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

• Published in: IEEE transaction on neural networks and learning systems Vol. 35; no. 5; pp. 6286 - 6300
• Main Authors: Yuan, Yuan, Xu, Xiaodong, Yang, Chunhua, Luo, Biao, Dubljevic, Stevan
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.05.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Adaptive control; Boundary observer; concurrent learning (CL); Differential equations; Distributed parameter systems; exponential convergence; Fault tolerance; Fault tolerant systems; Faults; Feedback control; Internal model principle; Learning; Mathematical models; Observational learning; Observers; Output feedback; output feedback regulator; parameter adaptation laws; Partial differential equations; Regulation; Regulators; Robust control; sliding mode control; State estimation; State feedback; Theoretical analysis; uncertain boundary fault parameters
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2022.3224245

This article develops a robust adaptive boundary output regulation approach for a class of complex anticollocated hyperbolic partial differential equations subjected to multiplicative unknown faults in both the boundary sensor and actuator. The regulator design is based on the internal model principle, which amounts to stabilize a coupled cascade system, which consists of a finite-dimensional internal model driven by a hyperbolic distributed parameter system (DPS). To this end, a systematic sliding mode equipped with a backstepping approach is developed such that the robust state feedback control can be realized. Moreover, since the available information is a faulty boundary measurement at the right side point, state estimation is required. However, due to the presence of boundary unknown faults, we need to solve an issue of joint fault-state estimation. Restrictive persistent excitation conditions are usually required to guarantee the exact estimation of faults but are unrealistic in practice. To this end, a novel concurrent learning (CL) adaptive observer is proposed so that exponential convergence is obtained. It is the first time that the spirit of CL is introduced to the field of DPSs. Consequently, the observer-based adaptive boundary fault tolerant control scheme is developed, and rigorous theoretical analysis is given such that the exponential output regulation can be achieved. Finally, the effectiveness of the proposed methodology is demonstrated via comparative simulations.