EVENT-TRIGGERED GAIN SCHEDULING OF REACTION-DIFFUSION PDEs

This paper deals with the problem of boundary stabilization of 1D reaction-diffusion PDEs with a time- and space-varying reaction coefficient. The boundary control design relies on the backstepping approach. The gains of the boundary control are scheduled under two suitable event-triggered mechanisms. More precisely, gains are computed/updated on events according to two state-dependent event-triggering conditions: static-based and dynamic-based conditions, under which the Zeno behavior is avoided and well-posedness and exponential stability of the closed-loop system are guaranteed. Numerical simulations are presented to illustrate the results.

Automated summary

This paper focuses on the boundary stabilization of 1D reaction-diffusion PDEs with a time- and space-varying reaction coefficient using the backstepping approach. The gains of the boundary control are scheduled under two event-triggered mechanisms to avoid Zeno behavior and guarantee the well-posedness and exponential stability of the closed-loop system. Numerical simulations are provided to demonstrate the results.