Delay-Adaptive Boundary Control of Coupled Hyperbolic PDE-ODE Cascade Systems

TL;DR

This paper introduces a novel delay-adaptive boundary control method for coupled hyperbolic PDE-ODE systems with unknown delays, ensuring exponential regulation and finite-time delay identification, demonstrated on a deep-sea vessel model.

Contribution

It is the first to develop a delay-adaptive control scheme for heterodirectional hyperbolic PDEs with unknown input delays using backstepping and least-squares identification.

Findings

Exponential regulation of system states achieved.

Finite-time exact delay identification demonstrated.

Validated on a deep-sea vessel control application.

Abstract

This paper presents a delay-adaptive boundary control scheme for a $2\times 2$ coupled linear hyperbolic PDE-ODE cascade system with an unknown and arbitrarily long input delay. To construct a nominal delay-compensated control law, assuming a known input delay, a three-step backstepping design is used. Based on the certainty equivalence principle, the nominal control action is fed with the estimate of the unknown delay, which is generated from a batch least-squares identifier that is updated by an event-triggering mechanism that evaluates the growth of the norm of the system states. As a result of the closed-loop system, the actuator and plant states can be regulated exponentially while avoiding Zeno occurrences. A finite-time exact identification of the unknown delay is also achieved except for the case that all initial states of the plant are zero. As far as we know, this is the first delay-adaptive control result for systems governed by heterodirectional hyperbolic PDEs. The effectiveness of the proposed design is demonstrated in the control application of a deep-sea construction vessel with cable-payload oscillations and subject to input delay.