Consider a given dynamical system, described by ẋ = f(x) (wheref is a nonlinear function) and [x0] a subset ofR. We present an algorithm, based on interval analysis, able to show that there exists a unique equilibrium statex∞ ∈ [x0] which is asymptotically stable. The effective method also provides a set[x] (subset of[x0]) which is included in the attraction domain of x∞.

Ieee transactions on automatic control

Annual Reviews in Control

Fault diagnosis is crucial for ensuring the safe operation of complex engineering systems. Many present-day systems combine physical and computational processes, and are best modeled as hybrid systems, where the dynamic behavior combines continuous evolution interspersed with discrete configuration changes. Due to the complexity of such modern engineering systems, formal methods are required for reliable and correct design, analysis, and implementation of hybrid system diagnosers. 
This dissertation presents a systematic, model-based approach to event-based diagnosis of hybrid systems based on qualitative abstractions of deviations from nominal behavior. The primary contributions of this work center on (i) incorporating relative measurement orderings into fault isolation for continuous and hybrid systems, which describe predicted temporal orderings of measurement deviations, (ii) providing algorithms for event-based diagnosis of single and multiple faults, (iii) developing an integrated framework for diagnosis of parametric, sensor, and discrete, i.e., switching faults in hybrid systems, and (iv) developing and implementing an efficient event-based diagnosis framework for continuous and hybrid systems that enables automatic design of event-based diagnosers and establishes notions of diagnosability for continuous and hybrid systems. 
The effectiveness of the approach is demonstrated on two practical systems. First, the single fault diagnosis method for continuous systems is applied in a distributed fashion to formations of mobile robots. The results include a formal diagnosability analysis, scalability results, and experiments performed on a formation of robots. Second, the approach developed for hybrid systems diagnosis is applied to the Advanced Diagnostics and Prognostics Testbed, which is a complex electrical distribution system for spacecraft and aircraft applications. The results focus on a subset of the testbed, and include a diagnosability analysis, experiments from the actual testbed, and detailed simulation experiments that examine the performance of the diagnosis algorithms for different fault magnitudes and noise levels.

A qualitative event-based approach to fault diagnosis of hybrid systems

Detectability of discrete event systems, defined as the ability to determine the current and subsequent states, is very important in diagnosis, control, and many other applications. So far only detectability of non-networked discrete event systems has been defined and investigated. Non-networked discrete event systems assume that all the communications are reliable and instantaneous without any delays or losses. This assumption is often violated in networked systems. In this paper, we study detectability for networked discrete event systems. We investigate the impact of communication delays and losses on detectability. We define two classes of detectabilities: network detectability for determining the state of a networked discrete event systems and network D-detectability for distinguishing certain pairs of states of the systems. Necessary and sufficient conditions for network detectability and network D-detectability are derived. Methods to check network detectability and network D-detectability are also developed. Examples are given to illustrate the results.

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Detectability of networked discrete event systems

Self-healing software is one of the challenges issues for IST research. The WS-Diamond project aims at making a step in this direction by developing a framework for self-healing Web Services. In this paper, we present the overall goals of the project, namely: i) defining an operational framework for self-healing service execution of conversationally complex Web Services, where monitoring, detection and diagnosis of anomalous situations, due to functional or non-functional errors (e.g., Quality of Service), are carried on and repair/reconfiguration is performed, thus guaranteeing reliability and availability of Web Services; and ii) defining a methodology and tools for service design that guarantee effective and efficient diagnosability/reparability during execution. Then the paper illustrates an application scenario showing principles of model-based diagnosis, and composed Web Service repair scenarios. An overall presentation of the architecture is given.

WS-DIAMOND an approach to Web services diagnosability, Monitoring and diagnosis

This paper is concerned with diagnosability analysis, which proves a requisite for several tasks during the system 's life cycle. The Model-Based Diagnosis (MBD) community has developed specific approaches for Continuous Systems (CS) and for Discrete Event Systems (DES) in two distinct and parallel tracks. In this paper, the correspondences between the concepts used in CS and DES approaches are clarified and it is shown that the diagnosability problem can be brought back to the same formulation using the concept of signatures. These results bridges CS and DES diagnosability and open perspectives for hybrid model based diagnosis.

Comparing diagnosability in continuous and discrete-events systems

In this paper we consider the diagnosis of intermittent and permanent faults in discrete event systems. We present a logic based modeling approach associated with conditional preferences in order to produce a single diagnosis at each time step. Like all incomplete diagnosis approaches, ours is subject to deadlocks between the system and its diagnoser. In this paper, we address the detection of such deadlocks at design time with the rich semantic model-checker ELECTRUM.

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Preferential Discrete Model-based Diagnosis for Intermittent and Permanent Faults

This paper provides a new definition of diagnosability, that allows one to check the diagnosability of any set of system states, and by extension of properties that depend on the system state. The existing definitions and approaches for checking diagnosability apply to faults or sets of faults, and comparison shows that the new definition generalizes the existing ones. This new definition is applied to repair preconditions, and an example shows how this brings complementary information compared to classical fault diagnosability.

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Another Point of View on Diagnosability

We address the problem of intermittent fault diagnosis as an instance of discrete signal estimation, in the context of fault management in autonomous systems and autonomous vehicles. We propose an estimation approach based on constrained optimization using conditional preference theories. We show that in some cases, our estimator can fail to find an estimation for the system. We provide a way to detect and eliminate these cases at design time.

/pdf/intermittent-fault-diagnosis-as-discrete-signal-estimation-jjfogp8r61.pdf

Intermittent Fault Diagnosis as Discrete Signal Estimation: Trackability analysis

In this paper we deal with the problem of model-based diagnosability analysis for Web Services. The goal of diagnosability analysis is to determine whether the information one can observe during service execution is sufficient to precisely locate (by means of diagnostic reasoning) the source of the problem. The major difficulty in the context of Web Services is that models are distributed and no single entity has a global view of the complete model. In the paper we propose an approach that computes diagnosability for the decentralized diagnostic framework, described in [1], based on a Supervisor coordinating several Local Diagnosers. We also show that diagnosability analysis can be performed without requiring the Local Diagnosers different operations than those needed for diagnosis. The proposed approach is incremental: each fault is first analyzed independently of the occurrence of other faults, then the results are used to analyze combinations of behavioral modes, avoiding in most cases an exhaustive check of all combinations.

Xavier Pucel

Papers

Comparing diagnosability in continuous and discrete-events systems

Preferential Discrete Model-based Diagnosis for Intermittent and Permanent Faults

Another Point of View on Diagnosability

Intermittent Fault Diagnosis as Discrete Signal Estimation: Trackability analysis

Model-Based Diagnosability Analysis for Web Services