Este trabalho estuda a observabilidade e controlabilidade para uma classe de sistema dinâmico markoviano com saltos nos parâmetros, e uma coleção de matrizes de observabilidade e controlabilidade associadas. São explorados alguns resultados de invariância, bem como certas propriedades envolvendo essas matrizes. Uma dessas propriedades, relacionada com a coleção de matrizes de observabilidade é conhecida na literatura desta classe de sistemas, mas não há uma prova disponível. Esses resultados de invariancia foram estendidos para o estudo da controlabilidade e sua respectiva coleção de matrizes associada, obtendo assim uma propriedade análoga ao caso da observabilidade. Os resultados obtidos são importantes para validar outros resultados existentes que se baseiam na propriedade referida / This work studies observability and controlability of a class of Markov systems with jumping parameters, and associated set of observability and controlability matrices. We explore some invariance results regarding the state trajectory and certain properties involving those matrices. One of these properties, related with the collection of observability matrices, is employed in the literature of this class of systems, but there is no available proof. The invariance results are extended similarly to the context of controlability leading to a property that is analogous to the observability case. The obtained results are important to validate other existing results that rely on that property

Estudamos sistemas lineares em grupos de Lie introduzido por Ayala e Tirao em [3]. Esta nova classe de sistemas de controle é obtido através de uma generalização aos grupos de Lie de campos de vetores lineares em espaços vetoriais. Eles extendem não somente a classe bem conhecida de sistemas lineares em \'R POT. n\' mas também sistemas invariantes em grupos de Lie e os avanços recentes mostram que eles aparecem como modelos para ampla classe de sistemas de controle proveniente de diversas áreas de ciência e engenharia. Focamos nossa atenção em normalizador, que tem tido um papel fundamental em formulação de sistemas lineares em grupos de Lie, e lidamos com curvas integrais de seus campos vetoriais. Finalmente mostramos que sob certas hipóteses sistemas lineares em grupos de Lie possuem a propriedade de controlabilidade local a partir de identidade do grupo / We study linear control systems on Lie groups introduced by Ayala and Tirao in [3]. This new class of control systems is obtained through a generalization to Lie groups of linear vector fields on vector spaces. They extend not only well-known class of linear control systems on \'R POT. n\' but also invariant systems on Lie groups and recent achievements show that they appear as models for a wide class of control systems coming from several areas of science and engineering. We focus our attention on the notion of normalizer which has been played a key role for formulation of linear systems on Lie groups and then deal with integral curves of its vector fields. Finally we show that under certain assumptions linear systems on Lie groups have local controllability property from the group identity

Neste trabalho estudamos a controlabilidade e a estabilização de certos tipos de sistemas com retardo. Obtemos um resultado de estabilização para sistema com retardo periódicos e um resultado que nos permite concluir a controlabilidade do sistema com retardo baseado na controlabilidade do mesmo sistema porém, sem retardo. Apresentamos a equação do calor como exemplo / In this work we study controllability and stabilizability of a type of delayed systems. We get a stabilization result for delayed periodic systems and we get a result that allow us to conclude the controllability of the delayed system based on the controllability of the same system without delay. We present the heat equation like example

Estudos sobre imunização do desamparo aprendido apresentam resultados contraditórios quando utilizam estímulos apetitivos na fase de imunização. Uma análise dos procedimentos utilizados nesses estudos sugere que eles diferem no grau de controle e previsibilidade da liberação do estímulo apetitivo. Além disso, foi demonstrado que quando a previsibilidade do estímulo é manipulada ela produz efeitos dependentes do sexo do sujeito. O presente estudo teve por objetivos avaliar se: 1) a previsibilidade e a controlabilidade de estímulos apetitivos na fase de imunização são variáveis críticas para imunizar ratos contra o desamparo; 2) esses efeitos são dependentes do sexo. Em paralelo, buscou-se explorar alguns efeitos das variáveis hormonais nesses comportamentos. Um Estudo Piloto demonstrou não haver diferença quanto ao desamparo em fêmeas nas fases de estro e diestro do ciclo estral. Quanto à imunização (Experimento 1), foi utilizado reforçamento positivo combinando-se as variáveis de controle (VI e VT) e previsão (com ou sem sinal antecedendo a disponibilização do reforço), utilizando-se grupos (n=16) com ratos machos e fêmeas em igual proporção. Em seguida esses animais foram submetidos a choques incontroláveis e por fim a um teste de fuga. Outro grupo de machos e fêmeas passou apenas pelas duas últimas fases e um grupo apenas pela fase final. Os resultados mostraram que o sexo dos animais não é uma variável importante para o desamparo, mas que essa é uma variável que interfere na imunização do desamparo aprendido. Fêmeas expostas a estímulos previsíveis e controláveis na fase de imunização apresentam um comportamento muito semelhante as fêmeas e machos do Grupo não choque. Por outro lado, apenas metade dos machos expostos a estímulos apetitivos previsíveis e controláveis na fase de imunização aprenderam a resposta de fuga no teste. Esses resultados sugerem que o sexo é uma variável que precisa ser mais investigada em experimentos que estudam o comportamento. No Experimento 2 as fêmeas foram distribuídas em dois grupos (castradas e sham), foram retirados os ovários dos animais do primeiro grupo, responsáveis pela produção do estrógeno, hormônio que as diferencia dos machos. Após a recuperação da cirurgia os animais de ambos os grupos foram expostos ao mesmo procedimento de imunização do Grupo imprevisível e controlável do Experimento 1, o único em que foram obsevadas diferenças estatísticas entre machos e fêmeas. Os resultados mostraram aproximadamente metade das fêmeas, de ambos os grupos, aprenderam fuga apresentando latências semelhantes entre si, sugerindo que a presença ou ausência do hormônio sexual em fêmeas não foi, aparentemente, o fator determinante da diferença de gênero na imunização. Discute-se a relevância dos estudos comportamentais entre gêneros mostrando a interação de fatores ambientais com orgânicos / Studies on immunization against learned helplessness have different results when using appetitive stimuli during immunization. An analysis of these studies procedures suggests that they differ in the degree of control and predictability of the release of appetitive stimulus. Furthermore, it was shown that when the predictability of the stimulus is manipulated it produces effects that depend of the subjects sex. The objective of the present study was to evaluate : 1) if the appetitive stimuli predictability and controllability during immunization are critical variables to immunize rats against learned helplessness; and if 2) these effects are sex dependent. In parallel, we explored t some effects of hormonal variables on these behaviors. A pilot study showed no difference regarding learned helplessness in estrus and diestrus phases of the estrous cycle. Concerning immunization (Experiment 1), positive reinforcement was used combining the variables of control (VI and VT) and predictability (with or without signal preceding the availability of reinforcement), using groups (n = 16) with equal proportion of male and female rats. Then these animals were subjected to uncontrollable shock and finally to an escape test. Another group with males and females was submitted only to the last two phases and a last group only to the final phase. The results showed that sex is not an important variable concerning learned helplessness, but it interferes with the immunization against learned helplessness. Females exposed to predictable and controllable stimuli during immunization showed similar behavior with females and males of Non Shock Group. On the other hand, only half of the males exposed to predictable and controllable appetitive stimuli during immunization phase learned the escape response during the test. These results suggest that sex is a variable that needs to be better investigated in behavior experiments. In Experiment 2, females were distributed into two groups (castrated and sham), the ovaries of the animals of the first group were removed, they are responsible for the estrogen production, a hormone that differentiates males from females. After recovery from surgery, both groups were exposed to the same immunization procedure of the unpredictable and controllable group from Experiment 1, the only group that statistical differences between males and females were observed. Females in both groups showed similar escape latencies suggesting that the presence or absence of sex hormone in females was apparently not the determining factor of gender difference in immunization. It is discussed the relevance of behavioral sex differences studies showing the interaction of environmental with organic factors

The general problem of multi-agent persistent monitoring finds applications in a variety of domains ranging from meter to kilometer-scale systems, such as surveillance or environmental monitoring, down to nano-scale systems such as tracking biological macromolecules for studying basic biology and disease. The problem can be cast as moving the agents between targets, acquiring information from or in some fashion controlling the states of the targets. Under this formulation, at least two questions need to be addressed. The first is the design of motion trajectories for the agents as they move among the spatially distributed targets and jointly optimize a given cost function that describes some desired application. The second is the design of the controller that an agent will use at a target to steer the target's state as desired. The first question can be viewed in at least two ways: first, as an optimal control problem with the domain of the targets described as a continuous space, and second as a discrete scheduling task. In this work we focus on the second approach, which formulates the target dynamics as a hybrid automaton, and the geometry of the targets as a graph. We show how to find solutions by translating the scheduling problem into a search for the optimal route. With a route specifying the visiting sequence in place, we derive the optimal time the agent spends at each target analytically. The second question, namely that of steering the target's state, can be formulated from the perspective of the target, rather than the agent. The mobile nature of the agents leads to intermittencontrol, such that the controller is assumed to be disconnected when no agent is at the target. The design of the visiting schedule of agents to one target can affect the reachability (controllability) of this target's control system and the design of any specific controller. Existing test techniques for reachability are combined with the idea of lifting to provide conditions on systems such that reachability is maintained in the presence of periodic disconnections from the controller. While considering an intermittently connected control with constraints on the control authority and in the presence of a disturbance, the concept of 'degree of controllability' is introduced. The degree is measured by a region of states that can be brought back to the origin in a given finite time. The size of this region is estimated to evaluate the performance of a given sequence.

Estudos sobre imunização do desamparo aprendido apresentam resultados contraditórios quando utilizam estímulos apetitivos na fase de imunização. Uma análise dos procedimentos utilizados nesses estudos sugere que eles diferem no grau de controle e previsibilidade da liberação do estímulo apetitivo. Além disso, foi demonstrado que quando a previsibilidade do estímulo é manipulada ela produz efeitos dependentes do sexo do sujeito. O presente estudo teve por objetivos avaliar se: 1) a previsibilidade e a controlabilidade de estímulos apetitivos na fase de imunização são variáveis críticas para imunizar ratos contra o desamparo; 2) esses efeitos são dependentes do sexo. Em paralelo, buscou-se explorar alguns efeitos das variáveis hormonais nesses comportamentos. Um Estudo Piloto demonstrou não haver diferença quanto ao desamparo em fêmeas nas fases de estro e diestro do ciclo estral. Quanto à imunização (Experimento 1), foi utilizado reforçamento positivo combinando-se as variáveis de controle (VI e VT) e previsão (com ou sem sinal antecedendo a disponibilização do reforço), utilizando-se grupos (n=16) com ratos machos e fêmeas em igual proporção. Em seguida esses animais foram submetidos a choques incontroláveis e por fim a um teste de fuga. Outro grupo de machos e fêmeas passou apenas pelas duas últimas fases e um grupo apenas pela fase final. Os resultados mostraram que o sexo dos animais não é uma variável importante para o desamparo, mas que essa é uma variável que interfere na imunização do desamparo aprendido. Fêmeas expostas a estímulos previsíveis e controláveis na fase de imunização apresentam um comportamento muito semelhante as fêmeas e machos do Grupo não choque. Por outro lado, apenas metade dos machos expostos a estímulos apetitivos previsíveis e controláveis na fase de imunização aprenderam a resposta de fuga no teste. Esses resultados sugerem que o sexo é uma variável que precisa ser mais investigada em experimentos que estudam o comportamento. No Experimento 2 as fêmeas foram distribuídas em dois grupos (castradas e sham), foram retirados os ovários dos animais do primeiro grupo, responsáveis pela produção do estrógeno, hormônio que as diferencia dos machos. Após a recuperação da cirurgia os animais de ambos os grupos foram expostos ao mesmo procedimento de imunização do Grupo imprevisível e controlável do Experimento 1, o único em que foram obsevadas diferenças estatísticas entre machos e fêmeas. Os resultados mostraram aproximadamente metade das fêmeas, de ambos os grupos, aprenderam fuga apresentando latências semelhantes entre si, sugerindo que a presença ou ausência do hormônio sexual em fêmeas não foi, aparentemente, o fator determinante da diferença de gênero na imunização. Discute-se a relevância dos estudos comportamentais entre gêneros mostrando a interação de fatores ambientais com orgânicos / Studies on immunization against learned helplessness have different results when using appetitive stimuli during immunization. An analysis of these studies procedures suggests that they differ in the degree of control and predictability of the release of appetitive stimulus. Furthermore, it was shown that when the predictability of the stimulus is manipulated it produces effects that depend of the subjects sex. The objective of the present study was to evaluate : 1) if the appetitive stimuli predictability and controllability during immunization are critical variables to immunize rats against learned helplessness; and if 2) these effects are sex dependent. In parallel, we explored t some effects of hormonal variables on these behaviors. A pilot study showed no difference regarding learned helplessness in estrus and diestrus phases of the estrous cycle. Concerning immunization (Experiment 1), positive reinforcement was used combining the variables of control (VI and VT) and predictability (with or without signal preceding the availability of reinforcement), using groups (n = 16) with equal proportion of male and female rats. Then these animals were subjected to uncontrollable shock and finally to an escape test. Another group with males and females was submitted only to the last two phases and a last group only to the final phase. The results showed that sex is not an important variable concerning learned helplessness, but it interferes with the immunization against learned helplessness. Females exposed to predictable and controllable stimuli during immunization showed similar behavior with females and males of Non Shock Group. On the other hand, only half of the males exposed to predictable and controllable appetitive stimuli during immunization phase learned the escape response during the test. These results suggest that sex is a variable that needs to be better investigated in behavior experiments. In Experiment 2, females were distributed into two groups (castrated and sham), the ovaries of the animals of the first group were removed, they are responsible for the estrogen production, a hormone that differentiates males from females. After recovery from surgery, both groups were exposed to the same immunization procedure of the unpredictable and controllable group from Experiment 1, the only group that statistical differences between males and females were observed. Females in both groups showed similar escape latencies suggesting that the presence or absence of sex hormone in females was apparently not the determining factor of gender difference in immunization. It is discussed the relevance of behavioral sex differences studies showing the interaction of environmental with organic factors

Physical systems modeled by networks are fully dynamic in the sense that the process of adding edges and vertices never ends, and no edge or vertex is necessarily eternal. Temporal networks enable to explicitly study systems with a changing topology by capturing explicitly the temporal changes. The controllability of temporal networks is the study of driving the state of a temporal network to a target state at deadline t_f within △t = t_f - t₀ steps by stimulating key nodes called driver nodes. In this research, the author aims to understand and analyze temporal networks from the controllability perspective at the global and nodal scales. To analyze the controllability at global scale, the author provides an efficient heuristic algorithm to build driver node sets capable of fully controlling temporal networks. At the nodal scale, the author presents the concept of Complete Controllable Domain (CCD) to investigate the characteristics of Maximum Controllable Subspaces (MCSs) of a driver node. The author shows that a driver node can have an exponential number of MCSs and introduces a branch and bound algorithm to approximate the CCD of a driver node. The proposed algorithms are evaluated on real-world temporal networks induced from ant interactions in six colonies and in a set of e-mail communications of a manufacturing company. At the global scale, the author provides ways to determine the control regime in which a network operates. Through empirical analysis, the author shows that ant interaction networks operate under a distributed control regime whereas the e-mails network operates in a centralized regime. At the nodal scale, the analysis indicated that on average the number of nodes that a driver node always controls is equal to the number of driver nodes that always control a node. <br>

<p>I denna avhandling studeras optimal återkopplad styrning av olinjära deskriptorsystem. Ett deskriptorsystem är en matematisk beskrivning som kan innehålla både differentialekvationer och algebraiska ekvationer. En av anledningarna till intresset för denna klass av system är att objekt-orienterade modelleringsverktyg ger systembeskrivningar på denna form. Här kommer det att antas att det, åtminstone lokalt, är möjligt att eliminera de algebraiska ekvationerna och få ett system på tillståndsform. Teoretiskt är detta inte så inskränkande för genom att använda någon indexreduktionsmetod kan ganska generella deskriptor\-system skrivas om så att de uppfyller detta antagande.</p><p>För system på tillståndsform kan Hamilton-Jacobi-Bellman-ekvationen användas för att bestämma den optimala återkopplingen. Ett liknande resultat finns för deskriptor\-system där istället en Hamilton-Jacobi-Bellman-liknande ekvation ska lösas. Denna ekvation innehåller dock en extra term för att hantera de algebraiska ekvationerna. Eftersom antagandena i denna avhandling gör det möjligt att skriva om deskriptorsystemet som ett tillståndssystem, undersöks hur denna extra term måste väljas för att båda ekvationerna ska få samma lösning.</p><p>Ett problem med att beräkna den optimala återkopplingen med hjälp av Hamilton-Jacobi-Bellman-ekvationen är att det leder till att en olinjär partiell differentialekvation ska lösas. Generellt har denna ekvation ingen explicit lösning. Ett lättare problem är att beräkna en lokal optimal återkoppling. För analytiska system på tillståndsform löstes detta problem på 1960-talet och den optimala lösningen beskrivs av serieutvecklingar. I denna avhandling generaliseras detta resultat så att även deskriptor-system kan hanteras. Metoden illustreras med ett exempel som beskriver en faslåsande krets.</p><p>I många situationer vill man veta om ett område är möjligt att nå genom att styra på något sätt. För linjära tidsinvarianta system fås denna information från styrbarhetgramianen. För olinjära system används istället styrbarhetsfunktionen. Tre olika metoder för att beräkna styrbarhetsfunktionen har härletts i denna avhandling. De framtagna metoderna är också applicerade på några exempel för att visa beräkningsstegen.</p><p>Dessutom har observerbarhetsfunktionen studerats. Observerbarhetsfunktionen visar hur mycket utsignalenergi ett visst initial tillstånd svarar mot. Ett par olika metoder för att beräkna observerbarhetsfunktionen för deskriptorsystem tagits fram. För att beskriva en av metoderna, studeras ett litet exempel bestående av en elektrisk krets.</p> / <p>In this thesis, optimal feedback control for nonlinear descriptor systems is studied. A descriptor system is a mathematical description that can include both differential and algebraic equations. One of the reasons for the interest in this class of systems is that several modern object-oriented modeling tools yield system descriptions in this form. Here, it is assumed that it is possible to rewrite the descriptor system as a state-space system, at least locally. In theory, this assumption is not very restrictive because index reduction techniques can be used to rewrite rather general descriptor systems to satisfy this assumption.</p><p>The Hamilton-Jacobi-Bellman equation can be used to calculate the optimal feedback control for systems in state-space form. For descriptor systems, a similar result exists where a Hamilton-Jacobi-Bellman-like equation is solved. This equation includes an extra term in order to incorporate the algebraic equations. Since the assumptions made here make it possible to rewrite the descriptor system in state-space form, it is investigated how the extra term must be chosen in order to obtain the same solution from the different equations.</p><p>A problem when computing the optimal feedback law using the Hamilton-Jacobi-Bellman equation is that it involves solving a nonlinear partial differential equation. Often, this equation cannot be solved explicitly. An easier problem is to compute a locally optimal feedback law. This problem was solved in the 1960's for analytical systems in state-space form and the optimal solution is described using power series. In this thesis, this result is extended to also incorporate descriptor systems and it is applied to a phase-locked loop circuit.</p><p>In many situations, it is interesting to know if a certain region is reachable using some control signal. For linear time-invariant state-space systems, this information is given by the controllability gramian. For nonlinear state-space systems, the controllabilty function is used instead. Three methods for calculating the controllability function for descriptor systems are derived in this thesis. These methods are also applied to some examples in order to illustrate the computational steps.</p><p>Furthermore, the observability function is studied. This function reflects the amount of output energy a certain initial state corresponds to. Two methods for calculating the observability function for descriptor systems are derived. To describe one of the methods, a small example consisting of an electrical circuit is studied.</p> / Report code: LiU-TEK-LIC-2006:8

In this paper, by a new constructive method, the authors reprove the global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws with linearly degenerate fields. It is shown that the system with nonlinear boundary conditions is globally exactly boundary controllable in the class of piecewise C¹ functions. In particular, the authors give the optimal control time of the system. Finally, a new application is also given.

I denna avhandling studeras optimal återkopplad styrning av olinjära deskriptorsystem. Ett deskriptorsystem är en matematisk beskrivning som kan innehålla både differentialekvationer och algebraiska ekvationer. En av anledningarna till intresset för denna klass av system är att objekt-orienterade modelleringsverktyg ger systembeskrivningar på denna form. Här kommer det att antas att det, åtminstone lokalt, är möjligt att eliminera de algebraiska ekvationerna och få ett system på tillståndsform. Teoretiskt är detta inte så inskränkande för genom att använda någon indexreduktionsmetod kan ganska generella deskriptor\-system skrivas om så att de uppfyller detta antagande. För system på tillståndsform kan Hamilton-Jacobi-Bellman-ekvationen användas för att bestämma den optimala återkopplingen. Ett liknande resultat finns för deskriptor\-system där istället en Hamilton-Jacobi-Bellman-liknande ekvation ska lösas. Denna ekvation innehåller dock en extra term för att hantera de algebraiska ekvationerna. Eftersom antagandena i denna avhandling gör det möjligt att skriva om deskriptorsystemet som ett tillståndssystem, undersöks hur denna extra term måste väljas för att båda ekvationerna ska få samma lösning. Ett problem med att beräkna den optimala återkopplingen med hjälp av Hamilton-Jacobi-Bellman-ekvationen är att det leder till att en olinjär partiell differentialekvation ska lösas. Generellt har denna ekvation ingen explicit lösning. Ett lättare problem är att beräkna en lokal optimal återkoppling. För analytiska system på tillståndsform löstes detta problem på 1960-talet och den optimala lösningen beskrivs av serieutvecklingar. I denna avhandling generaliseras detta resultat så att även deskriptor-system kan hanteras. Metoden illustreras med ett exempel som beskriver en faslåsande krets. I många situationer vill man veta om ett område är möjligt att nå genom att styra på något sätt. För linjära tidsinvarianta system fås denna information från styrbarhetgramianen. För olinjära system används istället styrbarhetsfunktionen. Tre olika metoder för att beräkna styrbarhetsfunktionen har härletts i denna avhandling. De framtagna metoderna är också applicerade på några exempel för att visa beräkningsstegen. Dessutom har observerbarhetsfunktionen studerats. Observerbarhetsfunktionen visar hur mycket utsignalenergi ett visst initial tillstånd svarar mot. Ett par olika metoder för att beräkna observerbarhetsfunktionen för deskriptorsystem tagits fram. För att beskriva en av metoderna, studeras ett litet exempel bestående av en elektrisk krets. / In this thesis, optimal feedback control for nonlinear descriptor systems is studied. A descriptor system is a mathematical description that can include both differential and algebraic equations. One of the reasons for the interest in this class of systems is that several modern object-oriented modeling tools yield system descriptions in this form. Here, it is assumed that it is possible to rewrite the descriptor system as a state-space system, at least locally. In theory, this assumption is not very restrictive because index reduction techniques can be used to rewrite rather general descriptor systems to satisfy this assumption. The Hamilton-Jacobi-Bellman equation can be used to calculate the optimal feedback control for systems in state-space form. For descriptor systems, a similar result exists where a Hamilton-Jacobi-Bellman-like equation is solved. This equation includes an extra term in order to incorporate the algebraic equations. Since the assumptions made here make it possible to rewrite the descriptor system in state-space form, it is investigated how the extra term must be chosen in order to obtain the same solution from the different equations. A problem when computing the optimal feedback law using the Hamilton-Jacobi-Bellman equation is that it involves solving a nonlinear partial differential equation. Often, this equation cannot be solved explicitly. An easier problem is to compute a locally optimal feedback law. This problem was solved in the 1960's for analytical systems in state-space form and the optimal solution is described using power series. In this thesis, this result is extended to also incorporate descriptor systems and it is applied to a phase-locked loop circuit. In many situations, it is interesting to know if a certain region is reachable using some control signal. For linear time-invariant state-space systems, this information is given by the controllability gramian. For nonlinear state-space systems, the controllabilty function is used instead. Three methods for calculating the controllability function for descriptor systems are derived in this thesis. These methods are also applied to some examples in order to illustrate the computational steps. Furthermore, the observability function is studied. This function reflects the amount of output energy a certain initial state corresponds to. Two methods for calculating the observability function for descriptor systems are derived. To describe one of the methods, a small example consisting of an electrical circuit is studied. / Report code: LiU-TEK-LIC-2006:8