Output‐feedback fault‐tolerant tracking control for coupled 2 × 2 hyperbolic PDE systems with multiplicative sensor faults

Abstract

This paper proposes an output-feedback fault-tolerant tracking control scheme for coupled 2 × 2 hyperbolic PDE systems with multiplicative sensor faults. In order to estimate the system states, an observer is designed by constructing four filters, which impose time delays to their input signals. For sensor fault identification problem, the gradient descent method is utilized based on a parametric model to estimate the fault parameter. With the filter-based observer and the estimated fault parameters, a novel control strategy is proposed via backstepping design technique to achieve the tracking objective. Finally, the simulation studies are given to verify the tracking performance of the proposed fault-tolerant tracking control scheme.

Delay‐adaptive control of first‐order hyperbolic partial integro‐differential equations

“…In addition to the fact that z(0, t) Ultimately, we have proven (113) and (114), owing to the invertibility of the backstepping transformations (28) and (38). ▪…”

“…The aforementioned results are built based on three traditional adaptive schemes, including the Lyapunov design, the passivity‐based design, and the swapping design, which were initially proposed for nonlinear ODEs, 34 and extended to the boundary adaptive control of PDEs 35–37 . Combined with backstepping design, a novel control strategy is proposed for coupled hyperbolic PDEs with multiplicative sensor faults in Reference 38, it employed a filter‐based observer and model‐based fault parameter estimation technique to achieve the tracking objective.…”

Delay-Adaptive Control of First-order Hyperbolic PIDEs

“…The aforementioned results are built based on three traditional adaptive schemes, including the Lyapunov design, the passivity-based design, and the swapping design, which were initially proposed for nonlinear ODEs [32], and extended to the boundary adaptive control of PDEs [33][34][35]. Combined with backstepping design, a novel control strategy is proposed for coupled hyperbolic PDEs with multiplicative sensor faults in [36], it utilized a filter-based observer and model-based fault parameter estimation technique to achieve the tracking objective.…”