Ce travail s’inscrit dans le projet plus global SHARE dont l’objectif principal est de concevoir une station de contrôle sol universelle mono-opérateur de nouvelle génération pour le contrôle et la commande de drones à voilure fixe et voilure tournante.L’objectif de cette thèse est de développer un simulateur générique de la station de contrôle capable de simuler en temps réels les différents types de drones, les capteurs embarqués (caméra), l’environnement et les différentes missions militaires définies par le standard STANAG 4586. Après une modélisation des différentes parties de la station, nous présentons l’architecture adoptée pour le simulateur et le module de contrôle. Ce dernier est divisé en plusieurs niveaux hiérarchiques, dont le niveau supérieur contient les algorithmes de planification de trajectoire pour les drones à voilure fixe HALE (haute altitude, longue endurance). Ces algorithmes servent à calculer un chemin admissible entre un point de départ et un point d’arrivée en minimisant une fonction de coût.Enfin nous avons développé un système d’aide à la décision pour la gestion en ligne des missions, capable de réaliser une sélection d’objectifs, et une sélection du meilleur chemin proposé par les algorithmes de planification de trajectoire. Cet outil a pour objectif d’aider l’opérateur de la station à prendre la meilleure décision en maximisant les récompenses obtenues lors de la réalisation des objectifs et en minimisant certains critères tels que la consommation des ressources, le danger, les conditions météorologiques, etc. / The presented work is part of a larger project called SHARE, which consists in developing a universal new generation ground control station for the monitoring and the control of fixed and rotary wing UAVs (Unmanned Aerial Vehicle).The objective of this PhD thesis is to develop a generic ground control station simulator capable of simulating in real time different types of UAVs, onboard sensors, several flight environments, and various military missions which are defined according to the STANAG 4586 standard. First, we introduce the model of the different parts of the station, and then we present the architecture adopted for the simulator and the control module. The latter is divided into several hierarchical levels; the upper level contains the path planning algorithms for fixed wing HALE (High Altitude, Long Endurance) UAV. These algorithms are used to calculate an admissible path between initial and final position by minimizing a cost function.Finally, in order to manage missions online, we developed a decision support system that is capable of performing a variety of objectives. This system also supplies the operator the best paths proposed by planning algorithms. This tool aims to help the station operator to make the decision by maximizing the rewards obtained during the achieving the objectives and minimizing certain criteria (resource consumption, danger, weather,..).

Research Doctorate - Doctor of Philosophy (PhD) / This thesis studies control systems with communication constraints. Such constraints arise due to the fact that practical control systems often use non-transparent communication links, i.e., links subject to data-rate constraints, random data-dropouts or random delays. Traditional control theory cannot deal with such constraints and the need for new tools and insights arises. We study two problems: control with average data-rate constraints and control over analog erasure channels with i.i.d. dropout profiles. When focusing on average data-rate constraints, it is natural to ask whether information theoretic ideas may assist the study of networked control systems. In this thesis we show that it is possible to use fundamental information theoretic concepts to arrive at a framework that allows one to tackle performance related control problems. In doing so, we show that there exists an exact link between control systems subject to average data-rate limits, and control systems which are closed over additive i.i.d. noise channels subject to a signal-to-noise ratio constraint. On the other hand, in the case of control systems subject to i.i.d. data-dropouts, we show that there exists a second-order moments equivalence between a linear feedback system which is interconnected over an analog erasure channel, and the same system when it is interconnected over an additive i.i.d. noise channel subject to a signal-to-noise ratio constraint. From the results foreshadowed above, it follows that the study of control systems closed over signal-to-noise ratio constrained additive i.i.d. noise channels is a task of relevance to many networked control problems. Moreover, the interplay between signal-to-noise ratio constraints and control objectives is an interesting issue in its own right. This thesis starts with such a study. Then, we use the resultant insights to address performance issues in control systems subject to either average data-rate constraints or i.i.d. data-dropouts. Our approach shows that, once key equivalences are exposed, standard control intuition and synthesis machinery can be used to tackle networked control problems in an exact manner. It also sheds light into fundamental results in the literature and gives (partial) answers to several previously open questions. We believe that the insights in this thesis are of fundamental importance and, to the best of the author's knowledge, novel.

Decisions on capacity are often treated separately from those of production and inventory. In most situations, capacity issues are longer-term, so capacity-related decisions are considered strategic and thus not part of supply planning. This research focuses on optimal supply planning with emphasis on variable capacity to meet uncertain demand. It also defines three levels of capacity change: operating hours, labor availability and production hardware availability. The work presented here deals with the fundamental decisions to determine capacity, production, and inventory to meet customer demand while optimizing revenue and costs over a planning horizon (typically the life of the product). With the Lagrangian technique for constrained optimization, it can be shown that the optimal supply capacity has upper and lower bounds. The optimal feedback policy prescribes increasing the supply capacity when at the beginning of the planning interval it is below the lower bound. Similarly, the supply capacity should be decreased to the upper bound when it is above the upper bound. This paper will present arguments for characterizing forecast evolution and information sharing in the supply chain to obtain a predictor-corrector approach to supply chain control. / Singapore-MIT Alliance (SMA)

The solution of optimal control problems through the Hamilton-Jacobi-Bellman (HJB) equation offers guaranteed satisfaction of both the necessary and sufficient conditions for optimality. However, finding an exact solution to the HJB equation is a near impossible task for many optimal control problems. This thesis presents an approximation method for solving finite-horizon optimal control problems involving nonlinear dynamical systems. The method uses finite-order approximations of the partial derivatives of the cost-to-go function, and successive higher-order differentiations of the HJB equation. Natural byproducts of the proposed method provide sensitivities of the controls to changes in the initial states, which can be used to approximate the solution to neighboring optimal control problems. For highly nonlinear problems, the method is modified to calculate control sensitivities about a nominal trajectory. In this framework, the method is shown to provide accurate control sensitivities at much lower orders of approximation. Several numerical examples are presented to illustrate both applications of the approximation method.

Despite the immense progress made by molecular biology in cataloging andcharacterizing molecular elements of life and the success in genome sequencing, therehave not been comparable advances in the functional study of complex phenotypes.This is because isolated study of one molecule, or one gene, at a time is not enough byitself to characterize the complex interactions in organism and to explain the functionsthat arise out of these interactions. Mathematical modeling of biological systems isone way to meet the challenge.My research formulates the modeling of gene regulation as a control problem andapplies systems and control theory to the identification, analysis, and optimal controlof genetic regulatory networks. The major contribution of my work includes biologicallyconstrained estimation, dynamical analysis, and optimal control of genetic networks.In addition, parameter estimation of nonlinear models of biological networksis also studied, as a parameter estimation problem of a general nonlinear dynamicalsystem. Results demonstrate the superior predictive power of biologically constrainedstate-space models, and that genetic networks can have differential dynamic propertieswhen subjected to different environmental perturbations. Application of optimalcontrol demonstrates feasibility of regulating gene expression levels. In the difficultproblem of parameter estimation, generalized EM algorithm is deployed, and a set of explicit formula based on extended Kalman filter is derived. Application of themethod to synthetic and real world data shows promising results.

In this thesis, different topics for models that consist of both differential and algebraic equations are studied. The interest in such models, denoted DAE models, have increased substantially during the last years. One of the major reasons is that several modern object-oriented modeling tools used to model large physical systems yield models in this form. The DAE models will, at least locally, be assumed to be described by a decoupled set of ordinary differential equations and purely algebraic equations. In theory, this assumption is not very restrictive because index reduction techniques can be used to rewrite rather general DAE models to satisfy this assumption. One of the topics considered in this thesis is optimal feedback control. For state-space models, it is well-known that the Hamilton-Jacobi-Bellman equation (HJB) can be used to calculate the optimal solution. For DAE models, a similar result exists where a Hamilton-Jacobi-Bellman-like equation is solved. This equation has an extra term in order to incorporate the algebraic equations, and it is investigated how the extra term must be chosen in order to obtain the same solution from the different equations. A problem when using the HJB to find the optimal feedback law is that it involves solving a nonlinear partial differential equation. Often, this equation cannot be solved explicitly. An easier problem is to compute a locally optimal feedback law. For analytic nonlinear time-invariant state-space models, this problem was solved in the 1960's, and in the 1970's the time-varying case was solved as well. In both cases, the optimal solution is described by convergent power series. In this thesis, both of these results are extended to analytic DAE models. Usually, the power series solution of the optimal feedback control problem consists of an infinite number of terms. In practice, an approximation with a finite number of terms is used. A problem is that for certain problems, the region in which the approximate solution is accurate may be small. Therefore, another parametrization of the optimal solution, namely rational functions, is studied. It is shown that for some problems, this parametrization gives a substantially better result than the power series approximation in terms of approximating the optimal cost over a larger region. A problem with the power series method is that the computational complexity grows rapidly both in the number of states and in the order of approximation. However, for DAE models where the underlying state-space model is control-affine, the computations can be simplified. Therefore, conditions under which this property holds are derived. Another major topic considered is how to include stochastic processes in nonlinear DAE models. Stochastic processes are used to model uncertainties and noise in physical processes, and are often an important part in for example state estimation. Therefore, conditions are presented under which noise can be introduced in a DAE model such that it becomes well-posed. For well-posed models, it is then discussed how particle filters can be implemented for estimating the time-varying variables in the model. The final topic in the thesis is model reduction of nonlinear DAE models. The objective with model reduction is to reduce the number of states, while not affecting the input-output behavior too much. Three different approaches are studied, namely balanced truncation, balanced truncation using minimization of the co-observability function and balanced residualization. To compute the reduced model for the different approaches, a method originally derived for nonlinear state-space models is extended to DAE models.

Localization and motion control (navigation) are two major tasks for a successful mobile robot navigation. The motion controller determines the appropriate action for the robot’s actuator based on its current state in an operating environment. A robot recognizes its environment through some sensors and executes physical actions through actuation mechanisms. However, sensory information is noisy and hence actions generated based on this information may be non-deterministic. Therefore, a mobile robot provides actions to its actuators with a certain degree of uncertainty. Moreover, when no prior knowledge of the environment is available, the problem becomes even more difficult, as the robot has to build a map of its surroundings as it moves to determine the position. Skilled navigation of a differential drive mobile robot (DDMR) requires solving these tasks in conjunction, since they are inter-dependent. Having resolved these tasks, mobile robots can be employed in many contexts in indoor and outdoor environments such as delivering payloads in a dynamic environment, building safety, security, building measurement, research, and driving on highways. This dissertation exploits the use of the emerging Radio Frequency IDentification (RFID) technology for the design and implementation of cost-effective and modular control techniques for navigating a mobile robot in an indoor environment. A successful realization of this process has been addressed with three separate navigation modules. The first module is devoted to the development of an indoor navigation system with a customized RFID reader. This navigation system is mainly pioneered by mounting a multiple antenna RFID reader on the robot and placing the RFID tags in three dimensional workspace, where the tags’ orthogonal position on the ground define the desired positions that the robot is supposed to reach. The robot generates control actions based on the information provided by the RFID reader for it to navigate those pre-defined points. On the contrary, the second and third navigation modules employ custom-made RFID tags (instead of the RFID reader) which are attached at different locations in the navigation environment (on the ceiling of an indoor office, or on posts, for instance). The robot’s controller generates appropriate control actions for it’s actuators based on the information provided by the RFID tags in order to reach target positions or to track pre-defined trajectory in the environment. All three navigation modules were shown to have the ability to guide a mobile robot in a highly reverberant environment with variant degrees of accuracy.

<p>Methodologies for the analysis and computer simulations of active optimal vibration control of complex elastic structures are considered. The structures, generally represented by a large number of degrees of freedom (DOF), are to be controlled by a comparatively small number of actuators.</p><p>Various techniques presently available to solve the optimal control problems are briefly discussed. A Parametric optimization technique that is versatile enough to solve almost any type of optimization problems is found to give poor accuracy and is time consuming. More promising is the optimality equations approach, which is based on Pontryagins principle. Several new numerical procedures are developed using this approach. Most of the problems in this thesis are analysed in the modal space. Even complex structures can be approximated accurately in the modal space by using only few modes. Different techniques have been first applied to the cases where the number of modes to control was the same as the number of actuators (determined optimal control problems), then to cases in which the number of modes to control is larger than the number of actuators (overdetermined optimal control problems). </p><p>The determined optimal control problems can be solved by applying the Independent Modal Space Control (IMSC) approach. Such an approach is implemented in the Beam Analogy (BA) method that solves the problem numerically by applying the Finite Element Method (FEM). The BA, which uses the ANSYS program, is numerically very efficient. The effects of particular optimization parameters involved in BA are discussed in detail. Unsuccessful attempts have been made to modify this method in order to make it applicable for solving overdetermined or underactuated problems. </p><p>Instead, a new methodology is proposed that uses modified optimality equations. The modifications are due to the extra constraints present in the overdetermined problems. These constraints are handled by time dependent Lagrange multipliers. The modified optimality equations are solved by using symbolic differential operators. The corresponding procedure uses the MAPLE programming, which solves overdetermined problems effectively despite of the high order of differential equations involved.</p><p>The new methodology is also applied to the closed loop control problems, in which constant optimal gains are determined without using Riccatis equations.</p>

In the future autonomous vehicles are expected to navigate independently and manage complex traffic situations. This thesis is one of two theses initiated with the aim of researching which methods could be used within the field of autonomous vehicles. The purpose of this thesis was to investigate how Model Predictive Control could be used in the field of autonomous vehicles. The tasks to generate a safe and economic path, to re-plan to avoid collisions with moving obstacles and to operate the vehicle have been studied. The algorithm created is set up as a hierarchical framework defined by a high and a low level planner. The objective of the high level planner is to generate the global route while the objectives of the low level planner are to operate the vehicle and to re-plan to avoid collisions. Optimal Control problems have been formulated in the high level planner for the use of path planning. Different objectives of the planning have been investigated e.g. the minimization of the traveled length between the start and the end point. Approximations of the static obstacles' forbidden areas have been made with circles. A Quadratic Programming framework has been set up in the low level planner to operate the vehicle to follow the high level pre-computed path and to locally re-plan the route to avoid collisions with moving obstacles. Four different strategies of collision avoidance have been implemented and investigated in a simulation environment.

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