Consider a time-dependent optimal control problem, where the state evolution is described by an initial value problem. There are a variety of numerical methods to solve these problems. The so-called indirect approach is considered detailed in this thesis. The indirect methods solve decoupled boundary value problems resulting from the necessary conditions for the optimal control problem. The so-called Pantoja method describes a computationally efficient stage-wise construction of the Newton direction for the discrete-time optimal control problem. There are many relationships between multiple shooting techniques and Pantoja method, which are investigated in this thesis. In this context, the equivalence of Pantoja method and multiple shooting method of Riccati type is shown. Moreover, Pantoja method is extended to the case where the state equations are discretised using one of implicit numerical methods. Furthermore, the concept of symplecticness and Hamiltonian systems is introduced. In this regard, a suitable numerical method is presented, which can be applied to unconstrained optimal control problems. It is proved that this method is a symplectic one. The iterative solution of optimal control problems in ordinary differential equations by Pantoja or Riccati equivalent methods leads to a succession of triple sweeps through the discretised time interval. The second (adjoint) sweep relies on information from the first (original) sweep, and the third (final) sweep depends on both of them. Typically, the steps on the adjoint sweep involve more operations and require more storage than the other two. The key difficulty is given by the enormous amount of memory required for the implementation of these methods if all states throughout forward and adjoint sweeps are stored. One of goals of this thesis is to present checkpointing techniques for memory reduced implementation of these methods. For this purpose, the well known aspect of checkpointing has to be extended to a `nested checkpointing` for multiple transversals. The proposed nested reversal schedules drastically reduce the required spatial complexity. The schedules are designed to minimise the overall execution time given a certain total amount of storage for the checkpoints. The proposed scheduling schemes are applied to the memory reduced implementation of the optimal control problem of laser surface hardening and other optimal control problems. / Es wird ein Problem der optimalen Steuerung betrachtet. Die dazugehoerigen Zustandsgleichungen sind mit einer Anfangswertaufgabe definiert. Es existieren zahlreiche numerische Methoden, um Probleme der optimalen Steuerung zu loesen. Der so genannte indirekte Ansatz wird in diesen Thesen detailliert betrachtet. Die indirekten Methoden loesen das aus den Notwendigkeitsbedingungen resultierende Randwertproblem. Das so genannte Pantoja Verfahren beschreibt eine zeiteffiziente schrittweise Berechnung der Newton Richtung fuer diskrete Probleme der optimalen Steuerung. Es gibt mehrere Beziehungen zwischen den unterschiedlichen Mehrzielmethoden und dem Pantoja Verfahren, die in diesen Thesen detailliert zu untersuchen sind. In diesem Zusammenhang wird die aequivalence zwischen dem Pantoja Verfahren und der Mehrzielmethode vom Riccati Typ gezeigt. Ausserdem wird das herkoemlige Pantoja Verfahren dahingehend erweitert, dass die Zustandsgleichungen mit Hilfe einer impliziten numerischen Methode diskretisiert sind. Weiterhin wird das Symplektische Konzept eingefuehrt. In diesem Zusammenhang wird eine geeignete numerische Methode praesentiert, die fuer ein unrestringiertes Problem der optimalen Steuerung angewendet werden kann. In diesen Thesen wird bewiesen, dass diese Methode symplectisch ist. Das iterative Loesen eines Problems der optimalen Steuerung in gewoenlichen Differentialgleichungen mit Hilfe von Pantoja oder Riccati aequivalenten Verfahren fuehrt auf eine Aufeinanderfolge der Durchlaeufetripeln in einem diskretisierten Zeitintervall. Der zweite (adjungierte) Lauf haengt von der Information des ersten (primalen) Laufes, und der dritte (finale) Lauf haeng von den beiden vorherigen ab. Ueblicherweise beinhalten Schritte und Zustaende des adjungierten Laufes wesentlich mehr Operationen und benoetigen auch wesentlich mehr Speicherplatzkapazitaet als Schritte und Zustaende der anderen zwei Durchlaeufe. Das Grundproblem besteht in einer enormen Speicherplatzkapazitaet, die fuer die Implementierung dieser Methoden benutzt wird, falls alle Zustaende des primalen und des adjungierten Durchlaufes zu speichern sind. Ein Ziel dieser Thesen besteht darin, Checkpointing Strategien zu praesentieren, um diese Methoden speichereffizient zu implementieren. Diese geschachtelten Umkehrschemata sind so konstruiert, dass fuer einen gegebenen Speicherplatz die gesamte Laufzeit zur Abarbeitung des Umkehrschemas minimiert wird. Die aufgestellten Umkehrschemata wurden fuer eine speichereffiziente Implementierung von Problemen der optimalen Steuerung angewendet. Insbesondere betrifft dies das Problem einer Oberflaechenabhaertung mit Laserbehandlung.

<div>Optimal control theory (OCT) exists since the 1950s. However, with the advent of modern computers, the design community delegated the task of solving the optimal control problems (OCPs) largely to computationally intensive direct methods instead of methods that use OCT. Some recent work showed that solvers using OCT could leverage parallel computing resources for faster execution. The need for near real-time, high quality solutions for OCPs has therefore renewed interest in OCT in the design community. However, certain challenges still exist that prohibits its use for solving complex practical aerospace problems, such as landing human-class payloads safely on Mars.</div><div><br></div><div>In order to advance OCT, this thesis introduces Epsilon-Trig regularization method to simply and efficiently solve bang-bang and singular control problems. The Epsilon-Trig method resolves the issues pertaining to the traditional smoothing regularization method. Some benchmark problems from the literature including the Van Der Pol oscillator, the boat problem, and the Goddard rocket problem verified and validated the Epsilon-Trig regularization method using GPOPS-II.</div><div><br></div><div>This study also presents and develops the usage of trigonometry for incorporating control bounds and mixed state-control constraints into OCPs and terms it as Trigonometrization. Results from literature and GPOPS-II verified and validated the Trigonometrization technique using certain benchmark OCPs. Unlike traditional OCT, Trigonometrization converts the constrained OCP into a two-point boundary value problem rather than a multi-point boundary value problem, significantly reducing the computational effort required to formulate and solve it. This work uses Trigonometrization to solve some complex aerospace problems including prompt global strike, noise-minimization for general aviation, shuttle re-entry problem, and the g-load constraint problem for an impactor. Future work for this thesis includes the development of the Trigonometrization technique for OCPs with pure state constraints.</div>

Cette thèse s’inscrit de manière indirecte dans la problématique des risques psychosociaux. A la demande d’un groupe mondial de l’industrie électrique, nous sommes entré dans la question en renversant le problème. Nous avons étudié les instruments psychosociaux de la santé au travail chez les managers de proximité. Le développement du pouvoir d’agir protège la santé et la formation de nouveaux buts est un organisateur de ce développement. Nous avons donc cherché à comprendre et à expliquer comment de nouveaux buts se forment dans et par les dialogues entre pairs sur le travail. L’analyse de discours a permis d’identifier une opération langagière et deux opérations psychologiques qui concourent au renouvellement des buts d’action : la reprise de discours dans le discours, la différenciation des sources de but et l’institution de liaison entre les activités. Sur la base de ces résultats, nous définissons les conditions que les dialogues entre pairs doivent réunir pour être un instrument de la santé. / This thesis is a contribution to the field of psychosocial risks at work. It reports how, in order to respond to the command of an international corporation of electrics industry, we entered the question of psychosocial risk at work, and how we managed to reverse the question. We ‘ve been studying, in a team managers’ group, the psychosocial tools used in order to build and maintain health at work. in the perspective of Clinic of Activity, we know firstly that the development of « power to act » in activity protects and promotes health at work, and secondly that the creation of new goals is a medium of this development. That is why , in this research project, we aimed to understand the creation process of new goals in activity, and we studied this process in a specific frame : in and by the way of dialogues about work activity among professional peers. Discourse analysis permit to identify three different processes, a language process and two psychological ones, that all participate to a renew of goals. Those processes are : 1) a new iteration, in the discourse, of a verbal statement taken from another discourse ; 2) the differentiation of goal’s origins ; and 3) the elaboration of new links between activities. Those issues allows us to define some of the significant properties of dialogue as a tool for health promotion between peers at work.

It is a well-known fact that criminals derive an income from their illegal activities, live lavish lifestyles, flaunt their wealth for all to see and acquire luxury goods. It is also a well known fact that criminals living from the proceeds of crime do not want to not want to keep financial records of their transactions or illegitimate business for fear of being detected by the authorities and to escape being taxed. It is also a known fact that criminals do not declare income from criminal activities for income tax purposes to the revenue authorities for fear of the illegal origin of the income being made known to the investigating authorities and law enforcement. During the investigation of financial crimes, such as tax evasion and money laundering, it may be required that the amount or value of money, income or assets accrued by a subject is determined in order to determine for instance their liability to pay tax. This research project examines the Net Worth method as an indirect method to circumstantially quantify income during the investigation of financial crime. / Police Practice / M.Tech. (Forensic Investigation)

It is a well-known fact that criminals derive an income from their illegal activities, live lavish lifestyles, flaunt their wealth for all to see and acquire luxury goods. It is also a well known fact that criminals living from the proceeds of crime do not want to not want to keep financial records of their transactions or illegitimate business for fear of being detected by the authorities and to escape being taxed. It is also a known fact that criminals do not declare income from criminal activities for income tax purposes to the revenue authorities for fear of the illegal origin of the income being made known to the investigating authorities and law enforcement. During the investigation of financial crimes, such as tax evasion and money laundering, it may be required that the amount or value of money, income or assets accrued by a subject is determined in order to determine for instance their liability to pay tax. This research project examines the Net Worth method as an indirect method to circumstantially quantify income during the investigation of financial crime. / Police Practice / M.Tech. (Forensic Investigation)