-S Fuzzy Systems With Unknown Stochastic Sampling Probability

In practical applications, sampled-data systems are often affected by unforeseen physical constraints that may cause deviations in the sampling interval from the expected value and result in fluctuations in a probabilistic way, where the probability distribution of stochastic sampling intervals is often time-varying and unknown. How to design a stable tracking controller for sampled-data control systems affected by unknown stochastic sampling probability is a challenging task. A stochastic sampled-data model predictive control (SSDMPC) strategy for T-S fuzzy systems (TSFSs) is proposed to overcome this challenge. First, based on the input delay approach, the considered system is modeled as a continuous-time TSFS with stochastic input delay. Then, the stochastic nature of the sampling interval is effectively mapped to the input delay within the TSFS. Second, considering the unknown characteristic of the sampling interval, a Q-learning-based online estimation algorithm is developed to acquire the sampling probability, and an event-triggered mechanism is designed to reduce the computational burden of the estimation algorithm. Furthermore, the mapped stochastic input delay probability can be obtained. Third, to achieve stable tracking control of the abovementioned continuous-time TSFS with stochastic input delay, a predictive controller is designed to obtain the control law. Finally, the stability of SSDMPC is analyzed theoretically to ensure its reliability. Additionally, the effectiveness of SSDMPC is confirmed through numerical simulations.