Concurrent Learning Robust Adaptive Fault Tolerant Boundary Regulation of Hyperbolic Distributed Parameter Systems

Area of Science:

• Control Systems Engineering
• Partial Differential Equations
• Fault Diagnosis and Tolerant Control

Background:

• Complex systems governed by hyperbolic partial differential equations (PDEs) often face performance degradation due to unknown faults in boundary sensors and actuators.
• Existing fault estimation methods typically require restrictive persistent excitation conditions, limiting their practical applicability.
• Adaptive output regulation for distributed parameter systems (DPSs) with boundary faults remains a significant challenge.

Purpose of the Study:

• To develop a robust adaptive boundary output regulation strategy for hyperbolic PDEs with unknown multiplicative boundary faults.
• To address the challenge of joint fault and state estimation in the presence of boundary faults.
• To introduce a novel concurrent learning (CL) approach for fault estimation in DPSs.

Main Methods:

• Design of a regulator based on the internal model principle to stabilize a coupled cascade system.
• Development of a sliding mode control strategy combined with a backstepping approach for robust state feedback.
• Proposal of a concurrent learning (CL) adaptive observer for joint fault-state estimation without persistent excitation.
• Formulation of an observer-based adaptive fault-tolerant control scheme.

Main Results:

• The proposed method achieves robust adaptive boundary output regulation for hyperbolic PDEs under multiplicative boundary faults.
• The concurrent learning adaptive observer ensures exponential convergence for joint fault and state estimation.
• The developed fault-tolerant control scheme demonstrates effectiveness through rigorous theoretical analysis and simulations.
• This work represents the first application of concurrent learning principles to distributed parameter systems.

Conclusions:

• The proposed observer-based adaptive fault-tolerant control scheme effectively achieves exponential output regulation.
• The concurrent learning adaptive observer provides a practical solution for fault estimation in DPSs.
• The methodology offers a robust and reliable approach for controlling complex systems with boundary faults.