In the guidance literature, minimizing miss distance along with optimizing the energy usage had been an objective for several decades. In current day applications, additional terminal performance such as impact angle and impact time are of paramount importance. These terminal constraints increase warhead effectiveness and survivability of the interceptor. This thesis contributes to the design of guidance laws addressing terminal constraints such as impact angle, impact time, and both impact time as well as impact angle, in addition to interception of targets. In the first part of the thesis, the guidance laws which ensure the alignment of the interceptor at a desired impact angle within a finite time is proposed using different variants of sliding mode control(SMC).The impact angle is first redefined in terms of line-of-sight angle and then the impact angle problem is converted to a simpler problem of controlling line-of-sight angle and their rates. The sliding mode capturability and interpretation of the guidance laws are presented. In order to cater to very large heading angle errors, which give rise to negative closing speed initially, modifications to the guidance laws are also suggested. The modifications to the guidance laws for avoiding singularities, which may be encountered during implementation, due to the inherent nature of terminal SMC, are suggested. However, the guidance laws, which alleviates the possibility of such singularities completely, are also designed by using non singular terminal SMC. The two loop guidance and control, for a skid-to-turn cruciform interceptor in the pitch plane, is also proposed with an autopilot designed using the concept of dynamic SMC. The guidance laws addressing impact angle constraint for three dimensional scenarios are also presented. Unlike the usual approach of decoupling the three dimensional engagement in to two mutually orthogonal planar engagements, the guidance laws are derived using coupled engagement dynamics. These guidance laws are designed using conventional and non singular terminal SMC and provide asymptotic and finite time alignment of the intercept or to the desired impact angles, respectively. Next, the SMC based guidance laws which ensure the interception of targets at pre-specified impact times is proposed in this thesis. The guidance law is first designed for stationary targets and then extended to constant velocity targets using the notion of predicted interception point. A switching surface is designed using the concepts of collision course and time-to-go with non-linear engagement dynamics and its role in achieving the objectives is also discussed. In order to account for large heading angle errors and even for negative initial closing speeds, different methods of estimation of time-to-go, resulting in two different guidance laws, are used. Unlike the existing guidance laws, the proposed guidance laws achieve an impact time even less than its initially estimated value. The flexibility in selecting a desired impact time is also exploited using the maximum available acceleration information. A cooperative salvo attack strategy, based on the proposed impact time guidance law, with a desired impact time chosen in real time using a centralized coordination algorithm, is proposed for stationary targets. The coordination manager determines a common impact time based on time-to-goof the interceptors, by minimizing the total switching surface deviations which in turn reduces the control effort. The thesis also proposes a SMC based guidance strategy which addresses impact angle and impact time constraints simultaneously. This guidance scheme is based on switching between impact time and impact angle guidance laws based on certain conditions. Unlike existing impact time guidance laws, the proposed guidance strategy takes into account the curvature of the trajectory due to the impact angle requirement. The interceptor first corrects its course to nullify the impact time error and then aims to achieve interception with desired impact angle. In order to reduce the transitions between the two guidance laws, a novel hysteresis loop is introduced in the switching conditions. Initially stationary targets are considered, and later the same guidance scheme is extended to constant velocity targets using the notion of predicted interception point. Theclaimsofalltheguidancelawsarevalidatedwithextensivesimulationsandtheir performances are compared with existing guidance laws. Although all the guidance laws derived in the thesis are based on the assumption of constant speed interceptors, their performances are evaluated with a time-varying speed interceptor model, subjected to aerodynamic conditions, to validate their efficacy. The implementation of impact time guidance on time-varying speed interceptors is a formidable challenge in the guidance literature. Such implementations have also been presented in the thesis after introducing the notion of average speed and shown to yield satisfactory performance.

Cette thèse traite de processus de détérioration en théorie du risque et en biomathématique.<p><p>En théorie du risque, le processus de détérioration étudié est celui des sinistres supportés par une compagnie d'assurance.<p><p>Le premier chapitre examine la distribution de Markov-Polya comme loi possible pour modéliser le nombre de sinistres et établit certains liens avec la famille de lois de Katz/Panjer. Nous construisons la loi de Markov-Polya sur base d'un modèle de survenance des sinistres et nous montrons qu'elle satisfait une récurrence élégante. Celle-ci permet notamment de déduire un algorithme efficace pour la loi composée correspondante. Nous déduisons la famille de Katz/Panjer comme famille limite de la loi de Markov-Polya.<p><p>Le second chapitre traite de la famille dite "Lagrangian Katz" qui étend celle de Katz/Panjer. Nous motivons par un problème de premier passage son utilisation comme loi du nombre de sinistres. Nous caractérisons toutes les lois qui en font partie et nous déduisons un algorithme efficace pour la loi composée. Nous examinons également son indice de dispersion ainsi que son comportement asymptotique. <p><p>Dans le troisième chapitre, nous étudions la probabilité de ruine sur horizon fini dans un modèle discret avec taux d'intérêt positifs. Nous déterminons un algorithme ainsi que différentes bornes pour cette probabilité. Une borne particulière nous permet de construire deux mesures de risque. Nous examinons également la possibilité de faire appel à de la réassurance proportionelle avec des niveaux de rétention égaux ou différents sur les périodes successives.<p><p>Dans le cadre de processus épidémiques, la détérioration étudiée consiste en la propagation d'une maladie de type SIE (susceptible - infecté - éliminé). La manière dont un infecté contamine les susceptibles est décrite par des distributions de survie particulières. Nous en déduisons la distribution du nombre total de personnes infectées à la fin de l'épidémie. Nous examinons en détails les épidémies dites de type Markov-Polya et hypergéométrique. Nous approximons ensuite cette loi par un processus de branchement. Nous étudions également un processus de détérioration similaire en théorie de la fiabilité où le processus de détérioration consiste en la propagation de pannes en cascade dans un système de composantes interconnectées. <p><p><p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Thermodynamic processes in finite time are in general irreversible. But there are chances to avoid irreversibility. For instance, there are canonical ensembles of special quantum systems with a given probability distribution describing the likelihood to find the system at time t=0 in a particular state with energy E_i(0), which can be controlled in a specific way, such that the initial probability distribution is recovered at the end of the process (t=T), but the state energies did change, hence E_i(0) is not equal to E_i(T). This allows to change thermodynamic quantities (expectation values) adiabatically, reversibly and in finite time. Such special processes are called Shortcuts to Adiabaticity. The presented thesis analyzes the origin of these shortcuts utilizing special Hamiltonian systems with dynamical algebra. Their main feature is to provide canonical invariance, which means a canonical ensemble stays canonical under Hamiltonian dynamics. This invariance carried by the dynamical algebra will be discussed using Lie group theory. In addition, the persistence of the dynamical algebra with respect to calculating expectation values will be deduced. This allows to benefit from all intrinsic symmetries within the discussion of ensemble trajectories. In consequence, these trajectories will evolve under Hamiltonian dynamics on a specific manifold given by the so-called Casimir companion. In addition, the deformation of this manifold due to non-Hamiltonian (dissipative) dynamics will be discussed, which allows to present a framework for modeling irreversible processes based on Hamiltonian systems with dynamical algebra. An application of this framework based on the parametric harmonic oscillator will be presented by determining time-optimal controls for transitions between two equilibrium as well as between non-equilibrium and equilibrium states. The latter one will lead to time-optimal equilibration strategies for a statistical ensemble of parametric harmonic oscillators. / Thermodynamische Prozesse in endlicher Zeit sind im Allgemeinen irreversibel. Es gibt jedoch Möglichkeiten, diese Irreversibilität zu umgehen. Ein kanonisches Ensemble eines speziellen quantenmechanischen Systems kann zum Beispiel auf eine ganz spezielle Art und Weise gesteuert werden, sodass nach endlicher Zeit T wieder eine kanonische Besetzungverteilung hergestellt ist, sich aber dennoch die Energie des Systems geändert hat (E(0) ungleich E(T)). Solche Prozesse erlauben das Ändern thermodynamischer Größen (Ensemblemittelwerte) der erwähnten speziellen Systeme in endlicher Zeit und auf eine adiabatische und reversible Art. Man nennt diese Art von speziellen Prozessen Shortcuts to Adiabaticity und die speziellen Systeme hamiltonsche Systeme mit dynamischer Algebra. Die vorliegende Dissertation hat zum Ziel den Ursprung dieser Shortcuts to Adiabaticity zu analysieren und eine Methodik zu entwickeln, die es erlaubt irreversible thermodynamische Prozesse adequat mittels dieser speziellen Systeme zu modellieren. Dazu wird deren besondere Eigenschaft ausgenutzt, die kanonische Invarianz, d.h. ein kanonisches Ensemble bleibt kanonisch bezüglich hamiltonscher Dynamik. Der Ursprung dieser Invarianz liegt in der dynamischen Algebra, die mit Hilfe der Theorie der Lie-Gruppen näher betrachtet wird. Dies erlaubt, eine weitere besondere Eigenschaft abzuleiten: Die Ensemblemittelwerte unterliegen ebenfalls den Symmetrien, die die dynamische Algebra widerspiegelt. Bei näherer Betrachtung befinden sich alle Trajektorien der Ensemblemittelwerte auf einer Mannigfaltigkeit, die durch den sogenannten Casimir Companion beschrieben wird. Darüber hinaus wird nicht-hamiltonsche/dissipative Dynamik betrachtet, welche zu einer Deformation der Mannigfaltigkeit führt. Abschließend wird eine Zusammenfassung der grundlegenden Methodik zur Modellierung irreversibler Prozesse mittels hamiltonscher Systeme mit dynamischer Algebra gegeben. Zum besseren Verständnis wird ein ausführliches Anwendungsbeispiel dieser Methodik präsentiert, in dem die zeitoptimale Steuerung eines Ensembles des harmonischen Oszillators zwischen zwei Gleichgewichtszuständen sowie zwischen Gleichgewichts- und Nichtgleichgewichtszuständen abgeleitet wird.