Opinion dynamics is extensively used in studying large-scale social, economical, political and natural phenomena that involve many interacting agents. It also can be used to model the evolution of teams of autonomous vehicles operating in a coordinated fashion with civilian and military applications, when arbitration among individual goals needs to be negotiated. Recently, research was conducted on how opinion dynamics can be the core of collective decision-making mechanisms for swarm robotics. Opinion dynamics with a time varying opinion space, which is the set of all possible opinions an agent may have, is a relatively recent research topic. In this work, the Deffuant-Weisbuch model (DW model), which allows to model opinion dynamics in shrinking opinion spaces, was applied. In simulating this class of systems and in extracting information from them it is crucial to establish reliable algorithms and criteria for counting the numbers of clusters, as this ultimately affects the determination of the steady state of the system. A method was applied to combine Fuzzy c-means clustering and subtractive clustering to check convergence of the system and avoid negative influence of outliers. Different scenarios are simulated to study the influence of characteristic parameters on the formation of opinions, which is quantified by the formation of clusters in the opinion space. Additionally, we simulate the scenario of a two dimensional opinion space in which one side shrinks, and evaluate how the rate of shrinking influences the steady state opinion space. This is a simplified model to gain some insight on the effect of extreme changes of opinions in multi-dimensional opinion space.

Cette thèse a pour objet la modélisation individu-centrée des systèmes sociaux. Une première partie orientée aide à la décision présente un modèle d’évolution des populations rurales fortement inspiré des données. Une seconde partie, plus théorique, étudie divers mécanismes permettant à un individu d’accepter ou de résister à une influence sociale. Nous proposons tout d’abord un modèle individu-centré de la dynamique des municipalités rurales européennes, implémenté pour le département du Cantal. Nous proposons un nouvel algorithme de génération des populations initiales ne nécessitant pas d’échantillon de population (approche classique). Nous concevons et paramétrons un modèle de la dynamique de l’individu face au marché du travail basé sur les données de la « European Labour Force Survey ». Il inclut des heuristiques originales de transition d’états tel qu’actifs, inactifs, chômeurs, … prenant en compte l’âge, la profession et le secteur d’activité de l’individu. Nous déterminons les dynamiques non fondés sur des données individuelles en testant la capacité de dynamiques simples à produire des résultats proches des données agrégées disponibles. Est ainsi conçu un modèle de mobilité résidentielle, expliquant partiellement la migration et intégrant décision de déménager et choix d’une nouvelle résidence. La seconde partie de la thèse étudie les effets collectifs de différents mécanismes permettant aux individus de résister à ou d’accepter une influence sociale. Un premier mécanisme étudié est un filtre cognitif impliquant qu’un individu ne reçoit pas une information incongruente ou peu importante. Les individus « filtreurs » exhibent le biais de primauté car leur attitude n’est déterminée que par les premiers éléments reçus et se montrent négatifs alors que le message diffusé par un media est neutre. Le taux d’individus négatifs dans la population est accru ou diminuer par l’échange direct d’information entre les individus. Un second mécanisme est un rejet de la tentative d’influence qui mène l’individu à différencier davantage son attitude de celle de son interlocuteur. Il intervient lorsque l’individu éprouve un inconfort lié au fait qu’il est à la fois en accord et en désaccord avec son interlocuteur. Le couplage de ce rejet à un mécanisme d’attraction entre individus en accord entraîne un nombre moindre de groupes d’opinion différentes à l’échelle de la population (ie par rapport au nombre de groupes obtenus avec le seul mécanisme d’attraction). / This thesis is dedicated to individual-based modeling of social systems. While the first part is very practical, decision-support oriented, presenting a model which studies the evolution of a rural population, the second part is more theoretical, interested in various mechanisms allowing individual to accept or resist to social influence. Firstly, we propose an individual-based model of the European rural municipalities implemented for the French Cantal département. We use a new sample-free algorithm for generating the initial population, while classical methods require an initial sample. We design and parameterize the individual activity dynamics with data from the European Labour Force Survey database. The individual dynamics includes an original heuristic for labour statuses and employments changes, based on individual age, profession and activity sector when she is occupied. The last part of the model deals with dynamics that we have not been able to derive from data, mainly the demographic dynamics. Based on the Occam razor principle, we test very simple dynamics and choose them on their capacity to lead to model results close to reference data. In particular, we propose a simple residential mobility model, partly ruling the emigration, which integrates decision to move and location choice. Secondly, we study the collective effects of various mechanisms leading individuals to resist or accept social influence. A first mechanism leads individuals to neglect some features of an object if they are not important enough or incongruent. These individuals exhibit the primacy bias because their attitudes are determined by the first accepted feature. We show that this bias increases when individuals directly exchange about features compared to when they only get the features from the media, in a random order. The second mechanism is a rejection reaction that we suppose occurring because of the discomfort taking place when individuals are close on one dimension of attitude and far on another dimension. The main effect of this rejection mechanism is to lead to a lower number of clusters than with the attraction mechanism alone.

Aplicações de processos estocásticos a dinâmicas sociais constituem tema de grande relevância nos últimos anos. Especialmente desafiadores são os modelos de opinião com confiança limitada dada a sua falta de linearidade. Com isso, simulações e resultados numéricos possuem elevada importância. Neste trabalho, focamos em dois dos principais modelos de confiança limitada, nomeadamente os modelos de Hegselmann-Krause e de Deffuant-Weisbuch. Em ambos os casos, e necessário que a diferença de opiniões entre dois dados agentes seja menor que o limite de confiança, parâmetro do modelo. Porém, enquanto no modelo de Hegselmann-Krause a interação a cada etapa se dá entre todos os agentes vizinhos entre si, no modelo de Deffuant-Weisbuch a interação ocorre entre apenas dois agentes por vez. Apresentamos aqui uma revisão da literatura associada ao tema, incluindo resultados numéricos e analíticos sobre o comportamento de ambos os modelos, principalmente no tocante a convergência e condições em que se estabelecem o consenso ou a fragmentação de opiniões. / Applications of stochastic processes to social dynamics constitute a prominent research field of the last years. Especially challenging are opinion models with bounded confidence, given their lack of linearity. Thus, simulations and numerical results are highly important. In this work, we focus on two of the main bounded confidence models, namely Hegelsemann-Krause and Deffuant-Weisbuch models. In both cases, it is necessary that the difference between two agents\' opinions is less than the confidence bound, a parameter of the model. However, while at the Hegselmann-Krause model the interaction at each step occurs among all neighboring agents, at the Deffuant-Weisbuch model the interaction happens between only two agents each time. We present here a review of the literature concerned to the subject, including numerical and analytical results about the behavior of both models, mainly those related to convergence and conditions under which consensus or fragmentation take place.

Aplicações de processos estocásticos a dinâmicas sociais constituem tema de grande relevância nos últimos anos. Especialmente desafiadores são os modelos de opinião com confiança limitada dada a sua falta de linearidade. Com isso, simulações e resultados numéricos possuem elevada importância. Neste trabalho, focamos em dois dos principais modelos de confiança limitada, nomeadamente os modelos de Hegselmann-Krause e de Deffuant-Weisbuch. Em ambos os casos, e necessário que a diferença de opiniões entre dois dados agentes seja menor que o limite de confiança, parâmetro do modelo. Porém, enquanto no modelo de Hegselmann-Krause a interação a cada etapa se dá entre todos os agentes vizinhos entre si, no modelo de Deffuant-Weisbuch a interação ocorre entre apenas dois agentes por vez. Apresentamos aqui uma revisão da literatura associada ao tema, incluindo resultados numéricos e analíticos sobre o comportamento de ambos os modelos, principalmente no tocante a convergência e condições em que se estabelecem o consenso ou a fragmentação de opiniões. / Applications of stochastic processes to social dynamics constitute a prominent research field of the last years. Especially challenging are opinion models with bounded confidence, given their lack of linearity. Thus, simulations and numerical results are highly important. In this work, we focus on two of the main bounded confidence models, namely Hegelsemann-Krause and Deffuant-Weisbuch models. In both cases, it is necessary that the difference between two agents\' opinions is less than the confidence bound, a parameter of the model. However, while at the Hegselmann-Krause model the interaction at each step occurs among all neighboring agents, at the Deffuant-Weisbuch model the interaction happens between only two agents each time. We present here a review of the literature concerned to the subject, including numerical and analytical results about the behavior of both models, mainly those related to convergence and conditions under which consensus or fragmentation take place.

O estudo de sistemas complexos nos ajuda a entender como regras locais simples podem gerar padrões agregados complexos e muitas vezes inesperados. Quando as regras são bem definidas e os padrões observáveis, o sistema pode ser modelado e seus resultados comparados. Um dos maiores desafios para a modelagem de sistemas complexos é definir a regra de interação responsável pelo comportamento complexo. Em dinâmica de opiniões, padrão complexo e inesperado pode ser o súbito consenso ou até mesmo a polarização, e objetivo, então, se torna verificar em que circunstâncias podemos observar pessoas concordarem ou descordarem. Embora haja uma série de modelos de dinâmica de opiniões para descrever como as pessoas interagem, cada um define a regra de formação da opinião de forma ad hoc. O modelo CODA (Continuous opinions and Discret Actions) propõe uma fundamentação teórica para os modelos de dinâmica de opiniões baseada em teoria de probabilidade. Suas aplicações se estendem desde estudos sobre inovação à epistemologia. Nesta dissertação, aprofundamos os estudos de epistemologia que envolvem o CODA, investigando principalmente o efeito da confiança no processo de confirmação cientifica. Nossas simulações corroboram investigações sociológicas e históricas sobre o papel fundamental da confiança no processo de aquisição e geração do conhecimento / The study of complex systems helps us understand how simple local rules can generate complex and often unexpected aggregate patterns. When the rules are well defined and patterns observed, the system can be modeled and its results compared. One of the major challenges for modeling complex systems is to define a rule of interaction responsible for complex behavior. In opinion dynamics, complex and unexpected pattern may be the sudden consensus or even a polarization, so the aim it is to verify under what circumstances we can observe agreement or disagreement. Although there are a number of models of opinion dynamics to describe how people should interact with each other, each one defines an ad hoc opinion formation rule. The model of opinion dynamics CODA (Continuous Opinions and Discret Actions) proposes a theoretical framework for the models of opinion dynamics, based on probability theory. Their applications range from studies on innovation to epistemology. In this dissertation, we deepen the studies of epistemology that involve the CODA, investigating mainly the effect of the trust in the process of scientific confirmation. Our simulations corroborates sociological and historical researches on the role of trust in the process of acquisition and generation of knowledge

O estudo de sistemas complexos nos ajuda a entender como regras locais simples podem gerar padrões agregados complexos e muitas vezes inesperados. Quando as regras são bem definidas e os padrões observáveis, o sistema pode ser modelado e seus resultados comparados. Um dos maiores desafios para a modelagem de sistemas complexos é definir a regra de interação responsável pelo comportamento complexo. Em dinâmica de opiniões, padrão complexo e inesperado pode ser o súbito consenso ou até mesmo a polarização, e objetivo, então, se torna verificar em que circunstâncias podemos observar pessoas concordarem ou descordarem. Embora haja uma série de modelos de dinâmica de opiniões para descrever como as pessoas interagem, cada um define a regra de formação da opinião de forma ad hoc. O modelo CODA (Continuous opinions and Discret Actions) propõe uma fundamentação teórica para os modelos de dinâmica de opiniões baseada em teoria de probabilidade. Suas aplicações se estendem desde estudos sobre inovação à epistemologia. Nesta dissertação, aprofundamos os estudos de epistemologia que envolvem o CODA, investigando principalmente o efeito da confiança no processo de confirmação cientifica. Nossas simulações corroboram investigações sociológicas e históricas sobre o papel fundamental da confiança no processo de aquisição e geração do conhecimento / The study of complex systems helps us understand how simple local rules can generate complex and often unexpected aggregate patterns. When the rules are well defined and patterns observed, the system can be modeled and its results compared. One of the major challenges for modeling complex systems is to define a rule of interaction responsible for complex behavior. In opinion dynamics, complex and unexpected pattern may be the sudden consensus or even a polarization, so the aim it is to verify under what circumstances we can observe agreement or disagreement. Although there are a number of models of opinion dynamics to describe how people should interact with each other, each one defines an ad hoc opinion formation rule. The model of opinion dynamics CODA (Continuous Opinions and Discret Actions) proposes a theoretical framework for the models of opinion dynamics, based on probability theory. Their applications range from studies on innovation to epistemology. In this dissertation, we deepen the studies of epistemology that involve the CODA, investigating mainly the effect of the trust in the process of scientific confirmation. Our simulations corroborates sociological and historical researches on the role of trust in the process of acquisition and generation of knowledge

Fenômenos coletivos em redes sociais como a formação de linguagem ou cultura, crenças, emergência de consenso em relação a algum assunto, aquisição de conhecimento e aprendizagem, dentre outros, tem conduzido a um grande interesse no estudo de comportamentos cooperativos e fenômenos sociais, resultando numa grande variedade de dinâmicas de opinião. Nestes modelos, uma população de agentes interagentes carrega uma variável (ou um conjunto delas) numérica cujo valor representa uma opinião sobre um tópico, com interpretações distintas em cada contexto. Inspirados em conceitos de mecânica estatística e mecanismos sociais, estes estados evoluem governados por regras matemáticas que controlam a dinâmica de interação entre os agentes e a influência de fatores externos. Outro ingrediente importante na modelagem de sistemas reais é que a representação das interações entre agentes difere bastante de reticulados ou misturas homogêneas, sendo mais bem descritas por redes complexas. Neste trabalho, estudamos a dinâmica de opinião de Krause e Hegselmann. Neste modelo, agentes possuem opiniões que assumem valores contínuos e são atualizados de acordo com a vizinhança compatível, definida pelo princípio da confiança limitada. Após apresentar uma revisão da literatura, estudamos a dinâmica de opinião no contexto de Redes Complexas, seguido de modificações do modelo que consideram a ação de ruído e campo externo (propaganda). Finalmente, propomos um modelo de consenso cuja interpretação está inserida no contexto de aquisição de conhecimento por agentes interagentes que realizam observações sujeitas a erros. Os resultados mostram como os diferentes tipos de topologia influenciam no comportamento das dinâmicas. / Collective phenomena in social networks such as formation of language or culture, beliefs, emergence of consensus on any subject, knowledge acquisition and learning, among others, has led to an increasing interest in the study of cooperative behavior and social phenomena, resulting in great variety of opinion dynamics. In these models, a population of interacting agents holds a variable (or a set of them) whose numerical value is an opinion on a topic, with different interpretations in each context. Inspired by concepts from statistical mechanics and social mechanisms, these states evolve governed by mathematical rules that control the dynamics of interaction between agents and the influence of external factors. Another important ingredient in the modeling of real systems is the representation of the interactions between agents, which strongly differs from lattices or fully mixed states, being better described by complex networks. In the present work, we study the opinion dynamics of Krause and Hegselmann. In this model, agents hold opinions that assume continuous values and are updated according to their compatible neighborhood, defined by the bounded confidence principle. After presenting a literature review, we studied the opinion dynamics in the context of complex networks, followed by modifications of the model considering the effect of noise and external field (advertising). Finally, we propose a consensus model interpreted as a process of knowledge acquisition by interacting agents that make observations subject to errors. The results show how the topology influences the dynamic behavior.

Fenômenos coletivos em redes sociais como a formação de linguagem ou cultura, crenças, emergência de consenso em relação a algum assunto, aquisição de conhecimento e aprendizagem, dentre outros, tem conduzido a um grande interesse no estudo de comportamentos cooperativos e fenômenos sociais, resultando numa grande variedade de dinâmicas de opinião. Nestes modelos, uma população de agentes interagentes carrega uma variável (ou um conjunto delas) numérica cujo valor representa uma opinião sobre um tópico, com interpretações distintas em cada contexto. Inspirados em conceitos de mecânica estatística e mecanismos sociais, estes estados evoluem governados por regras matemáticas que controlam a dinâmica de interação entre os agentes e a influência de fatores externos. Outro ingrediente importante na modelagem de sistemas reais é que a representação das interações entre agentes difere bastante de reticulados ou misturas homogêneas, sendo mais bem descritas por redes complexas. Neste trabalho, estudamos a dinâmica de opinião de Krause e Hegselmann. Neste modelo, agentes possuem opiniões que assumem valores contínuos e são atualizados de acordo com a vizinhança compatível, definida pelo princípio da confiança limitada. Após apresentar uma revisão da literatura, estudamos a dinâmica de opinião no contexto de Redes Complexas, seguido de modificações do modelo que consideram a ação de ruído e campo externo (propaganda). Finalmente, propomos um modelo de consenso cuja interpretação está inserida no contexto de aquisição de conhecimento por agentes interagentes que realizam observações sujeitas a erros. Os resultados mostram como os diferentes tipos de topologia influenciam no comportamento das dinâmicas. / Collective phenomena in social networks such as formation of language or culture, beliefs, emergence of consensus on any subject, knowledge acquisition and learning, among others, has led to an increasing interest in the study of cooperative behavior and social phenomena, resulting in great variety of opinion dynamics. In these models, a population of interacting agents holds a variable (or a set of them) whose numerical value is an opinion on a topic, with different interpretations in each context. Inspired by concepts from statistical mechanics and social mechanisms, these states evolve governed by mathematical rules that control the dynamics of interaction between agents and the influence of external factors. Another important ingredient in the modeling of real systems is the representation of the interactions between agents, which strongly differs from lattices or fully mixed states, being better described by complex networks. In the present work, we study the opinion dynamics of Krause and Hegselmann. In this model, agents hold opinions that assume continuous values and are updated according to their compatible neighborhood, defined by the bounded confidence principle. After presenting a literature review, we studied the opinion dynamics in the context of complex networks, followed by modifications of the model considering the effect of noise and external field (advertising). Finally, we propose a consensus model interpreted as a process of knowledge acquisition by interacting agents that make observations subject to errors. The results show how the topology influences the dynamic behavior.

This thesis introduces a new model to the field of social dynamics in which each node in a network moves to the mass center of the opinions in its neighborhood weighted by the changing certainty each node has in its own opinion. An upper bound of O(n) is proved for the number of timesteps until this model reaches a stable state. A second model is also analyzed in which nodes move to the mass center of the opinions of the nodes in their neighborhood unweighted by the certainty those nodes have in their opinions. This second model is shown to have a O(d) time complexity, where d is the diameter of the network, on a tree and is compared with a very similar model presented in 2013 by Frischknecht, Keller, and Wattenhofer who found a lower bound on some networks of Ω(3). 2 / Graduate

This dissertation concerns the self-organization behaviors in different types of multi-agent systems, and possible ways to apply interventions on top ofthat to achieve certain goals. A bounded confidence opinion dynamics modelis considered for the first two papers. Theoretical analysis of the model isperformed and modifications of the model are given so that it will have better properties in some aspect. Leader-follower based models are studied in the third to fifth papers where various optimal control problems are considered. Different methods such as Pontryagin minimum principle and dynamic programming are used to solve those optimal control problem. For complex problems, one may only get approximate solutions or suboptimal solutions.In Paper A and Paper B, we consider the continuous-time Hegselmann-Krause (H-K) model and its variations and target the problem of reaching consensus. A sufficient condition on the initial opinion distribution is givento guarantee consensus for the original continuous-time H-K model. A modified model is provided and proven to be able to lead a larger range of initial opinions to synchronization. An H-K model with an exo-system is also studied where sufficient conditions on the exo-system are given for the purpose of consensus.In Paper C and Paper D, optimal control problems with leader-followerbased multi-agent systems are discussed. Analytic solutions are derived if the dynamics is linear by applying Pontryagin minimum principle. For generalnon-linear leader-follower interactions, we provide a method that use sstatistic moments of the follower crowd to approximate the optimal control.The dynamic programming approach is used and certain approximation ofthe Hamilton-Jacobi-Bellman equations is needed. The computational burdenis so heavy that model predictive control method is required in practical applications.In Paper E, we apply a similar method to the approach used in PaperD to target a pollutant elimination problem. It implies that we can use themethod to attack optimal control problem with partial differential equation constraints by discretization in space. The dimension of the discretization is not related to the computational complexity since only the statistic moments are needed. / <p>QC 20161201</p>