Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs

Abstract : In this paper, we extend the modulating functions method to estimate the state and the unknown input of a linear time-varying system defined by a linear differential equation. We first estimate the unknown input by taking a truncated Jacobi orthogonal series expansion with unknown coefficients which can be estimated by the modulating functions method. Then, we estimate the state by using extended modulating functions and the estimated input. Both input and state estimators are given by exact integral formulae involving modulating functions and the noisy output. Hence, estimations at different instants can be non-asymptotically obtained using a sliding window of finite length. Numerical results are given to show the accuracy and the robustness of the proposed estimators against corrupting noises.
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Da-Yan Liu, Taous-Meriem Laleg-Kirati, Wilfrid Perruquetti, Olivier Gibaru. Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs. the 19th World Congress of the International Federation of Automatic Control 2014, Aug 2014, Cape Town, South Africa. ⟨hal-00968974⟩

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