There is a shared desire among public and private sectors to make more reliable predictions, accurate mapping, and appropriate scaling of soil moisture and associated parameters across landscapes. A discrepancy often exists between the scale at which soil hydrologic properties are measured and the scale at which they are modeled for management purposes. Moreover, little is known about the relative importance of hydrologic modeling parameters as soil moisture fluctuates with time. More research is needed to establish which observation scales in space and time are optimal for managing soil moisture variation over large spatial extents and how these scales are affected by fluctuations in soil moisture content with time. This research fuses high resolution geoelectric and light detection and ranging (LiDAR) as auxiliary measures to support sparse direct soil sampling over a 40 hectare inner BluegrassKentucky (USA) landscape. A Veris 3100 was used to measure shallow and deep apparent electrical conductivity (aEC) in tandem with soil moisture sampling on three separate dates with ascending soil moisture contents ranging from plant wilting point to near field capacity. Terrain attributes were produced from 2010 LiDAR ground returns collected at ≤1 m nominal pulse spacing. Exploratory statistics revealed several variables best associate with soil moisture, including terrain features (slope, profile curvature, and elevation), soil physical and chemical properties (calcium, cation exchange capacity, organic matter, clay and sand) and aEC for each date. Multivariate geostatistics, time stability analyses, and spatial regression were performed to characterize scale-dependent soil moisture patterns in space with time to determine which soil-terrain parameters influence soil moisture distribution. Results showed that soil moisture variation was time stable across the landscape and primarily associated with long-range (~250 m) soil physicochemical properties. When the soils approached field capacity, however, there was a shift in relative importance from long-range soil physicochemical properties to short-range (~70 m) terrain attributes, albeit this shift did not cause time instability. Results obtained suggest soil moisture’s interaction with soil-terrain parameters is time dependent and this dependence influences which observation scale is optimal to sample and manage soil moisture variation.

Near-surface soil moisture is a key state variable of the hydrologic cycle and plays a significant role in the global water and energy balance by affecting several hydrological, ecological, meteorological, geomorphologic, and other natural processes in the land-atmosphere continuum. Presence of soil moisture in the root zone is vital for the crop and plant life cycle. Soil moisture distribution is highly non-linear across time and space. Various geophysical factors (e.g., soil properties, topography, vegetation, and weather/climate) and their interactions control the spatio-temporal evolution of soil moisture at various scales. Understanding these interactions is crucial for the characterization of soil moisture dynamics occurring in the vadose zone. This dissertation focuses on understanding the spatio-temporal variability of near-surface soil moisture and the associated physical control(s) across varying measurement support (point-scale and passive microwave airborne/satellite remote sensing footprint-scale), spatial extents (field-, watershed-, and regional-scale), and changing hydro-climates. Various analysis techniques (e.g., time stability, geostatistics, Empirical Orthogonal Function, and Singular Value Decomposition) have been employed to characterize near-surface soil moisture variability and the role of contributing physical control(s) across space and time. Findings of this study can be helpful in several hydrological research/applications, such as, validation/calibration and downscaling of remote sensing data products, planning and designing effective soil moisture monitoring networks and field campaigns, improving performance of soil moisture retrieval algorithm, flood/drought prediction, climate forecast modeling, and agricultural management practices.

Un groupe de robots collaboratifs peut gérer des tâches qui sont difficiles, voire impossibles, à accomplir par un seul. On appelle un ensemble de robots coopérant un système multi-agents (SMA). L'interaction entre agents est un facteur clé dans la commande coopérative qui pose d'importants défis théoriques et pratiques. L'une des tâches du contrôle coopératif est le consensus dont l'objectif est de concevoir des protocoles de commande afin de parvenir à un accord entre leurs états respectifs. Cette thèse améliore la navigation pour les SMA, tout en tenant compte de certaines contraintes pratiques (modèle du robot et contraintes temporelles) dans la conception de contrôleurs coopératifs pour chaque agent, de manière décentralisée. Dans cette thèse, deux directions sont étudiées. D'une part, le taux de convergence est une spécification de performance importante pour la conception du contrôleur pour un système dynamique. La convergence rapide est toujours recherchée pour améliorer les performances et la robustesse. La plupart des algorithmes de consensus existants se concentrent sur la convergence asymptotique, où le temps d'établissement est infini. Cependant, de nombreuses applications nécessitent une convergence rapide généralement caractérisée par une stratégie de commande à temps fini. De plus, la commande à temps fini autorise certaines propriétés intéressantes, mais le temps de stabilisation dépend des conditions initiales des agents. L'objectif ici est de concevoir un protocole de consensus leader-follower à temps fixe pour les SMA décrits en temps continu. Ce problème est étudié en utilisant la théorie de la stabilisation à temps fixe, qui garantit que le temps de stabilisation est borné quelles que soient les conditions initiales. Les contrôleurs et les observateurs à modes glissants sont conçus pour que chaque agent résolve le problème du consensus à temps fixe lorsque le leader est dynamique. D'autre part, par rapport aux systèmes à temps continu, le problème du consensus dans un cadre à temps discret convient mieux aux applications pratiques en raison de la limitation des ressources de calcul pour chaque agent. Le modèle de commande prédictive (MPC) permet de gérer les contraintes de commande et d'état des systèmes. Dans cette thèse, cette méthode est appliquée pour traiter le problème du consensus en temps discret en laissant chaque agent résoudre, à chaque étape, un problème de commande optimale contraint impliquant uniquement l'état des agents voisins. Les performances de suivi sont également améliorées dans cette thèse en ajoutant de nouveaux termes à partir du MPC classique. Les contrôleurs proposés sont simulés et implémentés sur un groupe composé de plusieurs robots réels en utilisant ROS (Robotic Operating System). Dans cette thèse, quelques solutions correspondant au problème de la connexion entre plusieurs robots mobiles de manière décentralisée, du réglage des périodes d'échantillonnage et des paramètres de contrôle sont également abordées. / Nowadays, robots have become increasingly important to investigate hazardous and dangerous environments. A group of collaborating robots can often deal with tasks that are difficult, or even impossible, to be accomplished by a single robot. Multiple robots working in a cooperative manner is called as a Multi-Agent System (MAS). The interaction between agents to achieve a global task is a key in cooperative control. Cooperative control of MASs poses significant theoretical and practical challenges. One of the fundamental topics in cooperative control is the consensus where the objective is to design control protocols between agents to achieve a state agreement. This thesis improves the navigation scheme for MASs, while taking into account some practical constraints (robot model and temporal constraints) in the design of cooperative controllers for each agent, in a fully decentralized way. In this thesis, two directions are investigated. On one hand, the convergence rate is an important performance specification to design the controller for a dynamical system. As an important performance measure for the coordination control of MASs, fast convergence is always pursued to achieve better performance and robustness. Most of the existing consensus algorithms focus on asymptotic convergence, where the settling time is infinite. However, many applications require a high speed convergence generally characterized by a finite-time control strategy. Moreover, finite-time control allows some advantageous properties but the settling time depend on the initial states of agents. The objective here is to design a fixed-time leader-follower consensus protocol for MASs described in continuous-time. This problem is studied using the powerful theory of fixed-time stabilization, which guarantee that the settling time is upper bounded regardless to the initial conditions. Sliding mode controllers and sliding mode observers are designed for each agent to solve the fixed-time consensus tracking problem when the leader is dynamic. On the other hand, compared with continuous-time systems, consensus problem in a discrete-time framework is more suitable for practical applications due to the limitation of computational resources for each agent. Model Predictive Control (MPC) has the ability to handle control and state constraints for discrete-time systems. In this thesis, this method is applied to deal with the consensus problem in discrete-time by letting each agent to solve, at each step, a constrained optimal control problem involving only the state of neighboring agents. The tracking performances are also improved in this thesis by adding new terms in the classical MPC technique. The proposed controllers will be simulated and implemented on a team of multiple Mini-Lab Enova Robots using ROS (Robotic Operating System) which is an operating system for mobile robots. ROS provides not only standard operating system services but also high-level functionalities. In this thesis, some solutions corresponding to problem of connection between multiple mobile robots in a decentralized way for a wireless robotic network, of tuning of the sampling periods and control parameters are also discussed.

Ce mémoire de thèse traite de la stabilité en temps fini et de la stabilisation en temps fini des systèmes dynamiques. En effet, il est souvent important de garantir que pendant le régime transitoire, les trajectoires d'état ne dépassent pas certaines limites prédéfinies afin d'éviter les saturations et l'excitation des non-linéarités du système. Un système dynamique est dit stable en temps fini FTS si, pour tout état initial appartenant à un ensemble borné prédéterminé, la trajectoire d'état reste comprise dans un autre ensemble borné prédéterminé pendant un temps fini et fixé. Lorsque le système est perturbé, on parle de bornitude en temps fini FTB. Premièrement, des nouvelles conditions suffisantes assurant la synthèse d'un correcteur FTB par retour de sortie dynamique des systèmes linéaires continus invariants perturbés ont été développées via une approche descripteur originale. Le résultat a été établi par une transformation de congruence particulière. Les conditions obtenues sont sous forme de LMIs. Deuxièmement, l'utilisation de la notion d'annulateur combinée avec le lemme de Finsler, permet d’obtenir des nouvelles conditions sous formes LMIs garantissant la stabilité et la stabilisation en temps fini des systèmes non linéaires quadratiques. Enfin, pour obtenir des conditions encore moins pessimistes dans un contexte de stabilité en temps fini, de nouveaux développements ont été proposés en utilisant des fonctions de Lyapunov polynomiales / This dissertation deals with the finite time stability and the finite time stabilization of dynamic systems. Indeed, it is often important to ensure that during the transient regime, the state trajectories do not exceed certain predefined limits in order to avoid saturations and excitations of the nonlinearities of the system. Hence the interest is to study the stability of the dynamic system in finite time. A dynamic system is said to be stable in finite time (FTS) if, for any initial state belonging to a predetermined bounded set, the state trajectory remains within another predetermined bounded set for a finite and fixed time. When the system is disturbed, it is called finite time boundedness (FTB). In this manuscript, the goal is to improve the results of finite time stability used in the literature. First, new sufficient conditions expressed in terms of LMIs for the synthesis of an FTB controller by dynamic output feedback have been developed via an original descriptor approach. An original method has been proposed which consists in using a particular congruence transformation. Second, new LMI conditions for the study of finite time stability and finite time stabilization have been proposed for disturbed and undisturbed nonlinear quadratic systems. Third, to obtain even less conservative conditions, new developments have been proposed using polynomial Lyapunov functions