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

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.