A dynamical system's state evolves over time, and when the system stays near a particular state this state is known as a stable state of the system. Through control methods, dynamical systems can be manipulated such that virtually any state can be made stable. Although most real systems evolve continuously in time the application of digital control methods to these systems is inherently discrete. States are sampled (with sensors) and fed back into the system in discrete-time to determine the input needed to control the continuous system. Additionally, dynamical systems often experience time delays. Some examples of time delays are delays due to transmission distances, processing software, sampling information, and many more. Such delays are often a cause of poor performance and, at times, instability in these systems. Recently a criterion referred to as intrinsic stability has been developed that ensures that a dynamic system cannot be destabilized by delays. The goal of this thesis is to broaden the definition of intrinsic stability to closed-loop systems, which are systems in which the control depends on the state of the system, and to determine control parameters that optimize this resilience to time delays. Here, we give criteria describing when a closed-loop system is intrinsically stable. This allows us to give examples in which systems controlled using Linear Quadratic Regulator (LQR) control can be made intrinsically stable.

Time delays are an inherent part of real-world systems. Besides the apparent slowing of the system, these time delays often cause destabilization in otherwise stable systems, and perhaps even more unexpectedly, can stabilize an unstable system. Here, we propose the Stochastic Time-Delayed Adaptation as a method for improving optimization on certain high-dimensional surfaces, which simply wraps a known optimizer --such as the Adam optimizer-- and is able to add a variety of time-delays. We begin by exploring time delays on certain gradient-based optimization methods and their affect on the optimizer's convergence properties. These optimizers include the standard gradient descent method and the more recent Adam Optimizer, where the latter is commonly used in neural networks for deep learning. To begin to describe the effect of time-delays on these methods, we use the theory of intrinsic stability. It has been shown that a system that possesses the property of intrinsic stability (a stronger form of global stability) will maintain its stability when subject to any time delays, e.g., constant, periodic, stochastic, etc. In feasible cases, we find relevant conditions under which the optimization method adapted with time delays is intrinsically stable and therefore converges to the system's minimal value. Finally, we examine the optimizer's performance using common optimizer performance metrics. This includes the number of steps an algorithm takes to converge and also the final loss value in relation to the global minimum of the loss function. We test these outcomes using various adaptations of the Adam optimizer on multiple common test optimization functions, which are designed to be difficult for vanilla optimizer methods. We show that the Stochastic Time-Delayed Adaptation can greatly improve an optimizer's ability to find a global minimum of a complex loss function.

Les scandales sanitaires ayant émaillé le médicament ont mis la sécurité d’utilisation au cœur des préoccupations des acteurs de santé. Tout au long de son cycle de vie, le médicament est susceptible d’exposition à des conditions de stress pouvant conduire à sa dégradation et potentiellement, à la modification du rapport bénéfice/risque. Ce problème est d’autant plus marqué en milieu hospitalier où les médicaments en post – AMM sont manipulés pour des besoins spécifiques des patients. Quid de la maîtrise des modifications de leurs microenvironnements ? Etendre son espace de connaissances est admis comme étant le meilleur moyen pour circonscrire ces phénomènes. Dans le cadre de ce projet doctoral, une stratégie d’étude du cycle de vie des médicaments en post – AMM a été mise en place afin de renforcer leur sécurité d’utilisation. Compte tenu de la place prépondérante des formes solides dans l’arsenal thérapeutique, le ticagrelor, un récent antiagrégant plaquettaire (AAP) présenté sous forme de comprimés, a été choisi pour cette étude. La première étape a consisté à l’utilisation des conditions de stress pour évaluer sa stabilité intrinsèque et l’élucidation structurale des produits de dégradations grâce au couplage LC-HR-MSn donnant accès aux compositions élémentaires. Les voies de dégradation ont été proposées et la sécurité des produits a été évaluée grâce à l’approche in silico. Par ailleurs, compte tenu de l’utilisation des AAP en association, dans la seconde partie de ce travail, l’extension de l’espace de connaissances du ticagrelor a permis d’envisager une stratégie de préformulation avec l’aspirine à l’état solide en utilisant des techniques complémentaires comme la LC-HR-MSn, la DSC, la DRX ou l’ATG. La formation d’un simple eutectique a été observée avec le mélange des deux principes actifs. Nous avons démontré que la dégradation du ticagrelor est liée à la décomposition de l’aspirine, modulée par les conditions environnementales. Le modèle d’étude du ticagrelor ouvre clairement des perspectives sur la maîtrise de la sécurité en l’élargissant à d’autres médicaments et pourra contribuer à leur recyclage approprié. / Tragedies caused by the misuse of pharmaceuticals have put the drug safety at the core of the concerns of healthcare providers. Throughout its life cycle, a drug may be subjected to environmental stresses, which can lead to its degradation. Thorough understanding about the susceptibility of a drug to degrade is an essential step to avoid it. This problem is in particular relevant in a hospital setting, where commercial drugs are usually applied to specific cases without a clear understanding of its limitations. As part of this PhD project, a life cycle study strategy for a commercial drug has been implemented in order to increase its safety in use. Given the prominence of solid forms in the therapeutic arsenal, ticagrelor, a recent antiplatelet agent (APA) in tablet form, was chosen for this study. The first step was devoted to the evaluation of the intrinsic stability and the structural elucidation of the degradation products making use of LC-HR-MSn, providing access to the elemental composition. Degradation pathways have been proposed and the safety of the products has been evaluated via an in silico toxicological approach. Furthermore because antiplatelet agents are often used in combination therapy, in the second part, a preformulation strategy with aspirin in the solid state has been studied using the complementary techniques LC-HR-MSn, DSC, PXRD, and TGA. The mixture of the two active pharmaceutical ingredients gave rise to a simple eutectic. We have demonstrated that the degradation of ticagrelor in these mixtures is closely related to the stability of aspirin, which is modulated by environmental conditions. The ticagrelor study provides a model for the safety management of other drugs and can contribute to their appropriate recycling.