Finite/fixed-time bipartite consensus for networks of diffusion PDEs via event-triggered control

This paper investigates the finite/ fixed-time bipartite consensus for networks of diffusion partial differential equations (PDEs) via the event-triggered control strategy. A global con-vergence principle in fixed time, which plays an important role in the theoretical analysis later, is developed for nonlinear systems. The C0-semigroup method is adopted to explain the well-posedness of the considered network systems. Two new event-triggered control protocols are designed to realize the finite/ fixed-time bipartite consensus goal. By apply-ing the proposed convergence principle, Lyapunov functional approach and inequality analysis technique, the finite/ fixed-time bipartite consensus conditions are addressed under the designed control mechanism. Moreover, the settling time is estimated accu-rately. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the finite/fixed-time bipartite consensus problem for networks of diffusion partial differential equations (PDEs) using the event-triggered control strategy. A global convergence principle in fixed time is developed for theoretical analysis and a C0-semigroup method is adopted to ensure the well-posedness of the network systems. Two new event-triggered control protocols are designed to achieve finite/fixed-time bipartite consensus, and the consensus conditions and settling time are analyzed using the proposed convergence principle, Lyapunov functional approach, and inequality analysis technique. Numerical examples are provided to validate the theoretical results.