Conference Paper

Trajectory computation of dynamic uncertain systems

Lab. d'Automatique de Grenoble, ENSIEG, St. Martin d'Heres, France
DOI: 10.1109/CDC.2003.1272787 Conference: Decision and Control, 2003. Proceedings. 42nd IEEE Conference on, Volume: 2
Source: IEEE Xplore


Dependability analysis of a dynamic system consists in establishing the proof that all its feasible trajectories stay inside a specified domain. In simple cases, an analytical study of its model is sufficient for obtaining requested results. But for more complex systems, set-membership approaches give attractive perspectives. The idea consists in computing enclosures containing all feasible trajectories according to imprecision on initial conditions and/or uncertainty on model parameters.

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    • "Methods which have already been proposed treat the case in which only system's response in DS is interval. Moreover, depending on model structure and identification semantic, parameter characterization procedure differs [4], [3], [1]. In this section, a generic approach is proposed for parameter characterization of any linear structure while both system's inputs and responses are characterized by intervals. "
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    • "V. Puig, A. Stancu and J. Quevedo are with Automatic Control Department, Campus de Terrassa, Technical University of Catalonia, Rambla Sant Nebridi, 10, 08222 Terrassa, Spain, e-mail: described on a computer [1]. Typically, this set is approximated by, for example, a box, a polytope or an ellipsoid. "
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    ABSTRACT: In this paper, set and trajectory-based approaches to interval observation of uncertain systems are presented and compared. The kind of uncertain systems considered are those systems described by a discrete linear time-invariant model with parameters bounded in intervals. The aim of this paper is to study the viability of using set-based approaches coming from the interval analysis community to solve the interval observation problem. Set-based approaches are appealing because of a lower computational complexity compared to trajectory-based approaches but they suffer from the wrapping effect and do not preserve uncertain parameter time-invariance. On the other hand, trajectory-based approaches are immune to these problems but their computational complexity is higher. However, these two families of approaches are equivalent when the observer satisfies the isotonicity condition, which give criteria to tune the observer gain. Finally, these two families of interval observation philosophies will be presented, analysed and compared by using them in an example.
    Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on; 01/2006
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    ABSTRACT: A strategy is proposed to model the complex industrial systems using linear time-varying system (LT V S). The proposed methodology is independent of model structure and the model may take any classic linear structure such as finite impulse response, input-output relation structures etc. To take into account the error between system and model due to model order reduction, variation of system behavior in time and perturbations, model's parameters are considered varying but bounded variables characterized by intervals. The output of this model is characterized by a function of the piecewise linear parameters which contains all possible system's re-sponses taking into account modeling error as well as the perturbations.
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