On steady-state based reduced-order observer design for interlaced nonlinear systems

International audienceThis paper proposes an analytical expression for a nonlinear mapping between steady-state solutions of certain types of nonlinear interconnected systems. This mapping is found using tools from the theory of output regulation for systems presented in lower-triangular or upper-triangular canonical forms. Next, this mapping helps design an excitation input and a corresponding reduced-order observer for interlaced systems, a combination of both upper-and lower-triangular subsystems. A proposed global observer is proved to be robust to additive disturbance and measurement noise by applying the Lyapunov function method. An example involving a massspring system demonstrates the efficiency of our approach

On observer design for a class of time-varying Persidskii systems based on the invariant manifold approach

International audienceIn this work, we consider the state estimation problem for a class of non-autonomous Persidskii systems. This paper presents conditions on the existence and stability of a nonlinear observer based on the invariant manifold approach. The conditions are formulated using Linear Matrix Equalities (LME) and Inequalities (LMI). Two interesting applications of the result are presented: a reduced-order observer (e.g., an observer for unmeasured states) and regression, both in linear and nonlinear settings. An example to demonstrate the efficiency of results is provided

On Computer Mouse Pointing Model Online Identification and Endpoint Prediction

International audienceThis paper proposes a new simplified pointing model as a feedback-based dynamical system, including both human and computer sides of the process. It takes into account the commutation between the correction and ballistic phases in pointing tasks. We use the mouse position increment signal from noisy experimental data to achieve our main objectives: to estimate the model parameters online and predict the task endpoint. Some estimation tools and validation results, applying linear regression techniques on the experimental data are presented. We also compare with a similar prediction algorithm to show the potential of our algorithm's implementation

Méthodes constructives pour l’estimation et le contrôle des systèmes dynamiques non linéaires avec applications à la modélisation en IHM

This work presents results for modeling, estimating, and controlling particular classes of nonlinear dynamical systems, focusing on simplifying the practical implementation of these methods. The thesis is divided intotwo main parts. The first part is motivated by applying control theory to human-computer interaction (HCI)problems, with the modeling and parameter identification for computer mouse navigation.Chapter 2 proposes a simplified pointing model as a dynamic feedback-based system incorporating humansand computers in a single loop. Then, the model parameter identification is used to develop an online endpointprediction algorithm. The mouse position increment signal from noisy experimental data is used for validation.The second part presents advances in the estimation and control of nonlinear systems using the notion of anattractive steady-state solution of the system driven by a signal generator, often used in model reduction oroutput regulation frameworks. This notion is applied to two different classes of nonlinear systems. For the firstclass of models studied in Chapter 3, a simple analytical expression of the steady-state is obtained as a solutionof linear matrix inequalities and equalities without any partial differential equations used in classical theory.The advantage of these results is demonstrated in two applications. The first application is the design of robustreduced-order observers and tracking control for the case of two interconnected systems of the same class. Thesecond application, presented in Chapter 3, is the design of robust reduced-order observers in both continuousand discrete time for time-varying systems, which also incorporates adaptive linear and nonlinear regression.Chapter 4 considers the second class of nonlinear systems based on a triangular structure, i.e., upper triangular,lower triangular, or a mix between the two. It is shown that, in this case, the nonlinear steady-state solutioncan be found analytically using techniques similar to backstepping or forwarding. The result is applied to thedesign of a robust reduced-order observer with the corresponding system input.Numerical simulations validate the applications of the second part of the thesis based on real-world dynamicmodels and benchmark examples: an anaerobic digestion bioreactor model, Chua networks, a two-mass springsystem, and a mechanical armCe travail présente des résultats de modélisation, d’estimation et contrôle de classes particulières de systèmes dynamiques non linéaires en se concentrant sur la simplification de l’implémentation pratique de cesméthodes. La thèse est divisée en deux parties principales. La première partie est motivée par l’application de lathéorie du contrôle aux problèmes d’interaction humain-machine (IHM), avec la modélisation et l’identificationdes paramètres pour la navigation de la souris d’ordinateur.Le chapitre 2 propose un modèle de pointage simplifié en tant que système dynamique basé sur la rétroactionincorporant l’humain et l’ordinateur dans une seule boucle. Ensuite, l’identification des paramètres du modèleest utilisée pour développer un algorithme de prédiction de pointage en ligne. Le signal d’incrémentation de laposition de la souris provenant de données expérimentales bruitées est utilisé pour la validation.La deuxième partie présente les avancées dans l’estimation et le contrôle des systèmes non linéaires en utilisantla notion de solution attractive en régime permanent du système piloté par un générateur de signaux, souventutilisée dans les cadres de réduction de modèle ou de régulation de sortie. Cette notion est appliquée à deuxclasses différentes de systèmes non linéaires. Pour la première classe de modèles étudiés dans le chapitre 3, uneexpression analytique simple de l’état stationnaire est obtenue comme une solution d’inégalités et d’égalitésmatricielles linéaires sans aucune implication des équations différentielles partielles utilisées dans la théorieclassique. L’avantage de ces résultats est démontrée dans deux applications. La première application est la conception d’observateurs robustes d’ordre réduite et la commande de suivi pour le cas de deux systèmes interconnectés de même classe. La deuxième application, présentée dans le chapitre 3, est la conception d’observateursrobustes d’ordre réduite, à la fois en temps continu et en temps discret, pour des systèmes variant dans le temps,qui intègre également la régression linéaire et non linéaire adaptative. Dans le chapitre 4, la deuxième classe desystèmes non linéaires est considérée, basée sur une structure triangulaire, c’est-à-dire triangulaire supérieure,triangulaire inférieure, ou d’un mélange entre les deux. Il est démontré que, dans ce cas, la solution non linéaireen régime permanent peut être trouvée analytiquement en utilisant des techniques similaires au backsteppingou au forwarding. Le résultat est appliqué à la conception d’un observateur robuste d’ordre réduit avec l’entréecorrespondante du système.Des simulations numériques valident les applications de la deuxième partie de la thèse sur la base de modèles dynamiques du monde réel et d’exemples de référence, à savoir un modèle de bioréacteur de digestionanaérobie, les réseaux de Chua, un système de ressort à deux masses et un bras mécanique

On robust observer design for a class of time-varying continuous-and discrete-time Persidskii systems

International audienceThis paper considers the state estimation problem for a class of non-autonomous nonlinear systems. We propose conditions on the existence and stability of a nonlinear observer based on the invariant manifold approach in both continuousand discrete-time scenarios. The requirements are formulated using Linear Matrix Equalities (LME) and Inequalities (LMI). We present two possible applications of the result, a reducedorder observer (e.g., an observer for unmeasured states) and regression in linear and nonlinear, continuous-and discretetime settings. With nonlinear regression being a sophisticated case, the parameter estimation problem for a particular output equation (when the fusion of linear and nonlinear sensors is weighted) is investigated. Two nonlinear examples demonstrating the efficiency of results are provided

On observer design for a class of Persidskii systems based on steady-state estimation

International audienceThis work aims to propose conditions for the existence of an observer for a particular class of nonlinear systems, presented as an interconnection of two Persidskii systems. First, we establish analytical expressions for steady-state solutions of an interconnected system. Next, a reduced-order observer for this system is designed, and the stability and boundedness of the error dynamics are proven. An academic example and an example considering Chua's circuits illustrate our results

On Computer Mouse Pointing Model Online Identification and Endpoint Prediction

International audienceThis paper proposes a new simplified pointing model as a feedback-based dynamical system, including both human and computer sides of the process. It takes into account the commutation between the correction and ballistic phases in pointing tasks. We use the mouse position increment signal from noisy experimental data to achieve our main objectives: to estimate the model parameters online and predict the task endpoint. Some estimation tools and validation results, applying linear regression techniques on the experimental data are presented. We also compare with a similar prediction algorithm to show the potential of our algorithm's implementation