In this paper, an innovative cooperative navigation method is proposed for multiple Unmanned Air Vehicles (UAVs) based on online target position measurements. These noisy position measurement signals are used to estimate the target's velocity for non-maneuvering targets or the target's velocity and acceleration for maneuvering targets. The estimator's tracking capability is physically constrained due to the target's kinematic limitations and therefore is potentially improvable by designing a higher performance estimator. An H-infinity filter is implemented to increase the robustness of the estimation accuracy. The performance of the robust estimator is compared to a Kalman filter and the results illustrate more precise estimation of the target's motion in compensating for surrounding noises and disturbances. Furthermore, an adaptive guidance algorithm, based on the seeker's field-of-view and linear region, is used to deliver the pursuer to the maneuvering target. The initial guidance algorithm utilizes the velocity pursuit guidance law because of its insensitivity to target motion; while the terminal guidance algorithm leverages the acceleration estimates (from the H-infinity filter) to augment the proportional navigation guidance law for increased accuracy in engaging maneuvering targets. The main objective of this work is to develop a robust estimator/tracker and an adaptive guidance algorithm which are directly applicable UAVs.

This thesis explores the use and accuracy of several discrete-time image filters for the purpose of target tracking in Synthetic Aperture Radar imagery. Both extended targets and point targets are used for tracking, showing the need for different types of filters for each target type. Monte Carlo analysis is performed on the results of the extended target filter results to determine the absolute mean-squared error between the filter prediction of the target centroid and the actual location of the target centroid. Two different filters were chosen for the extended target: Kalman and H Infinity. Both the Kalman and H Infinity filters perform tracking by accurately estimating the state of the dynamic system, and in some cases it may be useful to simulate a situation when a target temporarily disappears from radar view. The ability of both filters to predict target location with no input measurements is investigated. A unique trait of the H Infinity filter is its ability to accurately and efficiently estimate the state of a dynamic system given no information about the noise environment. To simulate more realistic targets, smaller circular and square targets are created and a sensitivity analysis is performed using the Kalman and H Infinity filters to determine the shortfalls of these filter techniques as targets become smaller and smaller. The results indicate that these tracking methods are no longer useful as the targets become so small that they approach being only a single pixel in size. A new filter called the Prediction and Matching Detection (PAMD) filter is used for single-pixel point targets. This filter illustrates the importance of having very high frame rate images with little change in velocity over consecutive frames if choosing to use the PAMD algorithm. The PAMD filter is extended to track more than one target at a time. Tracking of raw SAR data is preferred over post-processed images due to the decreased amount of processing time. The Kalman and H Infinity filters are implemented to track raw radar data during its first 3 seconds of motion in 2-dimensions by accounting for the measurements of two parameters: the squint angle and slant range. Noise is added to the measurements to simulate platform inaccuracies. The project is a continuation of prior SAR research at Cal Poly under Dr. John Saghri with the sponsorship of Raytheon Space & Airborne Systems.

The role of infinity as an antagonist in Jorge Luis Borges's oeuvre is undeniable. His stories in El jardi­n de senderos que se bifurcan (1941), Ficciones (1944), and El Aleph (1949) exhibit Borges's tendency to evoke dreams, labyrinths, mirrors, and libraries as both conduits for infinity and sources of conflict. Oftentimes, Borges's characters experience discomfort upon encountering the limitations of secular temporal succession. This discomfort is rooted in Borges's pessimism about the subject which is explored in Borges's most comprehensive essay on the issue of time: "A New Refutation of Time." Consequently, this thesis considers Borges's attitude towards the issue of time as postulated in "A New Refutation of Time" and exhibited in his early fiction, continues to acknowledge infinity as a fundamental conflict in Borges's work, and proceeds to search for a solution to this conflict. The analysis in this thesis relies heavily on a comparative study of the themes and symbols in Borges's fiction in order to establish a pattern wherein infinity is portrayed negatively. More importantly, the use of interviews, biographies, and Borges's own fiction, facilitates the construction of cohesive conception of time in his work. Subsequently, this study looks to establish a solution to the problem of infinity and establish a new pattern wherein there is a positive resolution to the narrative. Ultimately, the goal of this thesis is to acknowledge the problem of infinity in Borges's work and then propose a way to escape it.

<p dir="ltr">The concept of infinity plays a pivotal role in mathematics, yet its precise definition remains elusive. This conceptual ambiguity has given rise to several puzzles in contemporary philosophy of mathematics. In response, this dissertation embarks on a rational reconstruction of Hegels concept of infinity and applies it to resolve two groups of mathematical puzzles, including challenges in applied mathematics, especially the application of differential calculus, and the conceptual ground of set theory, especially Cantors paradox.</p><p dir="ltr">The exploration begins with a historical survey of the concept of infinity in philosophy. It becomes evident that a prevailing interpretation characterizes infinity as the unlimited. In addition, this unlimitedness has taken various forms, including endlessness (Aristotle), all-inclusiveness (Spinoza), and self-sufficiency (Kant).</p><p dir="ltr">The heart of the dissertation lies in reconstructing Hegels concept of genuine infinity. Hegel argues that the unlimited as the negation of the limit entails either the completely indeterminate or another limited entity, neither of which is genuinely infinite. Instead, Hegel points out that genuine infinity is the self-relation of a limited entity. By self-relation, Hegel means that the limited entity alters into another limited entity that is isomorphic to the original one.</p><p dir="ltr">Subsequently, Hegel’s concept of genuine infinity can be translated into a mathematical framework as the intrinsic alteration of quantum (roughly speaking, quantum is Hegel’s term for the variable), which is captured by the corresponding relation among quanta. It is argued that this relation serves as the necessary condition for three mathematical entities traditionally considered infinite: arbitrarily large (small) numbers, infinite sets, and endless sequences. Thus, for Hegel, this intrinsic relation among quanta constitutes the essence of mathematical infinity.</p><p dir="ltr">Hegels concept of mathematical infinity can help us resolve difficulties within contemporary mathematics. First, it addresses the question of why infinite mathematical structures can be applied to describe and predict seemingly finite physical phenomena. The application of mathematics is usually explained by the similarity between mathematical structures and empirical systems, but the lack of apparent empirical counterpart leads one to doubt the application of infinite mathematical structures. Hegels concept of mathematical infinity directs us to focus on the structural similarity between infinite mathematical structures and empirical systems, specifically between the intrinsic alteration of quantum and the change of physical properties with time. With this structural similarity, the application of mathematics can be explained. Second, the dissertation investigates the conceptual ground of set theory, especially the relationship between a set and its members. Hegels analysis of genuine infinity provides a twofold clarification: (1) members of set must be a unit first, which entails that the set of all sets (the Universe) is not a set; (2) members of a set are simultaneously distinct (due to their independent logical content) yet indistinguishable (due to their common structure as a unit). Clarification 1 resolves Cantors paradox as it excludes the Universe; clarification 2 explains arithmetic operations.</p>

Due to increasingly difficult threats, current air defense missile systems are pushed to the limits of their performance capabilities. In order to defend against these more stressing threats, interceptor missiles require greater maneuverability, faster response time, and increased robustness to more severe environmental conditions. One of the most critical missile system elements is the flight control system, since its time constant is typically half of the total missile system time constant. Conventional autopilot design techniques have worked well in the past, but in order to satisfy future and more stringent design specifications, new design methods are necessary. Robust control techniques (in particular, H-Infinity Control and Mu-Synthesis) and their application to the design of missile autopilots are addressed in this thesis. In addition, conventional autopilot designs are performed as comparative benchmarks. This paper reviews the missile autopilot design problem and presents descriptions of the classical and H-Infinity/Mu design methods. Missile autopilot designs considering both rigid-body dynamics and elastic-body dynamics are presented. Comparisons of the design approaches and results are also discussed. The results show that the application of robust control techniques to the design of missile autopilots can improve the performance and stability robustness characteristics of the flight control system. / Master of Science

In this dissertation, we seek to improve the dynamic modeling and control of autonomous underwater vehicles (AUVs). We address nonlinear hydrodynamic modeling, simplifying modeling assumptions, and robust control for AUVs. In the literature, various hydrodynamic models exist with varying model complexity and with no universally accepted model. We compare various hydrodynamic models traditionally employed to predict the motion of AUVs by estimating model coefficients using least-squares and adaptive identifier techniques. Additionally, we derive several dynamic models for an AUV employing varying sets of simplifying assumptions. We experimentally assess the efficacy of invoking typical assumptions to simplify the equations of motion. For robust control design, we develop a procedure for designing robust attitude controllers based on loop-shaping ideas. We specifically address the challenge of adjusting the desired actuator bandwidth in a loop-shaping design framework. Finally, we present a novel receding horizon H-infinity control algorithm to improve the control of autonomous vehicle systems working in high-disturbance environments, employing a Markov jump linear system framework to model the stochastic and non-stationary disturbances experienced by the vehicle. Our main results include a new Bounded Real Lemma for stability analysis and an output feedback H-infinity control synthesis algorithm. This work uses numerical simulations and extensive field trials of autonomous underwater vehicles to identify and verify dynamic models and to validate control algorithms developed herein. / Ph. D. / In this dissertation, we seek to improve the dynamic modeling and control of autonomous underwater vehicles (AUVs). We compare different models employed to predict the motion of AUVs, and we derive several dynamic models for an AUV employing varying sets of simplifying assumptions. We experimentally assess the efficacy of invoking typical assumptions to simplify the equations of motion. For robust control design, we develop a procedure for designing robust controllers that do not produce excessive fin movements. Finally, we present a novel robust control algorithm to improve the control of autonomous vehicle systems working in high-disturbance environments. This work uses numerical simulations and extensive field trials of autonomous underwater vehicles to identify and verify dynamic models and to validate control algorithms developed herein.

This thesis describes the design of an inexpensive autonomous vehicle system using a small scaled model vehicle. The system is capable of operating in two different modes: telerobotic manual mode and automated driving mode. In telerobotic manual mode, the model vehicle is controlled by a human driver at a stationary remote control station with full-scale steering wheel and gas pedal. The vehicle can either be an unmodified toy remote-control car or a vehicle equipped with wireless radio modem for communication and microcontroller for speed control. In both cases the vehicle also carries a video camera capable of transmitting video images back to the remote control station where they are displayed on a monitor. In automated driving mode, the vehicle's lateral movement is controlled by a lateral control algorithm. The objective of this algorithm is to keep the vehicle in the center of a road. Position and orientation of the vehicle are determined by an image processing algorithm identifying a white middle marker on the road. Two different algorithm for image processing have been designed: one based on the pixel intensity profile and the other on vanishing points in the image plane. For the control algorithm itself, two designs are introduced as well: a simple classical P-control and a control scheme based on H-Infinity. The design and testing of this autonomous vehicle system are performed in the Flexible Low-cost Automated Scaled Highway (FLASH) laboratory at Virginia Tech. / Master of Science

Neste projeto apresentamos algumas direções de pesquisa desenvolvidas no estudo da geometria/topologia da singularidade, no ambiente real e complexo, para funções e aplicações polinomiais. Para isso, utilizaremos as ferramentas da teoria de estratificação, técnicas de decomposição Open book, condições de regularidade no sentido Malgrange, t-regularidade, \'rho\'E-regularidade e trivialidade topológica no infinito / On this project we present some research lines developed in the study of the geometry/ topology of singularity, on the real and complex settings, for functions and polynomial mappings. For this, we use tools from stratification theory, techniques of Open Book decomposition, Malgrange regularity condition, t-regularity condition, \'rho\'E-regularity and topological triviality at infinity

Cette thèse porte sur la modélisation et vérification des signatures en ligne. La première partie a pour thème principal la modélisation biomécanique des mouvements de la main. Un modèle basé sur le critère de Minimum de Secousse (MS) a été choisi parmi plusieurs théories du contrôle moteur. Ensuite, le problème de la segmentation des trajectoires en traits qui correspondent au modèle cinématique choisi a été étudié, ce qui a conduit à la mise au point d'une méthode de segmentation itérative. Le choix du modèle et de la méthode de segmentation sont basé sur le compromis entre la qualité de reconstruction et la compression. Dans la deuxième partie, le modèle polynomial issu du critère de MS est volontairement dégradé. Les zéros non-Réels des polynômes sont jetés et les effets de cette dégradation sont étudiés dans une perspective de vérification biométrique. Cette dégradation est équivalente à la technique connue sous le nom d’Infinity Clipping, initialement appliqué à des signaux de parole. Pour les signatures en ligne, comme pour la parole, la préservation de l'information essentielle a été observée sur des tâches de vérification de signature. En fait, en utilisant seulement la distance de Levenshtein sur la représentation dégradée, un taux d'erreur comparable à ceux des méthodes plus élaborées a été obtenu. En outre, la représentation symbolique issue de l’Infinity Clipping permet d’établir une relation conceptuelle entre le nombre de segments obtenus par la segmentation itératif basée sur le MS et la complexité de Lempel-Ziv. Cette relation est potentiellement utile pour l'analyse des signatures en ligne et pour l’amélioration des systèmes de reconnaissance / This thesis deals with the modelling and verification of online signatures. The first part has as main theme the biomechanical modelling of hand movements associated to the signing gesture. A model based on the Minimum Jerk (MJ) criterion was chosen amongst the several available motor control theories. Next, the problem of signature trajectory segmentation into strokes that better fit the chosen kinematic model is studied, leading to the development of an iterative segmentation method. Both the choice of the model and the segmentation method are strongly based on the tradeoff between reconstruction quality and compression. On the second part, the polynomial model provided by the MJ criterion is intentionally degraded. The non-Real zeroes of the polynomials are discarded and the effects of this degradation are studied from a biometric verification perspective. This degradation is equivalent to the signal processing technique known as Infinity Clipping, originally applied to speech signals. On signatures, as for speech, the preservation of essential information was observed on signature verification tasks. As a matter of fact, using only the Levenshtein distance over the infinitely clipped representation, verification error rates comparable to those of more elaborate methods were obtained. Furthermore, the symbolic representation yielded by the infinity clipping technique allows for a conceptual relationship between the number of polynomial segments obtained through the Minimum Jerk-Based iterative segmentation and the Lempel-Ziv complexity. This relationship is potentially useful for the analysis of online signature signals and the improvement of recognition systems

Ce travail propose de nouvelles structures de contrôle pour la téléopération bilatérale à travers des réseaux de communication non dédiés. L’enjeu est donc de concevoir et calculer des structures de commande garantissant la stabilisation et un bon degré de performance en termes de synchronisation (suivi des positions et vitesse) et de transparence (ressenti des forces) sous les retards variables et asymétriques.Nous faisons tout d’abord un tour d’horizon des recherches récentes dans le domaine des systèmes de téléopération et de leurs caractéristiques. Puis, nous considérons des modèles linéaires à plusieurs retards variables pour lesquels nous proposons une approche d’analyse de stabilité par fonctionnelles de Lyapunov-Krasovskii et contrôle robuste H [infinity symbol . Ensuite, trois structures de téléopération seront proposées en temps continu, la comparaison de ces architectures montre que, pour un retard de réseau maximum donné ou calculé, toutes garantissent un suivi de position et vitesse. Les deux dernières, qui utilisent les forces mesurées ou estimées de l’opérateur humain et de l’environnement, garantissent de plus un suivi en force. Au final, la troisième structure (avec proxy) présente la meilleure performance, même si elle demande un peu plus de calcul. Puis, afin d’analyser et d’améliorer les performances de la troisième structure pour des modèles encore plus réalistes, une étude est menée en temps discret, mais aussi sur un modèle non linéaire ou non stationnaire sous perturbations bornées en norme. L’implantation sur la plate-forme est décrite dans un quatrième et dernier chapitre, et puis l’analyse des résultats expérimentaux est alors menée / This PhD thesis is dedicated to the control scheme design of the bilateral teleoperation under asymmetric communication channels: the stabilization and a high-level performance under asymmetric time-varying delays and the perturbations of the human operator and environment. After a review of the recent researches and their features in the field of teleoperation system, a less conservative Lyapunov-Krasovskii functional together with H [infinity symbol] control theory has been applied to linear time delay systems, and then the LMI theorems have been obtained in order to calculate the controllers in the control schemes.Firstly, three novel teleoperation control schemes have been presented. Comparing three architectures, all of them guaranteed the stability and the position tracking thanks to the position/velocity information. Force-reflecting control scheme without or with proxy, in addition, ensured the force tracking by using the estimated/measured force of the human operator and the environment. Here, the control scheme with the proxy got a better performance. Secondly, a discrete-time approach has been developed to analyze the force-reflecting control scheme with proxy and obtain a better system performance. Besides, more general systems with time-varying uncertainties (the polytopic-type uncertainties and the norm-bounded model uncertainties) have been considered. Finally, the experimental test-bench and the real system implementation have been designed, which involved the identification and linearizing control of the subsystems (the master/slave robots). The experimental results have illustrated the effectiveness of the approaches proposed in this thesis