Output Feedback Periodic Event-triggered Control of Coupled 2× 2 Linear Hyperbolic PDEs
arxiv(2024)
摘要
This article introduces an observer-based periodic event-triggered control
(PETC) strategy for boundary control of a system characterized by 2×2
linear hyperbolic partial differential equations (PDEs). An anti-collocated
actuation and sensing configuration is considered, and an exponentially
convergent observer for state estimation from boundary data is designed.
Initially, a continuous-time dynamic event-triggering mechanism requiring
constant monitoring of the triggering function is developed. This mechanism is
subsequently adapted into a periodic event-triggering scheme, which
necessitates only periodic monitoring to identify when the control input needs
updating. The underlying control approach is the PDE backstepping boundary
control, implemented in a zero-order hold manner between events. This result
marks a substantial improvement over conventional observer-based
continuous-time event-triggered control for linear coupled hyperbolic PDEs by
removing the requirement for constant monitoring of the triggering function.
With the triggering function evaluated periodically, the closed-loop system is
inherently free from Zeno behavior. It is demonstrated that under the proposed
PETC, the closed-loop system globally exponentially converges to zero in the
spatial L^2 norm. A simulation study illustrating the theoretical results is
presented.
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