Fuzzy modeling and control for probabilistic-constrained nonlinear systems subject to fading channels

This paper addresses the fuzzy modeling and control problems for nonlinear systems under finite-state Markov fading channels as well as probabilistic state and input constraints. Both the state and input variables are allowed to exceed their prescribed boundaries with certain frequencies. Firstly, the fuzzy modeling for nonlinear plants subject to probabilistic state constraints is considered. By analyzing the distribution characteristics of probabilistic state constraints, the original nonlinear plant is represented as an interval type-2 (IT2) T-S fuzzy system with a stochastic nonlinear term related to the violation levels of state constraints. And then, the control design problem under fading channels and probabilistic constraints is further addressed. For adapting to the real-time network mode and restriction feature, a hidden Markov mode detector is utilized to estimate current channel status, based on which a memory feedback fuzzy controller is synthesized by employing the historical control signal as an augmented state. Benefiting from the well-known Markov inequality, probabilistic state and input constraints can be seamlessly integrated into the Lyapunov stability analysis framework. Sufficient conditions are derived such that the closed-loop IT2 T-S fuzzy system is locally stochastically stable even in the presence of both probabilistic constraints and fading channels. An optimization algorithm is further employed to obtain a larger domain of stochastic stability. Finally, the proposed methods are demonstrated via a simulation example.