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

• 成果类型: Article
• 署名作者: Wang, Ji; Diagne, Mamadou
• 署名单位: Xiamen University; University of California System; University of California San Diego
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3399629
• 发表日期: 2024
• 页码: 8156-8171
• 关键词: Delays; Backstepping; actuators; Adaptive control; CONVERGENCE; vibrations; regulation; Delay-adaptive control; event-triggered control; hyperbolic partial differential equations (PDEs); least-squares identifier

摘要

This article presents a delay-adaptive boundary control scheme for a 2 x 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.