Ce manuscrit est dédié à l'étude de la stabilité et la stabilisation en temps fini des systèmes dynamiques interconnectés et problème de consensus en temps fini. Après une large introduction, la première partie de ce mémoire se focalise sur la stabilité et stabilisation en temps fini des systèmes dynamiques perturbés et des systèmes dynamiques interconnectés. La deuxième partie de cette thèse est consacrée aux problèmes de : consensus en temps fini, consensus moyen en temps fini et stabilisation en temps fini des systèmes multi-agents. Cette notion a été abordé en ciblant les systèmes dynamiques contrôlés non linéaires et complexes de type avec et sans terme de dérive et affine en la commande. Des protocoles sont mis en exergue résolvant les problèmes de consensus/formation en temps fini entre les états de tels systèmes. De nombreuses applications avec des simulations permettent de confirmer les protocoles proposés. / This manuscript is dedicated to the study of finite time stability and stabilization of interconnected dynamical systems and finite time consensus problem. After a general introduction, the first part of this thesis focuses on finite time stability and stabilization of perturbed systems and interconnected systems. The second part of this thesis is devoted to the problems of: finite-time consensus, average consensus and finite time stabilization of multi-agent systems. This concept has been addressed by targeting non-linear controlled dynamical systems: with and without drift term. Some protocols are proposed to solve the finite time consensus problem. Many applications and simulations are illustrated.

Asymptotic stability is a key notion of system stability for controlled dynamical systems as it guarantees that the system trajectories are bounded in a neighborhood of a given isolated equilibrium point and converge to this equilibrium over the infinite horizon. In some applications, however, asymptotic stability is not the appropriate notion of stability. For example, for systems with a continuum of equilibria, every neighborhood of an equilibrium contains another equilibrium and a nonisolated equilibrium cannot be asymptotically stable. Alternatively, in stabilization of spacecraft dynamics via gimballed gyroscopes, it is desirable to find state- and output-feedback control laws that guarantee partial-state stability of the closed-loop system, that is, stability with respect to part of the system state. Furthermore, we may additionally require finite-time stability of the closed-loop system, that is, convergence of the system's trajectories to a Lyapunov stable equilibrium in finite time. The Hamilton-Jacobi-Bellman optimal control framework provides necessary and sufficient conditions for the existence of state-feedback controllers that minimize a given performance measure and guarantee asymptotic stability of the closed-loop system. In this research, we provide extensions of the Hamilton-Jacobi-Bellman optimal control theory to develop state-feedback control laws that minimize nonlinear-nonquadratic performance criteria and guarantee semistability, partial-state stability, finite-time stability, and finite-time partial state stability of the closed-loop system.

O presente trabalho teve por objetivo quantificar e caracterizar a variabilidade espacial e temporal da armazenagem de água no solo, do potencial mátrico, densidade de fluxo e evapotranspiração da água em um Latossolo Vermelho Amarelo Argissólico cultivado com citros. A parcela experimental constitui-se de duas transeções com 20 pontos de observação espaçados de 4,0 m, cada um deles localizado no centro da distância entre duas plantas ao longo da linha. A cultura de citros foi implantada em março de 1991 com espaçamento de 4,0 m entre plantas e 7,0 m entre linhas. Em cada ponto de observação foram instalados a) um tubo de acesso à uma sonda de nêutrons até a profundidade de 1,20 m, para a quantificação da armazenagem da água no solo, e b) três tensiômetros nas profundidades de 1,00 m, 1,10 m e 1,20 m para a quantificação do potencial mátrico e do gradiente de potencial total da água no solo. As medidas foram feitas ao longo de três anos. As medidas dos potenciais mátricos foram realizadas diariamente e as da armazenagem semanalmente. De cada ponto de observação e profundidade de 0,30 m, 0,50 m, 0,70 m, 0,90 m e 1,10 m foram coletadas amostras de solo com estrutura indeformada para a determinação da condutividade hidráulica saturada, da curva de retenção e a densidade do solo. Por meio da geoestatística, verificou-se uma dependência espacial para a armazenagem de água no solo com um alcance de 17,0 m em média e, para a densidade do solo, potencial mátrico e condutividade hidráulica saturada não se verificou estrutura de dependência espacial. A técnica da estabilidade temporal possibilita identificar no campo o ponto ou os pontos que, subestimam, superestimam ou representam a média de uma determinada variável. Pelo coeficiente de correlação de Spearman entre as datas, os valores de armazenagem e de potencial mátrico foram estáveis no tempo; para a armazenagem de água no solo, a correlação foi maior no período de recarga e, para o potencial mátrico, os coeficientes de correlação foram maiores para os períodos de secagem, ou seja, a estabilidade temporal foi maior para o os períodos de secagem. Por meio da diferença relativa foi possível identificar no estudo da estabilidade temporal, os pontos que mais se aproximaram da média que foram: o ponto 29 nos três anos, para a armazenagem de água no solo, pontos 24, 13 e 11 para o potencial mátrico da água no solo nos anos 1, 2 e 3, respectivamente. Por meio do balanço hídrico, verificou-se um consumo da água pela cultura de citros (evapotranspiração real) de 1.340 mm (consumo médio diário de 3,49 mm) e uma perda por drenagem interna que correspondeu a 10 %, em média nos três anos, da precipitação, para o solo e cultura em estudo. / The objective of the present work was to quantify and characterize spatial and temporal variability of water storage, matric potential, water flux density and actual evapotranspiration in an oxisol cropped to citrus. The experimental plot consisted of two transects with 20 observation points in a spacing of four meters. Each observation point was located in the central distance between two plants in the plant line. The citrus crop was installed in March of 1991 in a spacing of 4 x 7 m (four meters among plants in the line and seven meters among lines). In each observation point were installed a) one aluminiun tube to access a neutron probe till the depth of 1.2 m to determine water storage in the 0-1.2 m soil profile and b) three tensiometers at the depths of 1.0, 1.1 and 1.2 m to determine soil matric potential and soil water total potential gradient at the depth of 1.1 m then to calculated soil water flux density at the 1.1 m soil depth by means of Darcy-Buckingham equation. Measurements were made during three years, those of matric potential, dayly, and those of soil water content, weekly. In each observation point, undisturbed soil samples were removed from 0.3, 0.5, 0.7, 0.9 e 1.1 m soil depths to determine saturated soil hydraulic conductivity, soil water retention curve and soil bulk density. By means of geostatistical techniques, spatial dependence for soil water storage was verified with a range of 17 m in average. It was observed time stability for both soil water storage and matric potential that from the Spearman rank coefficients among dates. For the soil water storage, this coefficient showed higher values during the recharge period, that this, time stability for soil water storage was higher during the recharge period. For the matric potential occurred the inverse: time stability was higher during the drying period. By means of the relative difference from the mean, in the time stability study the following points closer were to the mean: point 29 (for the three years) for soil water storage and points 24, 13 and 11 for soil water matric potential for years 1, 2 and 3, respectively. By means of the soil water storage methodology, it was quantified a water consumption (actual evapotranspiration) for the citrus crop of 1,340 mm (daily average value of 3.49 mm) and a water loss by internal drainage that corresponded to 10 % in average, for the three years of experiment.

Considered in this research is a framework for effective formation control of multirobot systems in dynamic environments. The basic formation control involves two important considerations: (1) Real-time trajectory generation algorithms for distributed control based on nominal agent models, and (2) robust tracking of reference trajectories under model uncertainties. Proposed is a two-layer hierarchical architecture for collectivemotion control ofmultirobot nonholonomic systems. It endows robotic systems with the ability to simultaneously deal with multiple tasks and achieve typical complex formation missions, such as collisionfree maneuvers in dynamic environments, tracking certain desired trajectories, forming suitable patterns or geometrical shapes, and/or varying the pattern when necessary. The study also addresses real-time formation tracking of reference trajectories under the presence of model uncertainties and proposes robust control laws such that over each time interval any tracking errors due to system uncertainties are driven down to zero prior to the commencement of the subsequent computation segment. By considering a class of nonlinear systems with favorable finite-time convergence characteristics, sufficient conditions for exponential finite-time stability are established and then applied to distributed formation tracking controls. This manifests in the settling time of the controlled system being finite and no longer than the predefined reference trajectory segment computing time interval, thus making tracking errors go to zero by the end of the time horizon over which a segment of the reference trajectory is generated. This way the next segment of the reference trajectory is properly initialized to go into the trajectory computation algorithm. Consequently this could lead to a guarantee of desired multi-robot motion evolution in spite of system uncertainties. To facilitate practical implementation, communication among multi-agent systems is considered to enable the construction of distributed formation control. Instead of requiring global communication among all robots, a distributed communication algorithm is employed to eliminate redundant data propagation, thus reducing energy consumption and improving network efficiency while maintaining connectivity to ensure the convergence of formation control.

O presente trabalho teve por objetivo quantificar e caracterizar a variabilidade espacial e temporal da armazenagem de água no solo, do potencial mátrico, densidade de fluxo e evapotranspiração da água em um Latossolo Vermelho Amarelo Argissólico cultivado com citros. A parcela experimental constitui-se de duas transeções com 20 pontos de observação espaçados de 4,0 m, cada um deles localizado no centro da distância entre duas plantas ao longo da linha. A cultura de citros foi implantada em março de 1991 com espaçamento de 4,0 m entre plantas e 7,0 m entre linhas. Em cada ponto de observação foram instalados a) um tubo de acesso à uma sonda de nêutrons até a profundidade de 1,20 m, para a quantificação da armazenagem da água no solo, e b) três tensiômetros nas profundidades de 1,00 m, 1,10 m e 1,20 m para a quantificação do potencial mátrico e do gradiente de potencial total da água no solo. As medidas foram feitas ao longo de três anos. As medidas dos potenciais mátricos foram realizadas diariamente e as da armazenagem semanalmente. De cada ponto de observação e profundidade de 0,30 m, 0,50 m, 0,70 m, 0,90 m e 1,10 m foram coletadas amostras de solo com estrutura indeformada para a determinação da condutividade hidráulica saturada, da curva de retenção e a densidade do solo. Por meio da geoestatística, verificou-se uma dependência espacial para a armazenagem de água no solo com um alcance de 17,0 m em média e, para a densidade do solo, potencial mátrico e condutividade hidráulica saturada não se verificou estrutura de dependência espacial. A técnica da estabilidade temporal possibilita identificar no campo o ponto ou os pontos que, subestimam, superestimam ou representam a média de uma determinada variável. Pelo coeficiente de correlação de Spearman entre as datas, os valores de armazenagem e de potencial mátrico foram estáveis no tempo; para a armazenagem de água no solo, a correlação foi maior no período de recarga e, para o potencial mátrico, os coeficientes de correlação foram maiores para os períodos de secagem, ou seja, a estabilidade temporal foi maior para o os períodos de secagem. Por meio da diferença relativa foi possível identificar no estudo da estabilidade temporal, os pontos que mais se aproximaram da média que foram: o ponto 29 nos três anos, para a armazenagem de água no solo, pontos 24, 13 e 11 para o potencial mátrico da água no solo nos anos 1, 2 e 3, respectivamente. Por meio do balanço hídrico, verificou-se um consumo da água pela cultura de citros (evapotranspiração real) de 1.340 mm (consumo médio diário de 3,49 mm) e uma perda por drenagem interna que correspondeu a 10 %, em média nos três anos, da precipitação, para o solo e cultura em estudo. / The objective of the present work was to quantify and characterize spatial and temporal variability of water storage, matric potential, water flux density and actual evapotranspiration in an oxisol cropped to citrus. The experimental plot consisted of two transects with 20 observation points in a spacing of four meters. Each observation point was located in the central distance between two plants in the plant line. The citrus crop was installed in March of 1991 in a spacing of 4 x 7 m (four meters among plants in the line and seven meters among lines). In each observation point were installed a) one aluminiun tube to access a neutron probe till the depth of 1.2 m to determine water storage in the 0-1.2 m soil profile and b) three tensiometers at the depths of 1.0, 1.1 and 1.2 m to determine soil matric potential and soil water total potential gradient at the depth of 1.1 m then to calculated soil water flux density at the 1.1 m soil depth by means of Darcy-Buckingham equation. Measurements were made during three years, those of matric potential, dayly, and those of soil water content, weekly. In each observation point, undisturbed soil samples were removed from 0.3, 0.5, 0.7, 0.9 e 1.1 m soil depths to determine saturated soil hydraulic conductivity, soil water retention curve and soil bulk density. By means of geostatistical techniques, spatial dependence for soil water storage was verified with a range of 17 m in average. It was observed time stability for both soil water storage and matric potential that from the Spearman rank coefficients among dates. For the soil water storage, this coefficient showed higher values during the recharge period, that this, time stability for soil water storage was higher during the recharge period. For the matric potential occurred the inverse: time stability was higher during the drying period. By means of the relative difference from the mean, in the time stability study the following points closer were to the mean: point 29 (for the three years) for soil water storage and points 24, 13 and 11 for soil water matric potential for years 1, 2 and 3, respectively. By means of the soil water storage methodology, it was quantified a water consumption (actual evapotranspiration) for the citrus crop of 1,340 mm (daily average value of 3.49 mm) and a water loss by internal drainage that corresponded to 10 % in average, for the three years of experiment.

O objetivo do presente trabalho foi estudar a variabilidade espacial dos parâmetros da equação da condutividade hidráulica determinada no campo em função do conteúdo de água no solo, pelo método do perfil instantâneo, e avaliar a estabilidade temporal da armazenagem da água no solo, com vistas a identificação de um local de amostragem ótimo para a determinação da densidade de fluxo da água pela equação de Darcy-Buckingham. O estudo foi desenvolvido num Latossolo Vermelho Amarelo, textura areno-argiloso, em área experimental do Campus "Luiz de Queiroz", Universidade de São Paulo, município de Piracicaba, Estado de São Paulo, Brasil. Suas coordenadas geográficas são: 22° 42’ 43,3’’ de latitude sul, 47° 37’ 10,4’’ de longitude oeste e 456 m de altitude. A parcela experimental apresentava um comprimento de 45 m e uma largura de 15 m, na qual foram instalados 40 tubos de alumínio para acesso de uma sonda de nêutrons para medida do conteúdo da água no solo nas profundidades 0,20 m; 0,40 m; 0,60 m; 0,80 m e 1,00 m e cálculo da armazenagem da água no perfil 0- 1,0 m. A distribuição desses tubos foi feita na forma de uma grade de quatro colunas por dez linhas, com cada tubo distando de seu vizinho de 5 m. As funções K(θ) nos 40 pontos foram determinadas a partir das análises de regressão de θ em função de lnt e hz em função de lnt, durante o processo de redistribuição da água no solo. De posse das 40 funções K(θ) nas cinco profundidades estudadas, foram aplicadas as técnicas geoestatitisticas para o estudo da variabilidade espacial dos parâmetros θ0, K0 e γ da função. Foi realizada também a análise da estabilidade temporal da armazenagem da água no solo, ao longo do período de redistribuição da água no solo para verificar quais e quantos são os locais adequados para o monitoramento da água precisão aceitável e reduzido esforço amostral. Pelos resultados obtidos, pôde-se concluir que: a) os métodos geoestatísticos utilizados foram adequados para descrever a estrutura de dependência espacial dos parâmetros da relação da condutividade hidráulica em função da umidade do solo: θ0 , K0 e γ; b) para as três variáveis estudadas ( θ0 , K0 e γ) houve estrutura de dependência espacial dos parâmetros na escala utilizada com alcances máximos de 8,33, 19,09 e 10,35 m; c) a técnica da estabilidade temporal que possibilita identificar, no campo, o ponto, ou os pontos, que representam a média e os pontos que superestimam ou subestimam a média real de determinada variável, identificou, para os valores de armazenagem da água no solo do presente estudo, os pontos 19, 20 e 21 como os mais representativos da média geral do campo; d) a metodologia com base nos coeficientes de correlação de Spearman também permitiu concluir que os valores de armazenagem da água no solo, foram estáveis no tempo, para os 40 pontos amostrados. Palavras-chave: perfil instantâneo, estabilidade temporal, sonda de nêutrons, armazenagem / The objective of this work was to study the spatial variability of the parameters of the hydraulic conductivity equation determined in the field as a function of soil water content, by the instantaneous profile method, and to evaluate the soil water storage time stability, in order to identify a sampling location for the determination of soil water flux by means of Darcy-Buckingham equation. The study was carried out in a clay sandy Oxisol in the country of Piracicaba, State of São Paulo, Brazil (22º42’ 43,3’’ S, 47° 37’ 10,4’’ W, 546 m). The dimensions of the experimental plot were 45 m x 15 m in wich 40 aluminium tubes were installed to acess a neutron probe to measure the soil water content at the depths of 0.2, 0.4, 0.6, 0.8 and 1.0 m and, then, calculate the soil water storage of the 0 - 1.0 m soil layer. The distribution of these tubes were made in grid of four columns by ten lines in spacing of 5m x 5m. The Kθ functions were determined in the 40 points from regression analyses of θ as function lnt and hz as a function of lnt, being K the hydraulic conductivity, θ the volumetric soil water content, z h the soil water storage in the 0 - Z m layer and t the soil water redistribution time. With the 40 Kθ functions in the five studied soil depths, geostatistical techniques were used to evaluate the spatial variability of the parameters 0 θ , 0 K and γ of the function ( ) [ ] 0 0 exp θ θ γ − = K K , where the subindex o means lnt = 0. Soil water storage time stability analysis were also carried out along the soil water redistribution period in order to verify which and how many are the adequate locations for water monitoring with acceptable precisi on and reduced sample effort. From the results, the follwing could conclude: (i) the used geostatistical methods were adequate to described the spatial dependence structure of the parameters θ0 , Kθ0 and γ; (ii) there were a spatial dependence structure of the parameters in the used scale with maximum ranges of 8.33, 19.09 and 10.35 m; (iii) from the time stability technique, it was possible to identify the points 19,20 and 21 as the more representative of the field overall mean; (iv) the rank Spearmam coefficients also showed that the soil water storage of the 40 sampled points were in the time.

O objetivo do presente trabalho foi estudar a variabilidade espacial dos parâmetros da equação da condutividade hidráulica determinada no campo em função do conteúdo de água no solo, pelo método do perfil instantâneo, e avaliar a estabilidade temporal da armazenagem da água no solo, com vistas a identificação de um local de amostragem ótimo para a determinação da densidade de fluxo da água pela equação de Darcy-Buckingham. O estudo foi desenvolvido num Latossolo Vermelho Amarelo, textura areno-argiloso, em área experimental do Campus "Luiz de Queiroz", Universidade de São Paulo, município de Piracicaba, Estado de São Paulo, Brasil. Suas coordenadas geográficas são: 22° 42’ 43,3’’ de latitude sul, 47° 37’ 10,4’’ de longitude oeste e 456 m de altitude. A parcela experimental apresentava um comprimento de 45 m e uma largura de 15 m, na qual foram instalados 40 tubos de alumínio para acesso de uma sonda de nêutrons para medida do conteúdo da água no solo nas profundidades 0,20 m; 0,40 m; 0,60 m; 0,80 m e 1,00 m e cálculo da armazenagem da água no perfil 0- 1,0 m. A distribuição desses tubos foi feita na forma de uma grade de quatro colunas por dez linhas, com cada tubo distando de seu vizinho de 5 m. As funções K(θ) nos 40 pontos foram determinadas a partir das análises de regressão de θ em função de lnt e hz em função de lnt, durante o processo de redistribuição da água no solo. De posse das 40 funções K(θ) nas cinco profundidades estudadas, foram aplicadas as técnicas geoestatitisticas para o estudo da variabilidade espacial dos parâmetros θ0, K0 e γ da função. Foi realizada também a análise da estabilidade temporal da armazenagem da água no solo, ao longo do período de redistribuição da água no solo para verificar quais e quantos são os locais adequados para o monitoramento da água precisão aceitável e reduzido esforço amostral. Pelos resultados obtidos, pôde-se concluir que: a) os métodos geoestatísticos utilizados foram adequados para descrever a estrutura de dependência espacial dos parâmetros da relação da condutividade hidráulica em função da umidade do solo: θ0 , K0 e γ; b) para as três variáveis estudadas ( θ0 , K0 e γ) houve estrutura de dependência espacial dos parâmetros na escala utilizada com alcances máximos de 8,33, 19,09 e 10,35 m; c) a técnica da estabilidade temporal que possibilita identificar, no campo, o ponto, ou os pontos, que representam a média e os pontos que superestimam ou subestimam a média real de determinada variável, identificou, para os valores de armazenagem da água no solo do presente estudo, os pontos 19, 20 e 21 como os mais representativos da média geral do campo; d) a metodologia com base nos coeficientes de correlação de Spearman também permitiu concluir que os valores de armazenagem da água no solo, foram estáveis no tempo, para os 40 pontos amostrados. Palavras-chave: perfil instantâneo, estabilidade temporal, sonda de nêutrons, armazenagem / The objective of this work was to study the spatial variability of the parameters of the hydraulic conductivity equation determined in the field as a function of soil water content, by the instantaneous profile method, and to evaluate the soil water storage time stability, in order to identify a sampling location for the determination of soil water flux by means of Darcy-Buckingham equation. The study was carried out in a clay sandy Oxisol in the country of Piracicaba, State of São Paulo, Brazil (22º42’ 43,3’’ S, 47° 37’ 10,4’’ W, 546 m). The dimensions of the experimental plot were 45 m x 15 m in wich 40 aluminium tubes were installed to acess a neutron probe to measure the soil water content at the depths of 0.2, 0.4, 0.6, 0.8 and 1.0 m and, then, calculate the soil water storage of the 0 - 1.0 m soil layer. The distribution of these tubes were made in grid of four columns by ten lines in spacing of 5m x 5m. The Kθ functions were determined in the 40 points from regression analyses of θ as function lnt and hz as a function of lnt, being K the hydraulic conductivity, θ the volumetric soil water content, z h the soil water storage in the 0 - Z m layer and t the soil water redistribution time. With the 40 Kθ functions in the five studied soil depths, geostatistical techniques were used to evaluate the spatial variability of the parameters 0 θ , 0 K and γ of the function ( ) [ ] 0 0 exp θ θ γ − = K K , where the subindex o means lnt = 0. Soil water storage time stability analysis were also carried out along the soil water redistribution period in order to verify which and how many are the adequate locations for water monitoring with acceptable precisi on and reduced sample effort. From the results, the follwing could conclude: (i) the used geostatistical methods were adequate to described the spatial dependence structure of the parameters θ0 , Kθ0 and γ; (ii) there were a spatial dependence structure of the parameters in the used scale with maximum ranges of 8.33, 19.09 and 10.35 m; (iii) from the time stability technique, it was possible to identify the points 19,20 and 21 as the more representative of the field overall mean; (iv) the rank Spearmam coefficients also showed that the soil water storage of the 40 sampled points were in the time.

L’étude des variations temporelles de gravité ont une longue tradition en Europe Centrale. Dans la station, J9, située à Strasbourg depuis les années 1970, les trois principaux types de gravimètre (ressort, supraconducteur (SG), absolu) ont été utilisés. Ces séries permettent l’examen des améliorations instrumentales à partir de la stabilité à long terme et de la dérive instrumentale. Nous montrons que le SG est l’instrument le plus performant pour l’étude des marées de longues périodes et de faibles amplitudes. Nous montrons les résultats obtenus par analyse de marée de ces petites ondes. Nous estimons la période de la Free Core Nutation et nous recherchons celle de la Free Inner Core Nutation (FICN), qui n'a pas encore été observée. Pour cela nous faisons une étude précise, afin de séparer les ondes de faible amplitude, au voisinage de périodes possibles de la FICN. / The study of temporal variations of gravity has a long tradition in Central Europe. Since the 1970s three main gravimeter types (spring, superconducting (SG) and absolute) have been set up at the J9 gravity station located in Strasbourg. These series allow us to review the instrumental improvements from the analyses of long term stability and instrumental drift. We show that the SG is the most powerful tool for thestudy of the low frequency and small amplitudes tides. We show the tidal analysis results for these tidal waves. We estimate the period of the Free Core Nutation and we seek the one of the Free Inner Core Nutation (FICN), which has not yet been observed. For this we make a careful study, in order to separate the low-amplitude waves in the vicinity of possible periods of FICN. / La deformación elasto-gravitacional de la Tierra y las correspondientes variaciones temporales de la gravedad asociadas, registradas en la superficie terrestre mediante los gravímetros, son debidas a distintos fenómenos geofísicos con diferentes períodos y amplitudes, incluyendo entre otros a las denominadas mareas terrestres, que son el fenómeno que genera los efectos más fuertes (dichas mareas terrestres son los movimientos inducidos en la Tierra sólida y los cambios en su potencial gravitatorio derivados de las fuerzas de marea generadas por los cuerpos celestes).El objetivo principal de este trabajo consiste en mostrar la importancia tanto de la longitud de las series de datos de gravedad, como de la calidad de dichas series para mejorar nuestro conocimiento sobre la dinámica de la Tierra a través de los análisis de las mareas terrestres. [...]

The contributions of this thesis lie in the area of global finite-time observer design for a class of nonlinear systems with bounded rational and mixed rational powers imposed on the incremental rate of the nonlinear terms whose solutions exist and are unique for all positive time. In the thesis, two different kinds of nonlinear global finite-time observers are designed by employing of finite-time theory and homogeneity properties with different methods. The global finite-time stability of both proposed observers is derived on the basis of Lyapunov theory. For a class of nonlinear systems with rational and mixed rational powers imposed on the nonlinearities, the first global finite-time observers are designed, where the global finite-time stability of the observation systems is achieved from two parts by combining asymptotic stability and local finitetime stability. The proposed observers can only be designed for the class of nonlinear systems with dimensions greater than 3. The observers have a dynamic high gain and two homogenous terms, one homogeneous of degree greater than 1 and the other of degree less than 1. In order to prove the global finite-time stability of the proposed results, two homogeneous Lyapunov functions are provided, corresponding with the two homogeneous items. One is homogeneous of degree greater than 1, which makes the observation error systems converging into a spherical area around the origin, and the other is of degree less than 1, which ensures local finite-time stability. The second global finite-time observers are also proposed based on the high-gain technique, which does not place any limitation on the dimension of the nonlinear systems. Compared with the first global finite-time observers, the newly designed observers have only one homogeneous term and a new gain update law where two new terms are introduced to dominate some terms in the nonlinearities and ensure global finite-time stability as well. The global finite-time stability is obtained directly based on a sufficient condition of finite-time stability and only one Lyapunov function is employed in the proof. The validity of the two kinds of global finite-time observers that have been designed is illustrated through some simulation results. Both of them can make the observation error systems converge to the origin in finite-time. The parameters, initial conditions as well as the high gain do have some impact on the convergence time, where the high gain plays a stronger role. The bigger the high gain is, the shorter the time it needs to converge. In order to show the performance of the two kinds of observers more clearly, two examples are provided and some comparisons are made between them. Through these, it can be seen that under the same parameters and initial conditions, although the amplitude of the observation error curve is slightly greater, the global finite-time observers with a new gain update law can make the observation error systems converge much more quickly than the global finite-time observers with two homogeneous terms. In the simulation results, one can see that, as a common drawback of high gain observers, they are noise-sensitive. Finding methods to improve their robustness and adaptiveness will be quite interesting, useful and challenging. / Thesis (PhD)--University of Pretoria, 2013. / gm2014 / Electrical, Electronic and Computer Engineering / unrestricted

L’objectif principal de cette thèse est d’étudier le problème du contrôle de suivi distribué pour les systèmes de formation de multi-robots à contrainte non holonomique. Ce contrôle vise à entrainer une équipe de robots mobile de type monocycle pour former une configuration de formation désirée avec son centroïde se déplaçant avec une autre trajectoire de référence dynamique et pouvant être spécifié par le leader virtuel ou humain. Le problème du contrôle de suivi a été résolu au cours de cette thèse en développant divers contrôleurs distribués pratiques avec la considération d’un taux de convergence plus rapide, une précision de contrôle plus élevée, une robustesse plus forte, une estimation du temps de convergence explicite et indépendante et moins de coût de communication et de consommation d’énergie. Dans la première partie de la thèse nous étudions d’abord au niveau du chapitre 2 la stabilité à temps fini pour les systèmes de formation de multi-robots. Une nouvelle classe de contrôleur à temps fini est proposée dans le chapitre 3, également appelé contrôleur à temps fixe. Nous étudions les systèmes dynamiques de suivi de formation de multi-robots non holonomiques dans le chapitre 4. Dans la deuxième partie, nous étudions d'abord le mécanisme de communication et de contrôle déclenché par l'événement sur les systèmes de suivi de la formation de multi-robots non-holonomes au chapitre 5. De plus, afin de développer un schéma d'implémentation numérique, nous proposons une autre classe de contrôleurs périodiques déclenchés par un événement basé sur un observateur à temps fixe dans le chapitre 6. / The main aim of this thesis is to study the distributed tracking control problem for the multi-robot formation systems with nonholonomic constraint, of which the control objective it to drive a team of unicycle-type mobile robots to form one desired formation configuration with its centroid moving along with another dynamic reference trajectory, which can be specified by the virtual leader or human. We consider several problems in this point, ranging from finite-time stability andfixed-time stability, event-triggered communication and control mechanism, kinematics and dynamics, continuous-time systems and hybrid systems. The tracking control problem has been solved in this thesis via developing diverse practical distributed controller with the consideration of faster convergence rate, higher control accuracy, stronger robustness, explicit and independent convergence time estimate, less communication cost and energy consumption.In the first part of the thesis, we first study the finite-time stability for the multi-robot formation systems in Chapter 2. To improve the pior results, a novel class of finite-time controller is further proposed in Chapter 3, which is also called fixed-time controller. The dynamics of nonholonomic multi-robot formation systems is considered in Chapter 4. In the second part, we first investigate the event-triggered communication and control mechanism on the nonholonomic multi-robot formation tracking systems in Chapter 5. Moreover, in order to develop a digital implement scheme, we propose another class of periodic event-triggered controller based on fixed-time observer in Chapter 6.