By Linlin Li
Linlin Li addresses the research and layout problems with observer-based FD and FTC for nonlinear structures. the writer analyses the life stipulations for the nonlinear observer-based FD platforms to realize a deeper perception into the development of FD platforms. Aided through the T-S fuzzy procedure, she recommends diverse layout schemes, between them the L_inf/L_2 kind of FD platforms. The derived FD and FTC ways are demonstrated by means of benchmark tactics.
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Extra info for Fault Detection and Fault-Tolerant Control for Nonlinear Systems
Reliable FTC Approach The basic idea behind a reliable FTC approach lies in taking into account the prior knowledge of potential faults in the controller design. Significant effort has been devoted to study the FTC design for affine nonlinear systems or a class of nonlinear systems with norm-bounded uncertainties in terms of solutions of Hamilton-Jacobi inequalities (HJIs) [85, 90, 150, 115]. Moreover,  introduced a passive FTC scheme for affine nonlinear systems with actuator faults. The Lyapunov-based feedback controllers have been addressed to ensure the local uniform asymptotic stability of the systems under additive and loss-of-effectiveness faults.
2 L2 Observer-based FD Systems Considering that the L2 -norm is often used for the residual evaluation purpose, the following L2 type of re-constructability is introduced. 4. 1) is said to be L2 re-constructible if there ˆ) : exist (i) a function φ : Rn × Rp × Rm → Rn (ii) functions V (x, x Rn × Rn → R+ , ϕ1 (·) ∈ K, ϕ2 (·) ∈ K∞ and positive constants δ, δu such ˆ ∈ Bδ , u ∞ ≤ δu that ∀x, x ˆ )f (x, u)+Vxˆ (x, x ˆ )φ(ˆ Vx (x, x x, u, h(x, u)) ≤ −ϕ1 ( r )+ϕ2 ( u ). 3. 3. 2, function V (x, x definition is in fact a variant of the ROS-Lyapunov function (robust output stability) .
In the past two decades, great efforts have been made to the development of observer-based FD schemes for nonlinear systems, where the major focus is on the design of nonlinear observer-based residual generators, as summarized in the review papers [2, 16]. It has been observed that only few of recent studies have dealt with residual generator and evaluation as well as decision making in an integrated way [1, 73, 72]. In addition, most of research efforts on the FD design issues have been addressed based on an implicit assumption that a stable residual generator can be constructed.