Ultimately Bounded PID Control for T–S Fuzzy Systems Under FlexRay Communication Protocol

This article investigates the ultimately bounded proportional–integral–derivative (PID) control problem for a class of discrete-time Takagi–Sugeno fuzzy systems subject to unknown-but-bounded noises and protocol constraints. The signal transmissions from sensors to the remote controller are realized via a communication network, where the FlexRay protocol is employed to flexibly schedule the information exchange. The FlexRay protocol is characterized by both the time- and event-triggered mechanisms, which are conducted in a cyclic manner. By using a piecewise approach, the measurement outputs affected by the FlexRay protocol are established based on a switching model. Then, a fuzzy PID controller is proposed with a concise and realizable structure. To evaluate the performance of the controlled system, a special time sequence is introduced that accounts for the behavior of the FlexRay protocol. Subsequently, a general framework is obtained to verify the boundedness of the closed-loop system, and then, the controller gains are designed by minimizing the bound of the concerned variables. Finally, a simulation study is conducted to validate the effectiveness of the developed control scheme.