Event-triggered boundary control of 2x2 semilinear hyperbolic systems

TL;DR

This paper introduces an event-triggered boundary control method for 2x2 semilinear hyperbolic systems, ensuring stability and avoiding Zeno behavior, with practical implementation and numerical validation.

Contribution

It develops a novel event-triggered boundary control scheme for hyperbolic systems, including a closed-form trigger condition for linear cases and integration with observers for output feedback.

Findings

Proven stability and Zeno-free operation of the control scheme.

Closed-form trigger condition for linear hyperbolic systems.

Numerical simulation confirms effectiveness of the approach.

Abstract

We present an event-triggered boundary control scheme for hyperbolic systems. The trigger condition is based on predictions of the state on determinate sets, where the control input is only updated if the predictions deviate from the reference by a given margin. Closed-loop stability and absence of Zeno behaviour is established analytically. For the special case of linear systems, the trigger condition can be expressed in closed-form as an $L_2$-scalar product of kernels with the distributed state. The presented controller can also be combined with existing observers to solve the event-triggered output-feedback control problem. A numerical simulation demonstrates the effectiveness of the proposed approach.