Some control observation problems and their differential algebraic partial solutions

International audienceObservation problems in control systems literature generally refer to problems of estimation of state variables (or identification of model parameters) from two sources of information: dynamic models of systems consisting in first order differential equations relating all system quantities, and online measurements of some of these quantities. For nonlinear systems the classical approach stems from the work of R. E. Kalman on the distinguishability of state space points given the knowledge of time histories of the output and input. In the differential algebraic approach observability is rather viewed as the ability to recover trajectories. This approach turns out to be a particularly suitable language to describe observability and related questions as structural properties of control systems. The present paper is an update on the latter approach initiated in the late eighties and early nineties by J. F. Pommaret, M. Fliess, S. T. Glad and the author

Some control observation problems and their differential algebraic partial solutions

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On the Relation between Pommaret and Janet Bases

In this paper the relation between Pommaret and Janet bases of polynomial ideals is studied. It is proved that if an ideal has a finite Pommaret basis then the latter is a minimal Janet basis. An improved version of the related algorithm for computation of Janet bases, initially designed by Zharkov, is described. For an ideal with a finite Pommaret basis, the algorithm computes this basis. Otherwise, the algorithm computes a Janet basis which need not be minimal. The obtained results are generalized to linear differential ideals.Comment: 15 pages. LaTeX, uses the Springer file lncse.cls. Submitted to CASC'2000, the Third International Workshop on Computer Algebra in Scientific Computing, October 5-9, Samarkand, Uzbekista

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Algorithmic Methods for Lie Pseudogroups

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