The task of modeling and controlling the evolution of dynamical sys- tems is one of the main objectives in mechatronics engineering. When approaching the problem of controlling physical or digital systems, the dynamical models have been historically divided into continuous-time, described by differential equations, and discrete-time, described by difference equations. In the last decade, a new class of models, known as hybrid dynamical systems, has gained popularity in the control community because of its high versatility. This framework combines continuous-time and discrete- time evolution, thus allowing for both the description of a broader class of systems and the achievement of better-performing controllers, compared to the traditional continuous-time alternatives. After the first rigorous introduction of the framework, several Lyapunov-based results were published in the literature, and numerous application areas were shown to benefit from the introduction of a hybrid dynamics, like systems involving impacts or physical systems connected to digital controllers (cyber-physical systems). In this thesis, we use the hybrid framework to study different mechatronics-inspired control problems. The applications we consider are diverse, so we split the presentation into three parts. In the first part we further analyze a particular hybrid control strategy, known as reset control, providing some new theoretical guarantees, together with an application to adaptive control. In the second part we consider two applications of the hybrid framework to the network dynamics field, specifically we analyze the problems of distributed state estimation and of uniform synchronization of nonlinear oscillators. In the third part, we use a hybrid approach to study two applications where this framework has been rarely employed, or not at all, namely smart agriculture and trajectory tracking for a bipedal walking robot. We study these application-inspired problems from a theoretical point of view, giving robust Lyapunov-based stability guarantees. We complement the theoretical analysis with numerical results, obtained from simulations or from experiments.

Agent-based models are computer models made up of agents that can exist in a finite number of states. The state of the system at any given time is determined by rules governing agents' interaction. The rules may be deterministic or stochastic. Optimization is the process of finding a solution that optimizes some value that is determined by simulating the model. Optimal control of an agent-based model is the process of determining a sequence of control inputs to the model that steer the system to a desired state in the most efficient way. In large and complex models, the number of possible control inputs is too large to be enumerated by computers; hence methods must be developed for use with these models in order to find solutions without searching the entire solution space. Heuristic algorithms have been applied to such models with some success. Such algorithms are discussed; case studies of examples from biology are presented. The lack of a standard format for agent-based models is a major issue facing the study of agent-based models; presentation as polynomial dynamical systems is presented as a viable option. Algorithms are adapted and presented for use in this framework. / Master of Science

本研究旨在探討國民中學校長透明化優勢領導與學校混沌動力系統之間的關係。除探討國民中學校長透明化優勢領導、學校混沌動力系統的內涵及現況，瞭解教育人員人口變項及學校背景變項在校長透明化優勢領導及學校混沌動力系統得分的差異情形外，亦分析校長透明化優勢領導與學校混沌動力系統之相關程度，並探討校長透明化優勢領導對學校混沌動力系統的預測情形。 本研究係以台灣地區之國民中學教育人員為研究對象，以「國民中學校長透明化優勢領導與學校混沌動力系統調查問卷」為工具進行研究，內含基本資料、國民中學校長透明化優勢領導問卷及學校混沌動力系統問卷三部分，具有良好的信度、效度。正式施測有效樣本502位，分別以描述分析、t考驗、變異數分析、積差相關分析、多元逐步迴歸分析等統計方法進行分析，並得到以下數項結論： 一、國民中學教育人員在知覺「校長透明化優勢領導問卷」的總得分上，屬於中上程度，在各向度之得分中，以「誠實至上」最高，最低則是「勇於認錯」。國民中學教育人員在「學校混沌動力系統問卷」的總得分上，亦屬於中上程度，在各向度之得分中，以「回饋機制」最高，最低則是「亂中求序」。 二、教育人員人口變項與學校背景變項中，性別、年齡、服務年資、職務及區域在校長透明化優勢領導問卷上，均具有顯著差異，僅學歷無顯著差異。 三、教育人員人口變項與學校背景變項中，性別、年齡、服務年資、職務及區域在學校混沌動力系統問卷上，均具有顯著差異，僅學歷無顯著差異。 四、教育人員知覺校長透明化優勢領導問卷之得分中，低、中、高三組在整體學校混沌動力系統及學校混沌動力系統各向度上，均有顯著差異；同時，不論在整體學校混沌動力系統或各向度的得分上，高分組均顯著優於中、低分組；中分組顯著優於低分組。 五、校長透明化優勢領導及各向度，與學校混沌動力系統及各向度間呈現出顯著的正相關，亦即教育人員知覺校長透明化優勢領導行為愈高，則校長經營學校混沌動力系統之能力也愈佳。 六、在探討校長透明化優勢領導各向度中，以鼓勵讚賞、傳達警訊、信守承諾、勇於認錯、卸下防禦及沈著鎮靜等六者對學校混沌動力系統之聯合預測力最佳，尤以鼓勵讚賞最具有預測力。 最後，本研究擬根據上述研究結果進行分析討論，以形成結論及建議，並提供教育行政機關、國民中學校長及未來相關研究之參考。 / The purposes of this study were to explore relationships between principal's transparency edge leading and chaotic dynamical system in junior high school. The fist were to explore the reality for principal's transparency edge leading and chaotic dynamical system in schools. Secondary, the researcher also investigated the differences of school staff’s demographic variables and schools' background variables among principal's transparency edge leading and chaotic dynamical system in schools. Thirdly, to analyze the relationships among principal's transparency edge leading and chaotic dynamical system in schools. Finally, to explore predictive power of principal's transparency edge leading on chaotic dynamical system in schools. This study employed the survey method. The subject were 502 educational staff randomly sample from 70 junior high schools in Taiwan island. Data were analyzed using the method of descriptive and inferential statistics, included Frequencies, t-test, ANOVA, Correlation analysis, and Multiple stepwise regression analysis. The major findings were： 1. There is above average perception for principal's transparency edge leading and chaotic dynamical system in schools among the junior high school staff. 2. Significant difference existed among the gender, age, seniority, position, and district for principal's transparency edge leading. 3. Significant difference existed among the gender, age, seniority, position, and district for chaotic dynamical system in schools. 4. Significant difference existed among low, middle, and high teachers' perception of principal's transparency edge leading for chaotic dynamical system in schools. 5. Significant positive correlation between principal's transparency edge leading and chaotic dynamical system in schools. 6. In regression forecast of principal's transparency edge leading to chaotic dynamical system in schools, especially the variable of “encouragement and applause” has the biggest predictability. Based on the results of this study, to make some suggestions for educational administration, the junior high school principals and future study.

The neural net computer simulations which will be presented here are based on the acceptance of a set of assumptions that for the last twenty years have been expressed in the fields of information processing, neurophysiology and cognitive sciences. First of all, neural networks and their dynamical behaviors in terms of attractors is the natural way adopted by the brain to encode information. Any information item to be stored in the neural net should be coded in some way or another in one of the dynamical attractors of the brain and retrieved by stimulating the net so as to trap its dynamics in the desired item's basin of attraction. The second view shared by neural net researchers is to base the learning of the synaptic matrix on a local Hebbian mechanism. The last assumption is the presence of chaos and the benefit gained by its presence. Chaos, although very simply produced, inherently possesses an infinite amount of cyclic regimes that can be exploited for coding information. Moreover, the network randomly wanders around these unstable regimes in a spontaneous way, thus rapidly proposing alternative responses to external stimuli and being able to easily switch from one of these potential attractors to another in response to any coming stimulus. In this thesis, it is shown experimentally that the more information is to be stored in robust cyclic attractors, the more chaos appears as a regime in the back, erratically itinerating among brief appearances of these attractors. Chaos does not appear to be the cause but the consequence of the learning. However, it appears as an helpful consequence that widens the net's encoding capacity. To learn the information to be stored, an unsupervised Hebbian learning algorithm is introduced. By leaving the semantics of the attractors to be associated with the feeding data unprescribed, promising results have been obtained in term of storing capacity.

We investigate a system of nonlinear partial differential equations, specifically the so-called Ladyzhenskaya model, in three spatial dimensions. It will be shown that after inclusion of a perturbation of a higher order, the model exhibits a considerably better behavior, in particular it will become quite straightforward to prove differentiability of solutions with respect to the initial condition. Due to this fact we may consequently employ the method of Lyapunov exponents to estimate the fractal dimension of the exponential attractor. First, however, it will be necessary to show existence and uniqueness of solutions, improved regularity and existence of a compact invariant set for the entire system.

As robots start moving closer to our social and daily lives, issues of agency and social behavior become more important. However, despite noticeable advances in Human Robot Interaction (HRI), the developed technologies induce two major drawbacks : (i) HRI are highly demanding, (ii) humans have to adapt their way of thinking to the potential and limitations of the Robot. Thereby, HRI induce an important cognitive load which question the acceptability of the future robots. Consequently, we can address the question of understanding and mastering the development of pleasant yet efficient human-robot interactions which increase self- esteem, engagement (or pleasure), and efficacy of the human when interacting with the machine.In this race for more user-friendly HRI systems (robotic companion, intelligent objects etc.), working on the technical features (the design of appearance and superficial traits of behavior) can contribute to some partial solutions for punctual or short-term interactions. For instance, a major focus of interest has been put on the expressiveness and the appearance of robots and avatars. Yet, these approaches have neglected the importance of understanding the dynamics of interactions.In our opinion, intuitive communication refers to the ability of the robot to detect the crucial signals of the interaction and use them to adapt one's dynamics to the other's behavior. In fact, this central issue is highly dependent on the robot's capabilities to sense the human world and interact with it in a way that emulates human-human interactions.In early communication among humans, synchrony was found to be a funda- mental mechanism relying on very low-level sensory-motor networks, inducing the synchronization of inter-individual neural populations from sensory flows (vision, audition, or touch). Synchrony is caused by the interaction but also sustains the interaction itself in a circular way, as promoted by the enaction approach. Consequently, to become a partner in a working together scenario, the machine can obtain a minimal level of autonomy and adaptation by predicting the rhythmic structure of the interaction to build reinforcement signals to adapt the robot behavior as it can maintain the interest of the human in more long-term interactions.More precisely, as we are aiming for more “intuitive” and “natural” HRI, we took advantages of recent discoveries in low-level human interactions and studied Unintentional Synchronizations during rhythmic human robot interactions. We argue that exploiting natural stability and adaptability properties of unintentional synchronizations and rhythmic activities in human-human interactions can solve several of the acceptability problems of HRIs, and allow rethinking the current approaches to design them. / As robots start moving closer to our social and daily lives, issues of agency and social behavior become more important. However, despite noticeable advances in Human Robot Interaction (HRI), the developed technologies induce two major drawbacks : (i) HRI are highly demanding, (ii) humans have to adapt their way of thinking to the potential and limitations of the Robot. Thereby, HRI induce an important cognitive load which question the acceptability of the future robots. Consequently, we can address the question of understanding and mastering the development of pleasant yet efficient human-robot interactions which increase self- esteem, engagement (or pleasure), and efficacy of the human when interacting with the machine.In this race for more user-friendly HRI systems (robotic companion, intelligent objects etc.), working on the technical features (the design of appearance and superficial traits of behavior) can contribute to some partial solutions for punctual or short-term interactions. For instance, a major focus of interest has been put on the expressiveness and the appearance of robots and avatars. Yet, these approaches have neglected the importance of understanding the dynamics of interactions.In our opinion, intuitive communication refers to the ability of the robot to detect the crucial signals of the interaction and use them to adapt one's dynamics to the other's behavior. In fact, this central issue is highly dependent on the robot's capabilities to sense the human world and interact with it in a way that emulates human-human interactions.In early communication among humans, synchrony was found to be a funda- mental mechanism relying on very low-level sensory-motor networks, inducing the synchronization of inter-individual neural populations from sensory flows (vision, audition, or touch). Synchrony is caused by the interaction but also sustains the interaction itself in a circular way, as promoted by the enaction approach. Consequently, to become a partner in a working together scenario, the machine can obtain a minimal level of autonomy and adaptation by predicting the rhythmic structure of the interaction to build reinforcement signals to adapt the robot behavior as it can maintain the interest of the human in more long-term interactions.More precisely, as we are aiming for more “intuitive” and “natural” HRI, we took advantages of recent discoveries in low-level human interactions and studied Unintentional Synchronizations during rhythmic human robot interactions. We argue that exploiting natural stability and adaptability properties of unintentional synchronizations and rhythmic activities in human-human interactions can solve several of the acceptability problems of HRIs, and allow rethinking the current approaches to design them.

Este trabalho apresenta um estudo qualitativo das equações diferenciais nãolineares que descrevem o sincronismo de fase nos PLLs de 3ª ordem que compõem redes OWMS de topologia mista, Estrela Simples e Cadeia Simples. O objetivo é determinar, através da Teoria de Bifurcações, os valores ou relações entre os parâmetros constitutivos da rede que permitam a existência e a estabilidade do estado síncrono, quando são aplicadas, no oscilador mestre, duas funções de excitação muito comuns na prática: o degrau e a rampa de fase. Na determinação da estabilidade dos pontos de equilíbrio, sob o ponto de vista de Lyapunov, a existência de pontos de equilíbrio não-hiperbólicos não permite uma aproximação linear e, nesses casos, é aplicado o Teorema da Variedade Central. Essa técnica de simplificação de sistemas dinâmicos permite fazer uma aproximação homeomórfica em torno desses pontos, preservando a orientação no espaço de fases e possibilitando determinar localmente suas estabilidades. / This work presents a qualitative study of the non-linear differential equations that describe the synchronous state in 3rd order PLLs that compose One-way masterslave time distribution networks with Single Star and Single Chain topologies. Using bifurcation theory, the dynamical behavior of third-order phase-locked loops employed to extract the syncronous state in each node is analyzed depending on constitutive node parameters when two usual inputs, the step and the ramp phase pertubations, are supposed to appear in the master node. When parameter combinations result in non hyperbolic synchronous states, from Lyapunov point of view, the linear approximation does not provide any information about the local behavior of the system. In this case, the center manifold theorem permits the construction of an equivalent vector field representing the asymptotic behavior of the original system in the neighborhood of these points. Thus, the local stability can be determined.

Neste trabalho, são estudados os problemas de sincronismo de fase nas redes mestre-escravo de via única (OWMS), nas topologias Estrela Simples, Cadeia Simples e mista, através da Teoria Qualitativa de Equações Diferenciais, com ênfase no Teorema da Variedade Central. Através da Teoria das Bifurcações, analisa-se o comportamento dinâmico das malhas de sincronismo de fase (PLL) de segunda ordem que compõem cada rede, frente às variações nos seus parâmetros constitutivos. São utilizadas duas funções de excitação muito comuns na prática: o degrau e a rampa de fase, aplicadas pelo nó mestre. Em cada caso, discute-se a existência e a estabilidade do estado síncrono. A existência de pontos de equilíbrio não-hiperbólicos, não permite uma aproximação linear, e nesses casos é aplicado o Teorema da Variedade Central. Através dessa rigorosa técnica de simplificação de sistemas dinâmicos é possível fazer uma aproximação homeomórfica em torno desses pontos, preservando a orientação no espaço de fases. Desse modo, é possível determinar, localmente, suas estabilidades. / This work presents stability analysis of the syncronous state for three types of one-way master-slave time distribution network topologies: single star, single chain and both of them, mixed. Using bifurcation theory, the dynamical behavior of second-order phase-locked loops employed to extract the syncronous state in each node is analyzed in function of the constitutive parameters. Two usual inputs, the step and the ramp phase pertubations, are supposed to appear in the master node and, in each case, the existence and stability of the syncronous state are studied. For parameter combinations resulting in non hyperbolic synchronous states, the linear approximation does not provide any information, even about the local behaviour of the system. In this case, the center manifold theorem permits the construction of an equivalent vector field representing the asymptotic behaviour of the original system in the neighborhood of these points. Thus, the local stability can be determined.

La thérapie photodynamique (PDT) est un traitement médical destiné à certains types de cancer. Elle utilise un agent photosensibilisant qui se concentre dans les tissus pathologiques est qui sera. Cet agent est ensuite activé par une lumière d'une longueur d'onde précise produisant, après une cascade de réactions, des espèces réactives de l'oxygène qui endommagent les cellules cancéreuses.Cette thèse aborde les analyses d'identifiabilité et de sensibilité des paramètres du modèle dynamique non linéaire retenu.Après avoir précisé différents cadres d'analyse d'identifiabilité, nous nous intéressons plus particulièrement à l'identifiabilité a posteriori, pour des conditions expérimentales fixées, puis à l'identifiabilité pratique, prenant en plus en compte les bruits de mesure. Pour ce dernier cadre, nous proposons une méthodologie d'analyse locale autour de valeurs particulières des paramètres. En ce qui concerne l'identifiabilité des paramètres du modèle dynamique de la phase photocytotoxique de la PDT, nous montrons que parmi les dix paramètres localement identifiables a posteriori, seulement l'un d'entre eux l'est en pratique. Néanmoins, ces résultats locaux demeurent insuffisants en raison des larges plages de variation possibles des paramètres du modèle et nécessitent d'être complétés par une analyse globale.Le manque de méthode visant à tester l'identifiabilité globale a posteriori ou pratique, nous a orientés vers l'analyse de sensibilité globale de la sortie du modèle par rapport à ses paramètres. Une méthode d'analyse de sensibilité globale fondée sur l'étude de la variance a permis de mettre en évidence trois paramètres sensibilisants.Nous abordons ensuite les liens entre les analyses globales d'identifiabilité et de sensibilité des paramètres, en employant une décomposition de Sobol'. Nous montrons alors que les liens suivants existent : une fonction de sensibilité totale nulle implique un paramètre non-identifiable; deux fonctions de sensibilité colinéaires impliquent la non-identifiabilité mutuelle des paramètres en question ; la non-injectivité de la sortie par rapport à un de ses paramètres peut aussi entrainer la non-identifiabilité du paramètre en question mais ce dernier point ne peut être détecté en analysant les fonctions de sensibilité uniquement. En somme, la détection des paramètres non globalement identifiables dans un cadre expérimental donné à partir de résultats d'analyse de sensibilité globale ne peut être que partielle. Elle permet d'observer deux (sensibilité nulle ou négligeable et sensibilités corrélées) des trois causes de la non-identifiabilité / Photodynamic therapy (PDT) is a treatment of dysplastic tissues such as cancers. Mainly, it involves the selective uptake and retention of the photosensitizing drug (photosensitizer, PS) in the tumor, followed by its illumination with light of appropriate wavelength. The PS activation is thought to produce, after multiple intermediate reactions, singlet oxygen at high doses (in the presence of molecular oxygen) and thereby to initiate apoptotic and necrotic death of tumor. The PDT efficiency stems from the optimal interaction between these three factors: photosensitizing agent (its chemical and photobiological properties), light (illumination conditions) and oxygen (its availability in the target tissue). The relative contribution of each of these factors has an impact on the effectiveness of treatment. It is a dynamic process and the objective of the thesis is to characterize it by a mathematical model. The points raised relate primarily to the determination of a dynamic model of the photodynamic phase (production of singulet oxygen), to the global analyses of identifiability and sensitivity of the parameters of the model thus built. The main difficulties of this work are the nonlinearity structure of the photophysical model, the large range of possible values (up to four decades) of the unknown parameters, the lack of information (only one measured variable over six state variables), the limited degrees-of-freedom for the choice of the laser light stimulus (input variable).Another issue concerns the links between the non-identifiability of parameters and the properties of global sensitivity functions. Two relationships between these two concepts are presented. We stress the need to remain cautious about the parameter identifiability conclusions based on the sensitivity study. In perspective, these results could lead to the development of new approaches to test the non-identifiability of parameters in an experimental framework

In der vorliegenden Arbeit untersuchte ich die komplexen Strukturen von Netzwerken, deren zeitliche Entwicklung, die Interpretationen von verschieden Netzwerk-Massen und die Klassen der Prozesse darauf. Als Erstes leitete ich Masse für die Charakterisierung der zeitlichen Entwicklung der Netzwerke her, um räumlich Veränderungsmuster zu erkennen. Als Nächstes führe ich eine neue Methode zur Konstruktion komplexer Netzwerke von Flussfeldern ein, bei welcher man das Set-up auch rein unter Berufung Berufung auf das Geschwindigkeitsfeld ändern kann. Diese Verfahren wurden für die Korrelationen skalarer Grössen, z. B. Temperatur, entwickelt, welche eine Advektions-Diffusions-Dynamik in der Gegenwart von Zwingen und Dissipation. Die Flussnetzwerk-Methode zur Zeitreihenanalyse konstruiert die Korrelationsmatrizen und komplexen Netzwerke. Dies ermöglicht die Charakterisierung von Transport in Flüssigkeiten, die Identifikation verschiedene Misch-Regimes in dem Fluss und die Anwendung auf die Advektions-DiffusionsDynamik, Klimadaten und anderen Systemen, in denen Teilchentransport eine entscheidende Rolle spielen. Als Letztes, entwickelte ich ein neuartiges Heterogener Opinion Status Modell (HOpS) und Analysetechnik basiert auf Random Walks und Netzwerktopologie Theorien, um dynamischen Prozesse in Netzwerken zu studieren, wie die Verbreitung von Meinungen in sozialen Netzwerken oder Krankheiten in der Gesellschaft. Ein neues Modell heterogener Verbreitung auf einem Netzwerk wird als Beispielssystem für HOpS verwendent, um die vergleichsweise Einfachheit zu nutzen. Die Analyse eines diskreten Phasenraums des HOPS-Modells hat überraschende Eigenschaften, welches sensibel auf die Netzwerktopologie reagieren. Sie können verallgemeinert werden, um verschiedene Klassen von komplexen Netzwerken zu quantifizieren, Transportphänomene zu charakterisieren und verschiedene Zeitreihen zu analysieren. / In the thesis I studied the complex architectures of networks, the network evolution in time, the interpretation of the networks measures and a particular class of processes taking place on complex networks. Firstly, I derived the measures to characterize temporal networks evolution in order to detect spatial variability patterns in evolving systems. Secondly, I introduced a novel flow-network method to construct networks from flows, that also allows to modify the set-up from purely relying on the velocity field. The flow-network method is developed for correlations of a scalar quantity (temperature, for example), which satisfies advection-diffusion dynamics in the presence of forcing and dissipation. This allows to characterize transport in the fluids, to identify various mixing regimes in the flow and to apply this method to advection-diffusion dynamics, data from climate and other systems, where particles transport plays a crucial role. Thirdly, I developed a novel Heterogeneous Opinion-Status model (HOpS) and analytical technique to study dynamical processes on networks. All in all, methods, derived in the thesis, allow to quantify evolution of various classes of complex systems, to get insight into physical meaning of correlation networks and analytically to analyze processes, taking place on networks.