Event‐triggered predictor‐based control of distributed parameter systems

Abstract

Abstract This paper deals with the point control problem for a class of distributed parameter systems with time varying delay induced by the network. To eliminate the effect of time delay, a predictor with the time‐varying gain is designed to predict the state based on the sampled data. Meanwhile, the prediction error vanishes exponentially with the desired decay rate. To lighten greatly network loads and effectively improve the utilisation of the resource, an event‐triggered communication scheme is proposed to determine the transmitting of necessary sampled data. Then, based on the point feedback controller, the exponential stability condition of the distributed parameter system with the event‐triggered scheme is derived in the framework of linear matrix inequality. Furthermore, the feedback gain is given in this paper by using the Lyapunov–Krasovskii method where a novel Lyapunov–Krasovskii functional is constructed. The event‐triggered time interval is presented to show the number of maximum allowable packet loss. Finally, an example of a food web model is given to illustrate the effectiveness of the obtained results.

Keywords

• Algebra
• Control system analysis and synthesis methods
• Stability in control theory
• Time-varying control systems
• Distributed parameter control systems