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

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, assumin...

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Published inIEEE transactions on automatic control Vol. 69; no. 12; pp. 8156 - 8171
Main Authors Wang, Ji, Diagne, Mamadou
Format Journal Article
LanguageEnglish
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
Online AccessGet full text
ISSN0018-9286
1558-2523
DOI10.1109/TAC.2024.3399629

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Abstract 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.
AbstractList 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.
Author Wang, Ji
Diagne, Mamadou
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SubjectTerms 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
Title Delay-Adaptive Boundary Control of Coupled Hyperbolic PDE-ODE Cascade Systems
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