Model-based prognosis using an explicit degradation model and Inverse FORM for uncertainty propagation

International audienceIn this paper, an analytical method issued from the field of reliability analysis is used for prognosis. The inverse first-order reliability method (Inverse FORM) is an uncertainty propagation method that can be adapted to remaining useful life (RUL) calculation. An extended Kalman filter (EKF) is first applied to estimate the current degradation state of the system, then the Inverse FORM allows to compute the probability density function (pdf) of the RUL. In the proposed Inverse FORM methodology, an analytical or numerical solution to the differential equation that describes the evolution of the system degradation is required to calculate the RUL model. In this work, the method is applied to a Paris fatigue crack growth model, and then compared to filter-based methods such as EKF and particle filter using performance evaluation metrics (precision, accuracy and timeliness). The main advantage of the Inverse FORM is its ability to compute the pdf of the RUL at a lower computational cost

Interval observer design for unknown input estimation of linear time-invariant discrete-time systems

International audienceIn this paper, the problem of joint state and unknown input estimation for linear time-invariant (LTI) discrete-time systems using interval observer is addressed. This problem has already been studied in the context of continuous-time systems. To the best of our knowledge, unknown input interval-based estimation for discrete-time systems has not been considered in the litterature. Assuming that the measurement noise and disturbances are bounded, lower and upper bounds are first computed for the unmeasured state and then for the unknown inputs. The results obtained with a numerical example highlight the efficiency of the method

Interval Observer Design for Actuator Fault Estimation of Linear Parameter-Varying Systems

International audienceThis work is devoted to fault estimation of discrete-time Linear Parameter-Varying (LPV) systems subject to actuator additive faults and external disturbances. Under the assumption that the measurement noises and the disturbances are unknown but bounded, an interval observer is designed, based on decoupling the fault effect, to compute a lower and upper bounds for the unmeasured state and the faults. Stability conditions are expressed in terms of matrices inequalities. A case study is used to illustrate the effectiveness of the proposed approach

Interval observers design for continuous-time linear switched systems

International audienceThis paper is devoted to investigate interval observers design for linear switched systems. The considered systems are subject to disturbances which are assumed to be unknown but bounded. First, observer gains are computed to ensure the stability of the estimation error. Then, under some changes of coordinates an interval observer is designed. Efficiency of the proposed method is demonstrated through a numerical example

Fractional interval observers and initialization of fractional systems

International audienceIn this paper an interval observer is synthesized for fractional linear systems with additive noise and disturbances. The contribution of system whole past to future output is taken into account as an initialization function. Provided the initialization function is upper and lower bounded, it is shown in this paper that the fractional interval observer (FIO) allows to bound pseudo-state free responses by an upper and a lower trajectory. In case interval observers cannot be synthesized straightforwardly, so as to obtain a stable and non-negative estimation error, it is shown that a change of coordinates allows to overcome this problem. The proposed methodology allows to bound fractional systems trajectories when the whole past is unknown but can be bounded. Finally, a numerical example is given to show the effectiveness of the proposed methods on the initialization of fractional linear systems

A convexity approach to dynamic output feedback robust MPC for LPV systems with bounded disturbances

International audienceA convexity approach to dynamic output feedback robust model predictive control (OFRMPC) is proposed for linear parameter varying (LPV) systems with bounded disturbances. At each sampling time, the model parameters and disturbances are assumed to be unknown but bounded within pre-specified convex sets. Robust stability conditions on the augmented closed-loop system are derived using the techniques of robust positively invariant (RPI) set and the S-procedure. A convexity method reformulates the non-convex bilinear matrix inequalities (BMIs) problem as a convex optimization one such that the on-line computational burden is significantly reduced. The on-line optimized dynamic output feedback controller parameters steer the augmented states to converge within RPI sets and recursive feasibility of the optimization problem is guaranteed. Furthermore, bounds of the estimation error set are refreshed by updating the shape matrix of the future ellipsoidal estimation error set. The dynamic OFRMPC approach guarantees that the disturbance-free augmented closed-loop system (without consideration of disturbances) converges to the origin. In addition, when the system is subject to bounded disturbances, the augmented closed-loop system converges to a neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the approach

Interval Estimation Methods for Discrete-Time Linear Time-Invariant Systems

International audienc

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

Design of Interval Observers for Estimation and Stabilization of Discrete-Time LPV Systems

International audienceThis work is devoted to interval observers design for discrete-time Linear Parameter-Varying (LPV) systems under the assumption that the vector of scheduling parameters is not available for measurements. Two problems are considered: a pure estimation problem and an output stabilizing feedback design problem where the stability conditions are expressed in terms of Linear Matrix Inequalities (LMIs). The efficiency of the proposed approach is demonstrated through computer simulations

Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

Webpage: https://eleurent.github.io/interval-prediction/International audienceThe problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles