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Abstract

Hybrid systems serve as a powerful modeling paradigm for representing complex continuous controlled systems that exhibit discrete switches in their dynamics. The system and the models of the system are nondeterministic due to operation in uncertain environment. Bayesian belief update approaches to stochastic hybrid system state estimation face a blow up in the number of state estimates. Therefore, most popular techniques try to maintain an approximation of the true belief state by either sampling or maintaining a limited number of trajectories. These limitations can be avoided by using bounded intervals to represent the state uncertainty. This alternative leads to splitting the continuous state space into a finite set of possibly overlapping geometrical regions that together with the system modes form configurations of the hybrid system. As a consequence, the true system state can be captured by a finite number of hybrid configurations. A set of dedicated algorithms that can efficiently compute these configurations is detailed. Results are presented on two systems of the hybrid system literature.

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Abstract

Tracking the evolution of hybrid systems from partial observations means tracking the continuously-valued state evolution and the interleaved discrete mode changes. Existing estimation schemes suffer from the exponential blow up of the number of hypotheses to be tracked and fall into suboptimal methods. On the other hand, hybrid parity-based mode estimation ignores the continuous state. This paper proposes a novel scheme that uses this latter as a mode focusing procedure and then applies hybrid estimation on the resulting reduced number of hypotheses. The advantages of the mixed method are on both sides: it boosts the mode identification time and the convergence of continuous state estimation.

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Thales Alenia Space is developing a new generation of satellites dedicated to flexible and autonomous Space missions. It relies on a hierarchical component based architecture. Hierarchical layers are devoted to manage on one hand, different kind of knowledge from abstract (goal of the mission) to real (units, equipments), and on the other hand, different reaction times, from orbit's order of magnitude (planning activities) to real time (thrusting, sensing). Components are most of the time related to functional chains covering pure discrete behavior (battery management) to pure continuous one (Guidance, Navigation and Control), or mix of both leading to hybrid modeling. Due to the vast range of models (discrete, continuous, hybrid  real time, no time constraint  teleological, functional, structural, behavioral), defining a FDIR (Fault Detection, Isolation and Recovery) strategy is a challenge. Solutions have been defined by making collaborate different diagnosis techniques (analytical redundancy, consistency based approach, model checking and Hinf estimator) from several origins, locally in each component. Abstraction of the local diagnosis results is translated at satellite level under the form of events and managed by a discrete automaton based formalism. Focus of the paper is put on the knowledge's modeling from the different layers of the architecture, the diagnosis technique in relation with the different kinds of components and the description of the hierarchical diagnosis solution.

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On-line diagnosis must accommodate the existing sensoring capabilities of a system, which often results in limited diagnosability. However, in the context of hybrid systems, although faults may not be always discriminable, there are generally operating modes of the system in which they are. Active diagnosis relies on applying specific inputs to the system so as to exhibit additional symptoms that help refining the diagnosis. The idea of this paper is to use hybrid systems diagnosability analysis to drive the system towards modes with increased diagnosability with respect to safety considerations. The active diagnosis problem is formulated as a conditional planning problem. From an ambiguous state returned by the diagnoser, the plan defines how to find a controllable paths leading to a non ambiguous state. The decision about the active diagnosis actions is guided by the observable response of the system.

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This paper discusses the use of interval models (LTI models with interval parameters) to represent the dynamics of complex systems in fault detection. Fault detection methods using interval models, such as interval observers and parity equations, will be reviewed and compared. Tools used to implement such algorithms will also be presented. Finally, an overview of the real domain application of these methods and their experimental performance will end the paper.

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The issue of residual generation using structural analysis has been studied by several authors. Structural analysis does not permit to generate the analytical expressions of residuals since the model of the system is abstracted by its structure. However, it determines the set of constraints from which residuals can be generated and it provides the computation sequence to be used. This paper presents and compares four recently proposed algorithms that solve this problem.