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

• Published in: IEEE transactions on automatic control Vol. 69; no. 12; pp. 8156 - 8171
• Main Authors: Wang, Ji, Diagne, Mamadou
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Adaptive control; Adaptive systems; Backstepping; Boundary control; Closed loops; Control theory; Convergence; Deep sea vessels; Delay; Delay-adaptive control; Delays; Event detection; event-triggered control; Feedback control; Hyperbolic differential equations; hyperbolic partial differential equations (PDEs); Least squares approximations; least-squares identifier; Ordinary differential equations; Partial differential equations; Regulation; System effectiveness; Vibrations
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2024.3399629

This article presents a delay-adaptive boundary control scheme for a 2 × 2 coupled linear hyperbolic partial differential equation (PDE)-ordinary differential equation (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. To build the delay-adaptive boundary control law, 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. The prescribed-time identification of the unknown delay is also achieved. 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.