Sampled-Data Control of Distributed Parameter Systems via an Event-Based Communication Scheme

This paper studies the problem of event-triggered control for a class of networked distributed parameter systems with Markov jump parameters. To reduce the number of packages transmitted over the communication network, an adaptive event-triggered mechanism is introduced. The Galerkin method is employed to obtain the nonlinear ordinary differential equation systems, which can accurately describe the dynamics of the dominant modes of the considered distributed parameter systems. The systems are subsequently parameterized by a multilayer neural network with one-hidden layer and zero bias terms, and the linear ordinary differential equation systems are derived. Then, Lyapunov approach is used to analyze stability of the considered systems, and by employing the strong law of large numbers and Gronwall inequality technique, almost surely exponential stability condition is derived. Moreover, a linear sampled-data-based controller is designed to stabilize the closed-loop systems. Finally, a practical example is shown to demonstrate the effectiveness of the achieved theoretical results.