Various unmanned missions deploy vehicles such as missiles, torpedoes, ground robots, and unmanned aerial vehicles. Guidance strategies for these vehicles aim to intercept a target point and satisfy additional objectives such as specifications on impact angle and interception time. Certain impact angles are crucial for a greater warhead effectiveness, and minimizing the interception time is important for vehicles with limited endurance time and for reducing the probability of detection. This thesis considers the time-optimal impact angle constrained guidance problem for interception of moving targets. In the first part of the thesis, a Dubins paths–based guidance methodology for minimum-time lateral interception of a moving and non-maneuvering target is designed. The existence and the time-optimality of the paths are established for impact angle constrained interception of moving targets. The capture regions are analyzed and a classification of the initial geometries is developed for deducing the time-optimal path type. The corresponding guidance command for optimal interception can be generated from the information of initial engagement geometry and target’s speed. In the next part of the thesis, the concept of equivalent virtual target is introduced to address the problem of impact along a general direction. An algorithm is developed to obtain the optimal interception point for generalized interception scenarios. A proof of convergence is presented for the proposed algorithm. Achieving different impact angles, the interceptor often takes sharp turns. Following such curved trajectories, the interceptor may fail to keep the target inside the seeker field-of-view. In the next part of the thesis, the field-of-view characteristics of the proposed optimal guidance strategies are analyzed. Closed-form expressions are derived for the interceptor’s look-angle to the target. Satisfying field-of-view condition at endpoints of the path segments that constitute the optimal path is proven to guarantee target motion inside the field-of-view throughout the engagement. The stationary target case is also analyzed as a specific scenario. The last part of the thesis presents a method to extend the proposed guidance strategies to maneuvering target scenarios.

Collision avoidance is an essential component of autonomous shipping. As ships begin to advance towards autonomy, developing an advisory system is one of the first steps. An advisory system with a strong collision avoidance component can help the crew act more quickly and accurately in dangerous situations. One way to avoid colission is to make the vessel stop as fast as possible. In this work, two scenarios are studied, firstly, stopping along a predefined path, and secondly, stopping within a safe area defined by surrounding obstacles. The first scenario was further worked with to formulate a real-time solution. Movements of a vessel, described in three degrees of freedom with continuous dynamics, were simulated using mathematical models of the forces acting on the ship. Nonlinear optimal control problems were formulated for each scenario and solved numerically using discretization and a direct multiple shooting method. The results for the first problem showed that the vessel could stop without much deviation from the path. Paths with different curvatures were tested, and it was shown that a slightly longer distance was traveled when the curvature of the path was greater. The results for the second problem showed that the vessel stays within the safe area and chooses a relatively straight path as the optimal way of stoping. This results in a shorter distance traveled compared to the solution of the first problem. Two different real-time approaches were formulated, firstly a receding-horizon approach and secondly a lookup-based approach. Both approaches were solved with real-time feasibility, where the receding-horizon approach gave a better solution while lookup-based approach had a shorter computational time.

This research formulates and implements a novel closed-loop optimal control system that drives a train between two stations in an optimal time, energy efficient, or mixed objective manner. The optimal controller uses sensor feedback from the train and in real-time computes the most efficient control decision for the train to follow given knowledge of the track profile ahead of the train, speed restrictions and required arrival time windows. The control problem is solved both on an open track and while safely driving no closer than a fixed distance behind another locomotive. In contrast to other research in the field, this thesis achieves a real-time capable and embeddable closed-loop optimization with advanced modeling and numerical solving techniques with a non-linear optimal control problem. This controller is first formulated as a non-convex control problem and then converted to an advanced convex second-order cone problem with the intent of using a simple numerical solver, ensuring global optimality, and improving control robustness. Convex and non-convex numerical methods of solving the control problem are investigated and closed-loop performance results with a simulated vehicle are presented under realistic modeling conditions on advanced tracks both on desktop and embedded computer architectures. It is observed that the controller is capable of robust vehicle driving in cases both with and without modeling uncertainty. The benefits of pairing the optimal controller with a parameter estimator are demonstrated for cases where very large mismatches exists between the controller model and the simulated vehicle. Stopping performance is consistently within 25cm of target stations, and the worst case closed-loop optimization time was within 100ms for the computation of a 1000 point control horizon on an i7-6700 machine. / Thesis / Master of Applied Science (MASc) / This research formulates and implements a novel closed-loop optimal control system that drives a train between two stations in an optimal time, energy efficient, or mixed objective manner. It is deployed on a commuter vehicle and directly manages the motoring and braking systems. The optimal controller uses sensor feedback from the train and in real-time computes the most efficient control decision for the train to follow given knowledge of the track profile ahead of the train, speed restrictions and required arrival time windows. The final control implementation is capable of safe, high accuracy and optimal driving all while computing fast enough to reliably deploy on a rail vehicle.

An optimal dividend problem with investment opportunities, taking into consideration a source of strategic risk is being considered, as well as the effect of market frictions on the decision process of the financial entities. It concerns the problem of determining an optimal control of the dividend under debt constraints and investment opportunities in an economy with business cycles. It is assumed that the company is to be allowed to accept or reject investment opportunities arriving at random times with random sizes, by changing its outstanding indebtedness, which would impact its capital structure and risk profile. This work mainly focuses on the strategic risk faced by the companies; and, in particular, it focuses on the manager's problem of setting appropriate priorities to deploy the limited resources available. This component is taken into account by introducing frictions in the capital structure modification process. The problem is formulated as a bi-dimensional singular control problem under regime switching in presence of jumps. An explicit condition is obtained in order to ensure that the value function is finite. A viscosity solution approach is used to get qualitative descriptions of the solution. Moreover, a lending scheme for a system of interconnected banks with probabilistic constraints of failure is being considered. The problem arises from the fact that financial institutions cannot possibly carry enough capital to withstand counterparty failures or systemic risk. In such situations, the central bank or the government becomes effectively the risk manager of last resort or, in extreme cases, the lender of last resort. If, on the one hand, the health of the whole financial system depends on government intervention, on the other hand, guaranteeing a high probability of salvage may result in increasing the moral hazard of the banks in the financial network. A closed form solution for an optimal control problem related to interbank lending schemes has been derived, subject to terminal probability constraints on the failure of banks which are interconnected through a financial network. The derived solution applies to real bank networks by obtaining a general solution when the aforementioned probability constraints are assumed for all the banks. We also present a direct method to compute the systemic relevance parameter for each bank within the network. Finally, a possible computation technique for the Default Risk Charge under to regulatory risk measurement processes is being considered. We focus on the Default Risk Charge measure as an effective alternative to the Incremental Risk Charge one, proposing its implementation by a quasi exhaustive-heuristic algorithm to determine the minimum capital requested to a bank facing the market risk associated to portfolios based on assets emitted by several financial agents. While most of the banks use the Monte Carlo simulation approach and the empirical quantile to estimate this risk measure, we provide new computational approaches, exhaustive or heuristic, currently becoming feasible, because of both new regulation and the high speed - low cost technology available nowadays.

Résumé : Depuis la fin du XXème siècle, l’augmentation du prix du pétrole brut et les problématiques environnementales poussent l’industrie automobile à développer des technologies plus économes en carburant et générant moins d’émissions de gaz à effet de serre. Parmi ces technologies, les véhicules électriques hybrides constituent une solution viable et performante. En alliant un moteur électrique et un moteur à combustion, ces véhicules possèdent un fort potentiel de réduction de la consommation de carburant sans sacrifier son autonomie. La présence de deux moteurs et de deux sources d’énergie requiert un contrôleur, appelé système de gestion d’énergie, responsable de la commande simultanée des deux moteurs. Les performances du véhicule en matière de consommation dépendent en partie de la conception de ce contrôleur. Les véhicules électriques hybrides rechargeables, plus récents que leur équivalent non rechargeable, se distinguent par l’ajout d’un chargeur interne permettant la recharge de la batterie pendant l’arrêt du véhicule et par conséquent la décharge de celle-ci au cours d’un trajet. Cette particularité ajoute un degré de complexité pour ce qui est de la conception du système de gestion d’énergie. Dans cette thèse, nous proposons un modèle complet du véhicule dédié à la conception du contrôleur. Nous étudions ensuite la dépendance de la commande optimale des deux moteurs par rapport au profil de vitesse suivi au cours d’un trajet ainsi qu’à la quantité d’énergie électrique disponible au début d’un trajet. Cela nous amène à proposer une technique d’auto-apprentissage visant l’amélioration de la stratégie de gestion d’énergie en exploitant un certain nombre de données enregistrées sur les trajets antérieurs. La technique proposée permet l’adaptation de la stratégie de contrôle vis-à-vis du trajet en cours en se basant sur une pseudo-prédiction de la totalité du profil de vitesse. Nous évaluerons les performances de la technique proposée en matière de consommation de carburant en la comparant avec une stratégie optimale bénéficiant de la connaissance exacte du profil de vitesse ainsi qu’avec une stratégie de base utilisée couramment dans l’industrie. // Abstract : Since the end of the XXth century, the increase in crude oil price and the environmental concerns lead the automotive industry to develop technologies that can improve fuel savings and decrease greenhouse gases emissions. Among these technologies, the hybrid electric vehicles stand as a reliable and efficient solution. By combining an electrical motor and an internal combustion engine, these vehicles can bring a noticeable improvement in terms of fuel consumption without sacrificing the vehicle autonomy. The two motors and the two energy storage systems require a control unit, called energy management system, which is responsible for the command decision of both motors. The vehicle performances in terms of fuel consumption greatly depend on this control unit. The plug-in hybrid electric vehicles are a more recent technology compared to their non plug-in counterparts. They have an extra internal battery charger that allows the battery to be charged during OFF state, implying a possible discharge during a trip. This particularity adds complexity when it comes to the design of the energy management system. In this thesis, a complete vehicle model is proposed and used for the design of the controller. A study is then carried out to show the dependence between the optimal control of the motors and the speed profile followed during a trip as well as the available electrical energy at the beginning of a trip. According to this study, a self-learning optimization technique that aims at improving the energy management strategy by exploiting some driving data recorded on previous trips is proposed. The technique allows the adaptation of the control strategy to the current trip based on a pseudo-prediction of the total speed profile. Fuel consumption performances for the proposed technique will be evaluated by comparing it with an optimal control strategy that benefits from the exact a priori knowledge of the speed profile as well as a basic strategy commonly used in industry.

This thesis deals with the optimal control of PDEs. After a brief introduction in the theory of elliptic and parabolic PDEs, we introduce a software that solves systems of PDEs by the finite elements method. In the second chapter we derive optimality conditions in terms of function spaces, i.e. a systems of PDEs coupled by some pointwise relations. Now we present algorithms to solve the optimality systems numerically and present some numerical test cases. A further chapter deals with the so called lack of adjointness, an issue of gradient methods applied on parabolic optimal control problems. However, since optimal control problems lead to large numerical schemes, model reduction becomes popular. We analyze the proper orthogonal decomposition method and apply it to our model problems. Finally, we apply all considered techniques to a real world problem.

Approved for public release, distribution is unlimited / This thesis develops an integer linear program called MSAMT (Model to Schedule Army Maneuver Training) to schedule an Army installation's maneuver training. We demonstrate MSAMT using a data set containing 261 platoon-level, 67 company-level and 18 battalion-level units, and 7 major training areas located at Fort Hood, Texas. Using a typical near-term planning horizon from 6 to 8 weeks, MSAMT schedules daily training for a randomly selected set of the stationed units and training requirements. For a 6-week time period and almost 65% (63 platoons 16 companies and 5 battalions) of the units there are 151 platoon-level, 51 company-level and 11 battalion-level required tasks of which MSAMT can schedule 93%. When the subset of units is increased to 80% (75 platoons, 20 companies, 6 battalions), there are 187 platoon-level, 62 company-level and 11 battalion-level tasks of which MSAMT can schedule only 85%. Maintaining the 80% unit level but having an 8 weekperiod increases required training achieved to 94%. Such results can help determine the ability of an Army installation to satisfy training requirements of its stationed units as well as identify a shortage or excess in available training land. It can show the training impact of changing the quantity of units at an installation and thereby aid in base realignment and closure decisions. / First Lieutenant, Turkish Army

Les premiers résultats en analyse convexe ne nécessitant aucune condition de qualification datent à peu près d'une quinzaine d'années et constituent le début de l'analyse convexe séquentielle. Ils concernaient essentiellement: la somme d'un nombre fini de fonctions convexes, la composition avec une application vectorielle convexe, et les problèmes de programmation mathématique convexe. Cette thèse apporte un ensemble de contributions à l'analyse convexe séquentielle. La première partie de la thèse est consacrée à l'obtention sans condition de qualification de règles de calcul sous-differentiel exprimées séquentiellement. On considère les cas suivants:l'enveloppe supérieure d'une famille quelconque de fonctions convexes semi-continues inférieurement définies sur un espace de Banach; une fonctionnelle intégrale convexe générale définie sur un espace de fonctions intégrales;la somme continue (ou intégrale) de fonctions convexes semi-continues inférieurement définies sur un espace de Banach séparable. Dans la deuxième partie on établit sans hypothèse de qualification sur les données du problème, des conditions nécessaires et suffisantes d'optimalité séquentielle pour divers types de problèmes d'optimisation et de contrôle optimal discret ou continu. / The first results in convex analysis without any qualificationcondition have been established fifteen years ago, and one may say thatsequential convex analysis began with those results. They essentially concerned:The finite sum of convex functions, the composition with a vectorvaluedconvex mapping, and convex mathematical programming. The firstpart of this dissertation provides several contibutions to sequential convexanalysis. The following cases are considered: the upper envelop of a familyof lower semicontinuous convex functions; the integral functional overan integral space; the continuous sum of lower semicontinuous convex functions.In the second part, necessary and sufficient optimality conditions areestablished in sequential form for many types of programming problems anddicrete or continuous optimal control problems.

Approved for public release; distribution is unlimited / Reissued 30 May 2017 with correction to student's affiliation on title page. / Autonomous vehicle teams have great potential in a wide range of maritime sensing applications, including mine countermeasures (MCM). A key enabler for successfully employing autonomous vehicles in MCM missions is motion planning, a collection of algo-rithms for designing trajectories that vehicles must follow. For maximum utility, these algorithms must consider the capabilities and limitations of each team member. At a minimum, they should incorporate dynamic and operational constraints to ensure trajectories are feasible. Another goal is maximizing sensor performance in the presence of uncertainty. Optimal control provides a useful frame-work for solving these types of motion planning problems with dynamic constraints and di_x000B_erent performance objectives, but they usually require numerical solutions. Recent advances in numerical methods have produced a general mathematical and computational framework for numerically solving optimal control problems with parameter uncertainty—generalized optimal control (GenOC)— thus making it possible to numerically solve optimal search problems with multiple searcher, sensor, and target models. In this dissertation, we use the GenOC framework to solve motion planning problems for di_x000B_erentMCMsearch missions conducted by autonomous surface and underwater vehicles. Physics-based sonar detection models are developed for operationally relevant MCM sensors, and the resulting optimal search trajectories improve mine detection performance over conventional lawnmower survey patterns—especially under time or resource constraints. Simulation results highlight the flexibility of this approach for optimal mo-tion planning and pre-mission analysis. Finally, a novel application of this framework is presented to address inverse problems relating search performance to sensor design, team composition, and mission planning for MCM CONOPS development.

This thesis is concerned with mathematical modelling and optimal control of constrained systems. Each of the systems under consideration is a system that can be controlled by one of the variables, and this control is subject to constraints. First, we consider middle-distance running where a runner's horizontal propulsive force is the control which is constrained to be within a given range. Middle-distance running is typically a strategy-intensive race as slipstreaming effects come into play since speeds are still relatively fast and runners can leave their starting lane. We formulate a two-runner coupled model and determine optimal strategies using optimal control theory. Second, we consider two applications of control systems with delay related to R&D expenditure. The first of these applications relates to the defence industry. The second relates to the pharmaceutical industry. Both applications are characterised by a long delay between initial investment in R&D and seeing the benefits of R&D realised. We formulate models tailored to each application and use optimal control theory to determine the optimal proportion of available funds to invest in R&D over a given time horizon. Third, we consider a mathematical model of urban burglary based on the Short model. We make some modifications to this model including the addition of deterrence due to police officer presence. Police officer density is the control variable, which is constrained due to a finite number of police officers. We look at different control strategies for the police and their effect on burglary hot-spot formation.