No description available.

This thesis presents a method for managing periods of communication loss between multiple spacecraft in formation flying (MSFF), and analyzes the effects of this method on the stability of the formation keeping control algorithm. The controller of interest in this work in an adaptive nonlinear controller, where synchronization is also incorporated to force the position tracking errors to converge to zero at the same rate. The communication loss compensation technique proposed in this thesis is to use the previously communicated data in lieu of the lost data, which is an effective and computationally-efficient technique that is advantageous for small satellites. The performance parameter of interest in this research is the maximum rate of communication loss that an MSFF system can withstand before going unstable, and this is analyzed theoretically and through simulations. Finally, experiments involving multiple robots in formation with communication loss are conducted, and the results are presented.

This thesis presents a method for managing periods of communication loss between multiple spacecraft in formation flying (MSFF), and analyzes the effects of this method on the stability of the formation keeping control algorithm. The controller of interest in this work in an adaptive nonlinear controller, where synchronization is also incorporated to force the position tracking errors to converge to zero at the same rate. The communication loss compensation technique proposed in this thesis is to use the previously communicated data in lieu of the lost data, which is an effective and computationally-efficient technique that is advantageous for small satellites. The performance parameter of interest in this research is the maximum rate of communication loss that an MSFF system can withstand before going unstable, and this is analyzed theoretically and through simulations. Finally, experiments involving multiple robots in formation with communication loss are conducted, and the results are presented.

In the first part of this thesis, motivated by the development of deep brain stimulation for Parkinson's disease, we consider the problem of reducing the synchrony of a neuronal population via a closed-loop electrical stimulation. This, under the constraints that only the mean membrane voltage of the ensemble is measured and that only one stimulation signal is available (mean-field feedback). The neuronal population is modeled as a network of interconnected Landau-Stuart oscillators controlled by a linear single-input single-output feedback device. Based on the associated phase dynamics, we analyze existence and robustness of phase-locked solutions, modeling the pathological state, and derive necessary conditions for an effective desynchronization via mean-field feedback. Sufficient conditions are then derived for two control objectives: neuronal inhibition and desynchronization. Our analysis suggests that, depending on the strength of feedback gain, a proportional mean-field feedback can either block the collective oscillation (neuronal inhibition) or desynchronize the ensemble.In the second part, we explore two possible ways to analyze related problems on more biologically sound models. In the first, the neuronal population is modeled as the interconnection of nonlinear input-output operators and neuronal synchronization is analyzed within a recently developed input-output approach. In the second, excitability and synchronizability properties of neurons are analyzed via the underlying bifurcations. Based on the theory of normal forms, a novel reduced model is derived to capture the behavior of a large class of neurons remaining unexplained in other existing reduced models.

Dans la première partie de cette thèse, motivée par le développement de la stimulation cérébrale profonde comme traitement des symptômes moteurs de la maladie de Parkinson, nous considérons le problème de réduire la synchronie d'une population neuronale par l'intermédiaire d'une stimulation électrique en boucle fermée. Ceci, sous les contraintes que seule la tension de membrane moyenne de l'ensemble est mesurée et qu'un seul signal de stimulation est disponible (retour du champ moyen). La population neuronale est modélisée comme un réseau d'oscillateurs de Landau-Stuart contrôlé par un dispositif de rétroaction mono-entrée mono-sortie. En nous basant sur la dynamique de phase associée au système, nous analysons l'existence et la robustesse des solutions à verrouillage de phase, modélisant l'état pathologique, et nous dérivons des conditions nécessaires à une désynchronisation efficace par retour du champ moyen. Des conditions suffisantes sont ensuite dérivées pour deux objectifs de contrôle: l'inhibition et la désynchronisation neuronale. Notre analyse suggère que, en fonction de l'intensité du gain de rétroaction, le retour du champ moyen peut soit bloquer l'oscillation collective (inhibition neuronale) soit désynchroniser l'ensemble.Dans la deuxième partie, nous explorons deux voies possibles pour l'analyse des problèmes similaires dans des modèles biologiquement plus plausibles. Dans la première, la population est modélisée comme une interconnexion d'opérateurs entrée-sortie non-linéaires et la synchronisation neuronale est analysée en s'appuyant sur une approche entré-sortie récemment développée. Dans la seconde, les propriétés d'excitabilité et de synchronisabilité des neurones sont analysées via les bifurcations sous-jacentes. En nous basant sur la théorie des formes normales, un nouveau modèle réduit est dérivé pour capturer les comportements d'une grande classe de neurones qui restent inexpliqués dans les modèles réduits existants. / In the first part of this thesis, motivated by the development of deep brain stimulation for Parkinson's disease, we consider the problem of reducing the synchrony of a neuronal population via a closed-loop electrical stimulation. This, under the constraints that only the mean membrane voltage of the ensemble is measured and that only one stimulation signal is available (mean-field feedback). The neuronal population is modeled as a network of interconnected Landau-Stuart oscillators controlled by a linear single-input single-output feedback device. Based on the associated phase dynamics, we analyze existence and robustness of phase-locked solutions, modeling the pathological state, and derive necessary conditions for an effective desynchronization via mean-field feedback. Sufficient conditions are then derived for two control objectives: neuronal inhibition and desynchronization. Our analysis suggests that, depending on the strength of feedback gain, a proportional mean-field feedback can either block the collective oscillation (neuronal inhibition) or desynchronize the ensemble.In the second part, we explore two possible ways to analyze related problems on more biologically sound models. In the first, the neuronal population is modeled as the interconnection of nonlinear input-output operators and neuronal synchronization is analyzed within a recently developed input-output approach. In the second, excitability and synchronizability properties of neurons are analyzed via the underlying bifurcations. Based on the theory of normal forms, a novel reduced model is derived to capture the behavior of a large class of neurons remaining unexplained in other existing reduced models.