Set-Membership Estimation Improvement Applying HOSM Differentiators

International audienceThis work is devoted to design of interval observers for a class of Linear-Parameter-Varying (LPV) systems. Applying High Order Sliding Mode (HOSM) techniques it is possible to decrease the initial level of uncertainty in the system, which leads to improvement of set-membership estimates generated by an interval observer. In addition, it is shown that HOSM techniques may relax the applicability conditions of the interval observer design methods. The efficiency of the proposed approach is demonstrated through computer simulations

State estimation for linear switched systems with unstable invariant zeros and unknown inputs

International audienceIn this paper the problem of continuous and discrete state estimation for a class of linear switched systems is studied. The class of systems under study can contain non-minimum phase zeros in some of their "operating modes". The conditions for exact reconstruction of the discrete state are given using structural properties of the switched system. The state-space is decomposed into the strongly observable part, the nonstrongly observable part and the unobservable part, to analyze the effect of the unknown inputs. A state observer based on high-order sliding-mode and Luenberger-like observers is proposed. For the case when the exact reconstruction of the state cannot be achieved, the ultimate bounds on the estimation errors are provided. The workability of the proposed method is illustrated by simulations

Robust Full-Order and Reduced- Order Observers for a Class of Uncertain Switched Systems

This paper deals with the problem of robust state estimation for a class of switched linear systems with unknown inputs under average dwell time (ADT) switching, where the switching of the observers is synchronous with that of the estimated system. First, based on the feasibility of an optimization problem with linear matrix inequality (LMI) constraint, a robust sliding-mode switched observer is developed such that the asymptotic state reconstruction is guaranteed even if the switched system is with unknown inputs. Second, a reduced-order switched system which avoids the influence of unknown inputs is constructed by the technique of state transformation, and a reduced-order switched observer is proposed to estimate the continuous states of the original switched system. Next, the conditions under which a full-order switched observer exists also guarantee the existence of a reduced-order switched observer. The convergence of the state estimate is proved to be exponential by appropriate Lyapunov analysis. Finally, the simulation results confirm the predicted performance and applicability by a simplified three-tank system

SWITCHED OBSERVERS FOR SWITCHED LINEAR SYSTEMS WITH UNKNOWN INPUTS

Two state observers are designed for some classes of switched linear systems with unknown inputs. The design of the proposed observers assumes that all switching subsystems fulfill a property of "strong detectability" that allows to implement suitable reduced-order unknown-input switched observers. The synthesis of the observers is based on the feasibility of a certain system of LMIs. Two main schemes are presented. For the case when the set of possible unknown-input distribution matrices are linearly dependent, an observer is suggested that guarantees the asymptotic state reconstruction without imposing any slow-switching dwell-time constraint about the sequence of the switching times. For the general case, the existence of a minimal average dwell-time for every switching sequence is assumed. By appropriate Lyapunov analysis, the convergence of the state estimate is proven to be exponential in both cases. Simulation results confirm the predicted performance

Contribution au développement des techniques ensemblistes pour l'estimation de l'état et des entrées des systèmes à temps continu (application à la détection de défauts)

Cette thèse traite du problème d'observation et d'estimation des variables caractéristiques des systèmes dynamiques. Il s agit d une problématique fondamentale qui est au cœur de nombreux domaines relavant des sciences de l'ingénieur. Les travaux sont conduits dans un contexte ensembliste. Les techniques développées pour l estimation de l état et des variables d entrées ont pour objectif final le contrôle de cohérence des systèmes non linéaires à temps continu. Une première approche conjugue les relations de parité et les différentiateurs à modes glissants pour l estimation des entrées d un système non linéaire. Les domaines des entrées compatibles avec les mesures sont alors reconstruits grâce à l analyse par intervalles et aux techniques de satisfaction de contraintes. Il est montré que la relaxation des contraintes de stabilité/coopérativité pour la construction d un observateur intervalle peut se faire grâce à des changements de base déterminés de différentes manières et pouvant être variants ou invariants dans le temps. Des simulations numériques illustrent les techniques proposées. Une application à un système aéronautique est également présentée à l aide d un jeu de données réelles.This thesis deals with the problem of a dynamical system observation and the estimation of its characteristic variables; the latter point constitutes the core element in many engineering science fields. The final aim is to build a general framework for integrity control and fault detection of such systems within a bounded error context. The developments offered herein make use of parity relations, sliding mode differentiators, interval observers and constraint satisfaction problems. Input reconstruction techniques are developed for a general class of nonlinear continuous-time systems. Domains are reconstructed for the input values which are consistent with the measurements using interval analysis and constraint satisfaction techniques. It is shown that time-varying or invariant coordinate changes may relax the applicability conditions (stability/cooperativity) of the interval observer design methods. Sliding mode differentiators were also used to enhance interval observer accuracy. The proposed approaches are illustrated through computer simulations and they have been applied to aircraft servo loop control surface for robust and early detection of abnormal positions.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF