Cette thèse est dédiée à l’analyse du retard (de calcul ou induit par la communication), qui représente un des paramètres sensibles, et qui doit être pris en compte, pour la mise en œuvre de la Commande Prédictive en temps réel d’un processus dynamique. Dans la première partie, nous avons abordé le problème d’existence des ensembles D-invariants et avons fourni par la suite des conditions nécessaires et/ou suffisantes pour l’existence de ces ensembles. En outre, nous avons détaillé quelques nouvelles idées sur la construction des ensembles D-invariants en utilisant des algorithmes itératifs et d’autres algorithmes basés sur des techniques d’optimisation à deux niveaux. La seconde partie a été consacrée à l’étude du problème de robustesse des systèmes linéaires discrets affectés par un retard variable en boucle fermée avec un contrôleur affine par morceaux défini sur une partition polyédrale de l’espace d’état. L’étude a porté sur l’analyse de la fragilité d’une telle loi commande en présence du retard dans la boucle. Nous avons décrit les marges d’invariance robustes définies comme étant le plus grand sous-ensemble de l’incertitude paramétrique pour lequel l’invariance positive est garantie par rapport à la dynamique en boucle fermée en présence du retard. La dernière partie de cette thèse s’est articulée autour de la conception des lois de commande prédictives avec un attention particulière aux modèles linéaires discrets décrivant des dynamiques affectées par des contraintes en présence du retard. Nous avons proposé plusieurs méthodes offrant différentes solutions au problème de stabilisation locale sans contrainte. Afin d’assurer la stabilité et de garantir la satisfaction des contraintes, nous avons exploité le concept d’invariance et à l’aide du formalisme "ensemble terminal-coût terminal", un problème d’optimisation a été formulé où les états sont forcés d’atteindre l’ensemble maximal admissible d’états retardés/D-invariant à la fin de l’horizon de prédiction. Enfin, nous avons étudié le problème de stabilisation des systèmes continus commandés en réseau soumis à des retards incertains et éventuellement variant dans le temps. Nous avons montré que les ensembles λ-D-contractifs peuvent être utilisés comme ensembles cibles où la stratégie de commande consiste en un simple problème de programmation linéaire ’LP’ qui peut être résolu en ligne. / The research conducted in this thesis has been focusing on Model Predictive Control (MPC) and the implication of network induced time-varying delays. We have addressed, in the first part of this manuscript, the existence problem and the algorithmic computation of positive invariant sets in the state space of the original discrete delay difference equation. The second part of these thesis has been devoted to the study of the robustness problem for a specific class of dynamical systems, namely the piecewise affine systems, defined over a polyhedral partition of the state space in the presence of variable input delay. The starting point was the construction of a predictive control law which guarantees the existence of a non-empty robust positive invariant set with respect to the closed-loop dynamic. The variable delay inducing in fact a model uncertainty, the objective was to describe the robust invariance margins defined as the largest subset of the parametric uncertainty for which the positive invariance is guaranteed with respect to the closed-loop dynamics in the presence of small and large delays. The last part has been dedicated to Model Predictive Control design with a specific attention to linear discrete time-delay models affected by input/state constraints. The starting point in the analysis was the design of a local stabilizing control law using different feedback structures. We proposed several design methods offering different solutions to the local unconstrained stabilization problem. In order to ensure stability and guarantee input and state constraints satisfaction of the moving horizon controller, the concept of positive invariance related to time-delay systems was exploited. Using the "terminal setterminal cost" design, the states were forced to attain the maximal delayed-state admissible set at the end of the prediction horizon. Finally, we have investigated the stabilization problem of Networked Control Systems ’NCSs’ subject to uncertain, possibly time-varying, network-induced delays. We showed that λ-D-contractive sets can be used as a target sets in a set induced Lyapunov function control fashion where a simple Linear Programming ’LP’ problem is required to be solved at each sampling instance.

Indiana University-Purdue University Indianapolis (IUPUI) / Background. Despite widespread criticism of physician-performed evaluations of medical students’ clinical skills, clinical clerkship evaluations (CCEs) remain the foremost means by which to assess trainees’ clinical prowess. Efforts undertaken to improve the quality of feedback students receive have ostensibly led to higher assessment demands on physician faculty; the consequences of which remain unknown. Accordingly, this study investigated the extent to which physicians’ evaluative responsibilities influenced the quality of CCEs and qualitatively explored physicians’ perceptions of these evaluations. Methods. A questionnaire was delivered to physicians (n = 93) at Indiana University School of Medicine to gauge their perceived evaluative responsibilities. Evaluation records of each participant were obtained and were used to calculate one’s measurable quantity of CCEs, the timeliness of CCE submissions, and the quality of the Likert-scale and written feedback data included in each evaluation. A path analysis estimated the extent to which one’s evaluative responsibilities affected the timeliness of CCE submissions and CCE quality. Semi-structured interviews with a subset of participants (n = 8) gathered perceptions of the evaluations and the evaluative process. Results. One’s measurable quantity of evaluations did not influence one’s perceptions of the evaluative task, but did directly influence the quality of the Likert-scale items. Moreover, one’s perceptions of the evaluative task directly influenced the timeliness of CCE submissions and indirectly influenced the quality of the closed-ended CCE items. Tardiness in the submission of CCEs had a positive effect on the amount of score differentiation among the Likert-scale data. Neither evaluative responsibilities nor the timeliness of CCE submissions influenced the quality of written feedback. Qualitative analysis revealed mixed opinions on the utility of CCEs and highlighted the temporal burden and practical limitations of completing CCEs. Conclusions. These findings suggest physicians’ perceptions of CCEs are independent of their assigned evaluative quantity, yet influence both the timeliness of evaluation submissions and evaluative quality. Further elucidation of the mechanisms underlying the positive influence of evaluation quantity and timely CCE submissions on CCE quality are needed to fully rationalize these findings and improve the evaluative process. Continued research is needed to pinpoint which factors influence the quality of written feedback.

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This study investigated a tracking system to trace unknown signal in the presence oftime delay. A predictive control method is proposed in order to compensate the time delay. Root locus method is applied when designing the controller, parameter setting is carried out through error and trail technique in w-plane. State space equation is derived for the system, with special state chose of tracking error. To analyze the asymptotic stability of the proposed predictive control system, the Lyapunov function is constructed. It is shown that the designed system is asymptotically stable when input signal is rather low frequency signal. In order to illustrate the system performance, simulations are done based on the data profile technique. Signal profiles including acceleration pro le, velocity pro le, and trajectory profile are listed. Based on these profiles, simulations can be carried out and results can be taken as a good estimation for practical performance of the designed predictive control system. Signal noise is quite a common phenomenon in practical control systems. Under the situation that the input signal is with measurement noise, low pass filter is designed to filter out the noise and keep the low frequency input signal. Two typical kinds of noise are specified, i.e Gaussian noise and Pink noise. Simulations results are displayed to show that the proposed predictive control with low-pass filter design can achieve better performance in the case of both kinds of noise.

Significant progress has been made in understanding different scenarios for disease transmissions and behavior of epidemics in recent years. A considerable amount of work has been done in modeling the dynamics of diseases by systems of ordinary differential equations. But there are very few mathematical models that deal with the genetic mutations of a pathogen. In-fact, not much has been done to model the dynamics of mutations of pathogen explaining its effort to escape the host's immune defense system after it has infected the host. In this dissertation we develop an SIR model with variable infection age for the transmission of a pathogen that can mutate in the host to produce a second infectious mutant strain. We assume that there is a period of temporary immunity in the model. A temporary immunity period along with variable infection age leads to an integro-differential-difference model. Previous efforts on incorporating delays in epidemic models have mainly concentrated on inclusion of latency periods (this assumes that the force of infection at a present time is determined by the number of infectives in the past). We begin with reviewing some basic models. These basic models are the building blocks for the later, more detailed models. Next we consider the model for mutation of pathogen and discuss its implications. Finally, we improve this model for mutation of pathogen by incorporating delay induced by temporary immunity. We examine the influence of delay as we establish the existence, and derive the explicit forms of disease-free, boundary and endemic equilibriums. We will also investigate the local stability of each of these equilibriums. The possibility of Hopf bifurcation using delay as the bifurcation parameter is studied using both analytical and numerical solutions.

This work presents the Czochralski growth dynamics as time-varying delay based model, applied to the growth of La3Ga5.5Ta0.5O14 (LGT) piezoelectric crystals. The growth of high-quality large-diameter oxides by Czochralski technique requires the theoretical understanding and optimization of all relevant process parameters, growth conditions, and melts chemistry. Presently, proportional-integral- derivative (PID) type controllers are widely accepted for constant-diameter crystal growth by Czochralski. Such control systems, however, do not account for aspects such as the transportation delay of the heat from crucible wall to the crystal solidification front, heat radiated from the crucible wall above the melt surface, and varying melt level. During crystal growth, these time delays play a dominant role, and pose a significant challenge to the control design. In this study, a time varying linear delay model was applied to the identification of nonlinearities of the growth dynamics. Initial results reveled the benefits of this model with actual growth results. These results were used to develop a long-range model predictive control system design. Two different control techniques using long range prediction are studied for the comparative study. Development and testing of the new control system on real time growth system are discussed in detail. The results are promising and suggest future work in this direction. Other discussion about the problems during the crystal growth, optimization of crystal growth parameters are also studied along with the control system design.

Current research indicates that the inability to spontaneously communicate needs or wants may result in the acquisition of unconventional forms of requesting such as aggression and tantrums. This in turn limits the amount of access that students with autism have to neurotypical peers and social environments. The purpose of this study was to investigate the effect of using a stimulus control transfer procedure on the acquisition of spontaneous mands. Four school-aged children with autism, two boys and two girls, participated in the study. A multiple baseline design across participants was utilized to demonstrate a functional relation between the stimulus control transfer procedures and the rate of spontaneous mands. Measurement variables included the frequency of spontaneous versus multiply-controlled mands during discrete trial training on a variety of verbal operants. Effectiveness of the intervention was analyzed through visual analysis and the magnitude of effect was assessed through effect size. Visual analysis indicated that three of the four participants learned to spontaneously mand for items out of view and demonstrated generalization across targets, staff and environments. The effect size for three participants were large (d = 1.94; d = 2.2; and d = 1.4), whereas the outcome of intervention for one participant (d = 0.98) indicated moderate effect. The overall (d = 1.15) outcome demonstrated a large effect of the intervention on the rate of mands. Based on the results of this study, it is recommended that early and intensive behavior intervention programs for children with autism incorporate this type of procedure for socially significant outcomes.

This document is Sajad Azizi's doctoral thesis titled 'Three Aspects of Photoionization in Ultrashort Pulses.' The research was conducted under the supervision of Prof. Dr. Jan Michael Rost at the Max Planck Institute for the Physics of Complex Systems.:Contents 1 Introduction 1 1.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Fundamental Concepts 5 2.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Introduction to strong field ionization . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 From the photoelectric effect to strong-field ionization . . . . . . . . . 6 2.3 Non-relativistic time-dependent Hamiltonian . . . . . . . . . . . . . . . . . . 10 2.3.1 Dipole approximation and choice of gauges . . . . . . . . . . . . . . . 11 2.3.2 Interaction of an electron with a classical field . . . . . . . . . . . . . 12 2.4 Ultrashort laser pulse shaping . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4.1 Fourier-limited pulse: Gaussian envelope . . . . . . . . . . . . . . . . . 17 2.4.2 Modulated pulse: sinusoidal phase modulation . . . . . . . . . . . . . 18 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Controlling Non-adiabatic Photoionization with Ultrashort Pulses 20 3.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Introduction to non-adiabatic ionization . . . . . . . . . . . . . . . . . . . . . 21 3.2.1 Intuitive picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.2 Mathematical picture . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3 Non-adiabatic ionization with tailored laser pulses . . . . . . . . . . . . . . . 25 3.3.1 Ionization by single Gaussian pulses . . . . . . . . . . . . . . . . . . . 26 3.3.2 Sensitivity of non-adiabatic photoionization to the modulation phase . 28 3.3.3 The role of the catalyzing state . . . . . . . . . . . . . . . . . . . . . . 31 3.3.4 Second-order perturbation theory . . . . . . . . . . . . . . . . . . . . . 32 3.3.5 Pulse optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4 Time-dependent Perturbation Theory for Ultrashort Pulses 37 4.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.2 Introduction to time-dependent perturbation theory . . . . . . . . . . . . . . 39 4.2.1 Higher order time-dependent perturbation theory . . . . . . . . . . . . 42 4.2.2 Perturbation theory in shaped short laser pulse . . . . . . . . . . . . . 45 4.3 Application I: non-adiabatic ionization . . . . . . . . . . . . . . . . . . . . . . 47 4.3.1 Slowly varying envelope approximation . . . . . . . . . . . . . . . . . 50 4.3.2 Zero-photon transition . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.3.3 Zero-photon ionization probability . . . . . . . . . . . . . . . . . . . . 55 4.3.4 Oscillation in zero-photon transition . . . . . . . . . . . . . . . . . . . 58 4.4 Application II: interference stabilization . . . . . . . . . . . . . . . . . . . . . 59 4.4.1 Third-order time-dependent perturbation theory . . . . . . . . . . . . 61 4.4.2 Ionization probability and stabilization . . . . . . . . . . . . . . . . . . 62 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5 Molecular Photoionization Time Delay 65 5.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.2 Introduction to time delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.2.1 Time delay in scattering scenario . . . . . . . . . . . . . . . . . . . . 69 5.2.2 Asymptotic behavior of ⟨r⟩ . . . . . . . . . . . . . . . . . . . . . . . . 71 5.3 Photoionization time delay from a scattering theory perspective . . . . . . . 74 5.3.1 Asymptotic solutions and scattering matrix . . . . . . . . . . . . . . . 75 5.3.2 Energy normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.3.3 Boundary condition and final molecular wavefunction . . . . . . . . . 79 5.3.4 Matrix element and photoionization time delay . . . . . . . . . . . . . 81 5.3.5 Two-center system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.4 Photoionization time delay from a wavepacket perspective . . . . . . . . . . 87 5.4.1 Partial time delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.4.2 Photoelectron wavepacket and photoionization time delay . . . . . . . 92 5.4.3 Anisotropic potential and half-collision checking . . . . . . . . . . . . 94 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6 Conclusions and Outlook 97 A Renormalized Numerov Method 101 A.1 Introduction to Numerov method . . . . . . . . . . . . . . . . . . . . . . . . 103 A.1.1 Eigenvalue calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 A.2 Johnson renormalized Numerov method . . . . . . . . . . . . . . . . . . . . . 106 A.2.1 Proper initialization for extreme values of potential . . . . . . . . . . . 108 A.2.2 Matching point and bound states solutions . . . . . . . . . . . . . . . 110 A.2.3 Discretized continuum states solutions . . . . . . . . . . . . . . . . . . 111 A.2.4 Continuum states solutions . . . . . . . . . . . . . . . . . . . . . . . . 112 B Derivation of the Asymptotic Behavior of ⟨r⟩ 114 C Classical Time Delay 117 D Temporal Airy Pulse 119 E Numerical Details of Perturbation Theory 122 F Atomic Units

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