Functional sets with typed symbols: Framework and mixed Polynotopes for hybrid nonlinear reachability and filtering

Verification and synthesis of Cyber-Physical Systems (CPS) are challenging and still raise numerous issues so far. In this paper, an original framework with mixed sets defined as function images of symbol type domains is first proposed. Syntax and semantics are explicitly distinguished. Then, both continuous (interval) and discrete (signed, boolean) symbol types are used to model dependencies through linear and polynomial functions, so leading to mixed zonotopic and polynotopic sets. Polynotopes extend sparse polynomial zonotopes with typed symbols. Polynotopes can both propagate a mixed encoding of intervals and describe the behavior of logic gates. A functional completeness result is given, as well as an inclusion method for elementary nonlinear and switching functions. A Polynotopic Kalman Filter (PKF) is then proposed as a hybrid nonlinear extension of Zonotopic Kalman Filters (ZKF). Bridges with a stochastic uncertainty paradigm are outlined. Finally, several discrete, continuous and hybrid numerical examples including comparisons illustrate the effectiveness of the theoretical results.Comment: 21 pages, 8 figure

Diario oficial del Ministerio de Marina: Año LI Número 167 - 1938 julio 6

Trabajo presentado a la 36th Chinese Control Conference (CCC), celebrada en Dalian (China) del 26 al 28 de julio de 2017.This paper proposes a robust fault detection observer based on zonotopes for discrete-time uncertain systems with sensor faults and unknown but bounded uncertainties. The main advantage of this method is that the observer gain of the robust zonotopic observer is designed to be robust against bounded uncertainties while being sensitive to faults. In order to detect sensor faults with low magnitudes, the fault sensitivity is taken into account by measuring the H_ performance. The designed zonotopic observer gain can be obtained by solving an optimization problem including a sequence of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to demonstrate the proposed method.This work has been partially funded by the Spanish Government and FEDER through the projects CICYT ECOCIS (ref. DPI2013-48243-C2-1-R), CICYT DEOCS (ref. DPI2016-76493-C3-3-R), CICYT HARCRICS (ref. DPI2014-58104-R) and by National Natural Science Foundation of China (Grant No. 61273162, 61403104).Peer Reviewe

Zonotopic unknown input observer of discrete-time descriptor systems for state estimation and robust fault detection

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper studies a set-based unknown input observer based on zonotopes for discrete-time descriptor systems affected by uncertainties with application to state estimation and robust fault detection. In this paper, two types of uncertainties are considered: (i) disturbances and noise both bounded by zonotopes; (ii) unknown inputs that can be decoupled. In terms of different applications, the observer gain for state estimation is designed to minimize the effects of unknown-but-bounded disturbances and noise as well as state estimation errors. On the other hand, for robust fault detection, in addition to attenuating uncertainties, the designed observer gain is also expected to be sensitive to faults. To achieve this goal, we propose an iterative algorithm to design the fault detection gain. Finally, some illustrative results in an application example show the effectiveness of the proposed algorithms.Peer ReviewedPostprint (author's final draft

FD-ZKF: A Zonotopic Kalman Filter optimizing fault detection rather than state estimation

Enhancing the sensitivity to faults with respect to disturbances, rather than optimizing the precision of the state estimation using Kalman Filters (KF) is the subject of this paper. The stochastic paradigm (KF) is based on minimizing the trace of the state estimation error covariance. In the context of the bounded-error paradigm using Zonotopic Kalman Filters (ZKF), this is analog to minimize the covariation trace. From this analogy and keeping a similar observer-based structure as in ZKF, a criterion jointly inspired by set-membership approaches and approximate decoupling techniques coming from parity-space residual generation is proposed. Its on-line maximization provides an optimal time-varying observer gain leading to the so-called FD-ZKF filter that allows enhancing the fault detection properties. The characterization of minimum detectable fault magnitude is done based on a sensitivity analysis. The effect of the uncertainty is addressed using a set-membership approach and a zonotopic representation reducing set operations to simple matrix calculations. A case study based on a quadruple-tank system is used both to illustrate and compare the effectiveness of the results obtained from the FD-ZKF approach compared to a pure ZKF approachPostprint (author's final draft

Robust fault estimation based on zonotopic Kalman filter for discrete-time descriptor systems

This paper proposes a set-based approach for robust fault estimation of discrete-time descriptor systems. The considered descriptor systems are subject to unknown-but-bounded uncertainties (state disturbances and measurement noise) in predefined zonotopes and additive actuator faults. The zonotopic fault estimation filter for descriptor systems is built based on fault detectability indices and matrix to estimate fault magnitude in a deterministic set. The zonotopic fault estimation filter gain is designed in a parameterized form. Within a set-based framework, following the zonotopic Kalman filter, the optimal filter gain is computed by minimizing the size of the corresponding zonotopes to achieve robustness against uncertainties and the identification of occurred actuator faults. Besides, boundedness of the proposed zonotopic fault estimation is analyzed, which proves that the size of obtained fault estimation bounds is not growing in time. Finally, the simulation results with two application examples are provided to show the effectiveness of the proposed approach.Peer ReviewedPostprint (author's final draft

Méthodes d'aide à la décision pour la détection et la localisation de défauts dans les entraînements électriques

LE DIAGNOSTIC DES ENTRAINEMENTS ELECTRIQUES PERMET D'ENVISAGER UNE AMELIORATION DE LA DISPONIBILITE ET DE LA POLITIQUE DE MAINTENANCE DANS LES SYSTEMES DE PRODUCTION. L'OBJECTIF DE LA THESE EST DE DETECTER ET DE LOCALISER EN LIGNE DES DEFAUTS SURVENANT DANS UN ENTRAINEMENT ELECTRIQUE. UNE ANALYSE CAUSALE SERT TOUT D'ABORD A DECOMPOSER SYSTEMATIQUEMENT UN MODELE GLOBAL EN MODELES LOCAUX, INDEPENDAMMENT DE LA NATURE DU MODELE. UN PREMIER JEU DE RESIDUS (INDICATEURS DE DEFAUT) EST AINSI OBTENU. DES METHODES CLASSIQUES DE GENERATION DE RESIDUS, FONDEES SUR DES MODELES NUMERIQUES, SONT EGALEMENT UTILISEES : OBSERVATEURS, EQUATIONS DE PARITE. DANS CE CADRE, DES TECHNIQUES DE DECOUPLAGE PARFAIT ET APPROXIMATIF SONT APPLIQUEES. UNE ETUDE DE SENSIBILITE DES RESIDUS EST MENEE. CERTAINES DE CES METHODES SONT APPLIQUEES A UNE MACHINE A COURANT CONTINU ET D'AUTRES LE SONT A UNE MACHINE ASYNCHRONE. DES OBSERVATEURS ADAPTATIFS REALISANT DES TESTS DE MODELES SONT UTILISES POUR LE DIAGNOSTIC D'UNE MACHINE ASYNCHRONE. L'ETAPE DE DECISION (CLASSIFICATION) REPOSE SUR UN ENSEMBLE DE CRITERES LIES AUX RESIDUS. LA DECISION INDIQUE QUELLES CLASSES DE DEFAUTS SONT LES PLUS COHERENTES AVEC LES OBSERVATIONS DISPONIBLES. LES SENSIBILITES DES RESIDUS PEUVENT SERVIR A SELECTIONNER LES PLUS PERTINENTS (AU SENS D'UN CRITERE DE PERFORMANCE) SOIT PAR L'APPLICATION DE REGLES ELEMENTAIRES, SOIT PAR UNE OPTIMISATION (ALGORITHME GENETIQUE). LES ORDRES DE GRANDEUR RELATIFS DES RESIDUS FOURNISSENT EGALEMENT UNE INFORMATION PLUS RICHE QUE CELLE D'UNE TABLE DE SIGNATURE BOOLEENNE ET PERMETTENT D'AMELIORER AINSI LES PERFORMANCES DE LA LOCALISATION.non disponibl