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This paper presents an observer-based event-triggered boundary control strategy for the one-phase Stefan problem, utilising the position and velocity measurements of the moving interface. The design of the observer and controller is founded on the infinite-dimensional backstepping approach. To implement the continuous-time observer-based controller in an event-triggered framework, we propose a dynamic event triggering condition. This condition specifies the instances when the control input must be updated. Between events, the control input is maintained constant in a Zero-Order-Hold manner. We demonstrate that the dwell-time between successive triggering moments is uniformly bounded from below, thereby precluding Zeno behaviour. The proposed event-triggered boundary control strategy ensures the wellposedness of the closed-loop system and the satisfaction of certain model validity conditions. Additionally, the global exponential convergence of the closed-loop system to the setpoint is established using Lyapunov approach. A simulation example is provided to validate the theoretical findings.
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Global exponential stability of event-triggered control of a parabolic PDE with switching dynamic triggering designs
Abstract This paper presents dynamic design techniques—namely, continuous-time event-triggered control (CETC), periodic event-triggered control (PETC) and self-triggered control (STC)—for a class of unstable one-dimensional reaction-diffusion partial differential equations (PDEs) with boundary control and an anti-collocated sensing mechanism. For the first time, global exponential stability (GES) of the closed-loop system is established using a PDE backstepping control design combined with dynamic event-triggered mechanisms for parabolic PDEs—a result not previously achieved even under full-state measurement. When the emulated continuous-time backstepping controller is implemented on the plant using a zero-order hold, our design guarantees $$ L^{2} $$-GES through the integration of novel switching dynamic event triggers and a newly developed Lyapunov functional. While CETC requires the continuous monitoring of the triggering function to detect events, PETC only requires the periodic evaluation of this function. The STC design assumes full-state measurements and, unlike CETC, does not require continuous monitoring of any triggering function. Instead, it computes the next event time at the current event time using only full-state measurements available at the current event time and the immediate previous event time. Thus, STC operates entirely with event-triggered measurements, in contrast to CETC and PETC, which rely on continuous measurements. The well-posedness of the closed-loop systems under all three strategies is established, and simulation results are provided to illustrate the theoretical results.
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- PAR ID:
- 10651516
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- IMA Journal of Mathematical Control and Information
- Volume:
- 42
- Issue:
- 4
- ISSN:
- 0265-0754
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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