Delay-compensated event-triggered boundary control of hyperbolic PDEs for deep-sea construction

Abstract

In this paper, we present delay-compensated event-triggered boundary control of heterodirectional coupled hyperbolic PDE–ODE systems, with the purpose of employing a piecewise-constant control input which makes the control law more user-friendly in deep-sea construction vessels where the actuator, i.e., the ship-mounted crane, is massive, and compensating delays that exist in transmission of sensing signals from the seabed to the vessel on the ocean surface through a set of acoustics devices. After treating the time delay of arbitrary length as a transport PDE whose boundary connects with the plant, a state observer is built to estimate the states of the overall system of heterodirectional coupled hyperbolic PDEs–ODE–transport PDE, only using the measurements at the right boundary of the last transport PDE. An observer-based output-feedback continuous-in-time controller is designed to stabilize the overall system using the backstepping method, followed by an observer-based event-triggering mechanism, which is designed based on the evolution of the overall PDE–ODE–PDE system, to determine the updating times of the actuation signal. The absence of a Zeno behavior and exponential convergence in the event-based closed-loop system are proved. In the simulation, the obtained theoretical result is verified in control of a deep-sea construction vessel to place the equipment in the target area on the seabed. Performance deterioration under extreme and unmodeled disturbances is also illustrated.