# Search Results

###### Observer-based fault-tolerant control against sensor failures for fuzzy systems with time delays

## Observer-based fault-tolerant control against sensor failures for fuzzy systems with time delays

This paper addresses the problems of robust fault estimation and fault-tolerant control for Takagi-Sugeno (T-S) fuzzy systems with time delays and unknown sensor faults. A fuzzy augmented state and fault observer is designed to achieve the system state and sensor fault estimates simultaneously. Furthermore, based on the information of on-line fault estimates, an observer-based dynamic output feedback fault-tolerant controller is developed to compensate for the effect of faults by stabilizing the resulting closed-loop system. Sufficient conditions for the existence of both a state observer and a fault-tolerant controller are given in terms of linear matrix inequalities. A simulation example is given to illustrate the effectiveness of the proposed approach.

###### Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

## Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

###### Signed directed graph based modeling and its validation from process knowledge and process data

## Signed directed graph based modeling and its validation from process knowledge and process data

This paper is concerned with the fusion of information from process data and process connectivity and its subsequent use in fault diagnosis and process hazard assessment. The Signed Directed Graph (SDG), as a graphical model for capturing process topology and connectivity to show the causal relationships between process variables by material and information paths, has been widely used in root cause and hazard propagation analysis. An SDG is usually built based on process knowledge as described by piping and instrumentation diagrams. This is a complex and experience-dependent task, and therefore the resulting SDG should be validated by process data before being used for analysis. This paper introduces two validation methods. One is based on cross-correlation analysis of process data with assumed time delays, while the other is based on transfer entropy, where the correlation coefficient between two variables or the information transfer from one variable to another can be computed to validate the corresponding paths in SDGs. In addition to this, the relationship captured by data-based methods should also be validated by process knowledge to confirm its causality. This knowledge can be realized by checking the reachability or the influence of one variable on another based on the corresponding SDG which is the basis of causality. A case study of an industrial process is presented to illustrate the application of the proposed methods.

###### An Automatic Hybrid Method for Retinal Blood Vessel Extraction

## An Automatic Hybrid Method for Retinal Blood Vessel Extraction

The extraction of blood vessels from retinal images is an important and challenging task in medical analysis and diagnosis. This paper presents a novel hybrid automatic approach for the extraction of retinal image vessels. The method consists in the application of mathematical morphology and a fuzzy clustering algorithm followed by a purification procedure. In mathematical morphology, the retinal image is smoothed and strengthened so that the blood vessels are enhanced and the background information is suppressed. The fuzzy clustering algorithm is then employed to the previous enhanced image for segmentation. After the fuzzy segmentation, a purification procedure is used to reduce the weak edges and noise, and the final results of the blood vessels are consequently achieved. The performance of the proposed method is compared with some existing segmentation methods and hand-labeled segmentations. The approach has been tested on a series of retinal images, and experimental results show that our technique is promising and effective.

###### Reliability Modeling of Fault Tolerant Control Systems

## Reliability Modeling of Fault Tolerant Control Systems

This paper proposes a novel approach to reliability evaluation for active Fault Tolerant Control Systems (FTCSs). By introducing a reliability index based on the control performance and hard deadline, a semi-Markov process model is proposed to describe system operation for reliability evaluation. The degraded performance of FTCSs in the presence of imperfect Fault Detection and Isolation (FDI) is reflected by semi-Markov states. The semi-Markov kernel, the key parameter of the process, is determined by four probabilistic parameters based on the Markovian model of FTCSs. Computed from the transition probabilities of the semi-Markov process, the reliability index incorporates control objectives, hard deadline, and the effects of imperfect FDI, a suitable quantitative measure of the overall performance.

###### Existence of positive solutions of four-point BVPs for one-dimensional generalized Lane-Emden systems on whole line

## Abstract

This paper is concerned with four-point boundary value problems of the one-dimensional generalized Lane-Emden systems on whole lines. The Green’s functions *G*(*t, s*) for the problem *−*(*ρ*(*t*)*x′*(*t*))*′* = 0 with boundary conditions
*G*(*t, s*) ≥ 0 under some assumptions which actually generalize a corresponding result in [J. Math. Anal. Appl. 305 (2005) 253-276]. Sufficient conditions to guarantee the existence of positive solutions of this kind of models are established. Examples are given at the end of the paper.

###### New Formulae for the Decycling Number of Graphs

## Abstract

A set S of vertices of a graph G is called a decycling set if G−S is acyclic. The minimum order of a decycling set is called the decycling number of G, and denoted by ∇(G). Our results include: (a) For any graph G,, where T is taken over all the spanning trees of G and α(G − E(T)) is the independence number of the co-tree G − E(T). This formula implies that computing the decycling number of a graph G is equivalent to finding a spanning tree in G such that its co-tree has the largest independence number. Applying the formula, the lower bounds for the decycling number of some (dense) graphs may be obtained. (b) For any decycling set S of a k-regular graph G, where β(G) = |E(G)|−|V (G)|+1 and m(S) = c+|E(S)|−1, c and |E(S)| are, respectively, the number of components of G − S and the number of edges in G[S]. Hence S is a ∇-set if and only if m(S) is minimum, where∇-set denotes a decycling set containing exactly ∇(G) vertices of G. This provides a new way to locate ∇(G) for k-regular graphs G. (c) 4-regular graphs G with the decycling number are determined.

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Simultaneous Disturbance Compensation and H_{1}/H_{∞} Optimization In Fault Detection Of UAVs

## Abstract

This paper deals with the problem of robust fault detection (FD) for an unmanned aerial vehicle (UAV) flight control system (FCS). A nonlinear model to describe the UAV longitudinal motions is introduced, in which multiple sources of disturbances include wind effects, modeling errors and sensor noises are classified into groups. Then the FD problem is formulated as fault detection filter (FDF) design for a kind of nonlinear discrete time varying systems subject to multiple disturbances. In order to achieve robust FD performance against multiple disturbances, simultaneous disturbance compensation and H_{1}/H_{∞} optimization are carried out in designing the FDF. The optimality of the proposed FDF is shown in detail. Finally, both simulations and real flight data are applied to validate the proposed method. An improvement of FD performance is achieved compared with the conventional H_{1}/H_{∞}-FDF.

###### Supervisory fault tolerant control with integrated fault detection and isolation: A switched system approach

## Supervisory fault tolerant control with integrated fault detection and isolation: A switched system approach

This paper focuses on supervisory fault tolerant control design for a class of systems with faults ranging over a finite cover. The proposed framework is based on a switched system approach, and relies on a supervisory switching within a family of pre-computed candidate controllers without individual fault detection and isolation schemes. Each fault set can be accommodated either by one candidate controller or by a set of controllers under an appropriate switching law. Two aircraft examples are included to illustrate the efficiency of the proposed method.