Nonlinear bounded-error state estimation of continuous-time systems

International audienceThis paper presents a first study on the application of interval analysis and consistency techniques to state estimation of continuous-time systems described by nonlinear ordinary differential equations. The approach is presented in a bounded-error context and the resulting methodology is illustrated on an example

Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

The 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.Comment: 6 pages, CDC 2019. Website: https://eleurent.github.io/interval-prediction

Propagation garantie de contraintes ODE par morceaux pour l'optimisation globale

Prix du jeune chercheurNational audienceL'objectif est de proposer un algorithme d'optimisation garantie d'un problème de dimensionnement dynamique et multi-physique. Le caractère dynamique est modélisé par des contraintes ODE (équations différentielles). Nous traitons le problème particulier pour lequel les fonctions décrivant le système ODE sont des contraintes définies par morceaux permettant de traduire des changements de comportement induits par l'état du système. C'est un problème difficile de part la nature des variables (paramétriques et d'états) et du type de contraintes (algébriques et fonctionnelles, non-linéaires et non-convexes). Nous proposons d'utiliser des approches déterministes d'optimisation globale. Nous développons des algorithmes de type Branch & Bound à base de calcul d'intervalle. Dans la littérature, ces algorithmes sont largement utilisés pour résoudre des problèmes statiques mais aussi dynamiques. Notre contribution porte sur la résolution garantie des ODE définies par morceaux. Nous proposons un ensemble de méthodes de propagation garantie des contraintes ODE par morceaux dans un algorithme de Branch & Bound à base d'intervalle. Nous adaptons pour cela l'approche classique utilisant (1) l'opérateur de Picard-Lindelöf pour déterminer un encadrement global de la solution sur un intervalle de temps, (2) le modèle de Taylor pour la contraction du domaine de la solution et enfin (3) les techniques de propagation de contraintes afin de guider la résolution.</p

Non Parametric Distributed Inference in Sensor Networks Using Box Particles Messages

This paper deals with the problem of inference in distributed systems where the probability model is stored in a distributed fashion. Graphical models provide powerful tools for modeling this kind of problems. Inspired by the box particle filter which combines interval analysis with particle filtering to solve temporal inference problems, this paper introduces a belief propagation-like message-passing algorithm that uses bounded error methods to solve the inference problem defined on an arbitrary graphical model. We show the theoretic derivation of the novel algorithm and we test its performance on the problem of calibration in wireless sensor networks. That is the positioning of a number of randomly deployed sensors, according to some reference defined by a set of anchor nodes for which the positions are known a priori. The new algorithm, while achieving a better or similar performance, offers impressive reduction of the information circulating in the network and the needed computation times

A multiple model adaptive architecture for the state estimation in discrete-time uncertain LPV systems

@2017 Personal use of these materials is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating news collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThis paper addresses the problem of multiple model adaptive estimation (MMAE) for discrete-time linear parameter varying (LPV) systems that are affected by parametric uncertainty. The MMAE system relies on a finite number of local observers, each designed using a selected model (SM) from the set of possible plant models. Each local observer is an LPV Kalman filter, obtained as a linear combination of linear time invariant (LTI) Kalman filters. It is shown that if some suitable distinguishability conditions are fulfilled, the MMAE will identify the SM corresponding to the local observer with smallest output prediction error energy. The convergence of the unknown parameter estimation, and its relation with the varying parameters, are discussed. Simulation results illustrate the application of the proposed method.Peer ReviewedPostprint (author's final draft

Monte Carlo Set-Membership Filtering for Nonlinear Dynamic Systems

This chapter considers the nonlinear filtering problem involving noises that are unknown and bounded. We propose a new filtering method via set-membership theory and boundary sampling technique to determine a state estimation ellipsoid. In order to guarantee the online usage, the nonlinear dynamics are linearized about the current estimate, and the remainder term is then bounded by an optimization ellipsoid, which can be described as the solution of a semi-infinite optimization problem. It is an analytically intractable problem for general nonlinear dynamic systems. Nevertheless, for a typical nonlinear dynamic system in target tracking, some certain regular properties for the remainder are analytically derived; then, we use a randomized method to approximate the semi-infinite optimization problem efficiently. Moreover, for some quadratic nonlinear dynamic systems, the semi-infinite optimization problem is equivalent to solving a semi-definite program problem. Finally, the set-membership prediction and measurement update are derived based on the recent optimization method and the online bounding ellipsoid of the remainder other than a priori bound. Numerical example shows that the proposed method performs better than the extended set-membership filter, especially in the situation of the larger noise