Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem

Multiscale Geometric Methods for Isolating Exercise Induced Morphological Adaptations in the Proximal Femur

The importance of skeletal bone in the functioning of the human body is well-established and acknowledged. Less pervasive among the populace, is the understanding of bone as an adaptive tissue which modulates itself to achieve the most construction sufficient for the role it is habituated to. These mechanisms are more pronounced in the long load bearing bones such as the femur. The proximal femur especially, functions under significant loads and does so with high degree of articulation, making it critical to mobility. Thus, exercising to buttress health and reinforce tissue quality is just as applicable to bone as it is to muscles. However, the efficiency of the adaptive (modelling/remodelling) processes is subdued after maturity, which makes the understanding of its potential even more important. Classically, studies have translated the evaluation of strength in terms of its material and morphology. While the morphology of the femur is constrained within a particular phenotype, minor variations can have a significant bearing on its capability to withstand loads. Morphology has been studied at different scales and dimensions wherein parameters quantified as lengths, areas, volumes and curvatures in two and three dimensions contribute towards characterising strength. The challenge has been to isolate the regions that show response to habitual loads. This thesis seeks to build on the principles of computational anatomy and develop procedures to study the distribution of mechanically relevant parameters. Methods are presented that increase the spatial resolution of traditional cross-sectional studies and develop a conformal mapping procedure for proximal femur shape matching. In addition, prevalent methods in cross-sectional analyses and finite element simulations are employed to analyse the morphology of the unique dataset. The results present the spatial heterogeneity and a multi-scale understanding of the adaptive response in the proximal femur morphology to habitual exercise loading

Analyse de séries temporelles d’images à moyenne résolution spatiale : reconstruction de profils de LAI, démélangeage : application pour le suivi de la végétation sur des images MODIS

This PhD dissertation is concerned with time series analysis for medium spatial resolution (MSR) remote sensing images. The main advantage of MSR data is their high temporal rate which allows to monitor land use. However, two main problems arise with such data. First, because of cloud coverage and bad acquisition conditions, the resulting time series are often corrupted and not directly exploitable. Secondly, pixels in medium spatial resolution images are often “mixed” in the sense that the spectral response is a combination of the response of “pure” elements.These two problems are addressed in this PhD. First, we propose a data assimilation technique able to recover consistent time series of Leaf Area Index from corrupted MODIS sequences. To this end, a plant growth model, namely GreenLab, is used as a dynamical constraint. Second, we propose a new and efficient unmixing technique for time series. It is in particular based on the use of “elastic” kernels able to properly compare time series shifted in time or of various lengths.Experimental results are shown both on synthetic and real data and demonstrate the efficiency of the proposed methodologies.Cette thèse s’intéresse à l’analyse de séries temporelles d’images satellites à moyenne résolution spatiale. L’intérêt principal de telles données est leur haute répétitivité qui autorise des analyses de l’usage des sols. Cependant, deux problèmes principaux subsistent avec de telles données. En premier lieu, en raison de la couverture nuageuse, des mauvaises conditions d’acquisition, ..., ces données sont souvent très bruitées. Deuxièmement, les pixels associés à la moyenne résolution spatiale sont souvent “mixtes” dans la mesure où leur réponse spectrale est une combinaison de la réponse de plusieurs éléments “purs”. Ces deux problèmes sont abordés dans cette thèse. Premièrement, nous proposons une technique d’assimilation de données capable de recouvrer des séries temporelles cohérentes de LAI (Leaf Area Index) à partir de séquences d’images MODIS bruitées. Pour cela, le modèle de croissance de plantes GreenLab estutilisé. En second lieu, nous proposons une technique originale de démélangeage, qui s’appuie notamment sur des noyaux “élastiques” capables de gérer les spécificités des séries temporelles (séries de taille différentes, décalées dans le temps, ...)Les résultats expérimentaux, sur des données synthétiques et réelles, montrent de bonnes performances des méthodologies proposées

Stochastic Derivative-Free Optimization of Noisy Functions

Optimization problems with numerical noise arise from the growing use of computer simulation of complex systems. This thesis concerns the development, analysis and applications of randomized derivative-free optimization (DFO) algorithms for noisy functions. The first contribution is the introduction of DFO-VASP, an algorithm for solving the problem of finding the optimal volumetric alignment of protein structures. Our method compensates for noisy, variable-time volume evaluations and warm-starts the search for globally optimal superposition. These techniques enable DFO-VASP to generate practical and accurate superpositions in a timely manner. The second algorithm, STARS, is aimed at solving general noisy optimization problems and employs a random search framework while dynamically adjusting the smoothing step-size using noise information. rate analysis of this algorithm is provided in both additive and multiplicative noise settings. STARS outperforms randomized zero-order methods in both additive and multiplicative settings and has an advantage of being insensitive to the level noise in terms of number of function evaluations and final objective value. The third contribution is a trust-region model-based algorithm STORM, that relies on constructing random models and estimates that are sufficiently accurate with high probability. This algorithm is shown to converge with probability one. Numerical experiments show that STORM outperforms other stochastic DFO methods in solving noisy functions

Analyse der Knochendeformation und Muskelkräfte der menschlichen Tibia

Für die Erforschung des Weltraums durch den Menschen, aber auch für die Gesundheit auf der Erde allgemein, ist ein grundlegendes Verständnis über die Adaption des Knochens essentiell. Die Regulierung des Auf- und Abbaus des Knochens wird über seine Deformation gesteuert, welche wiederum aus der mechanischen Belastung dessen resultiert. Diese Zusammenhänge zu verstehen, die Auswirkungen von verschiedenen Aktivitäten auf die Deformation des Knochens zu kennen und in Relation setzten zu können, ist der Schlüssel zu dem gesuchten, grundlegenden Verständnis. Im Zuge dieser Arbeit wurde hierfür eine Methode entwickelt, diese Zusammenhänge qualitativ und quantitativ herzuleiten. Basierend auf in vivo Messungen an der Tibia wurde ein Algorithmus zur in silico Analyse der vorliegenden Daten entwickelt. Dieser macht sich die Konsequenzen des Hookeschen Gesetzes in Form des Superpositionsprinzips zu Nutze, um quasi-invers aus der gemessenen Deformationsbewegung die dafür notwendigen Kräfte zu bestimmen. Diese können in einer Finite Elemente Analyse (FEA) mit den rekonstruierten Tibia-Knochen verwendet werden, um deren Spannungs-Dehnungs-Zustand zu bestimmen. Zur Validierung der Annahmen und Randbedingungen des Algorithmus wurde ein biomechanischer Messstand konstruiert. In diesem konnten in replica und ex vivo Untersuchungen durchgeführt werden. Zu diesem Zweck wurden Tibia-Replikate aus Komposite-Material bzw. Leichenbeine künstlich über Aktuatoren mit Kräften beaufschlagt und über eine spezielle Anwendung von Motion Capturing die Deformationsbewegung des Knochens gemessen. Die Auswertung der in vivo Daten mittels der in silico Analyse lieferte quantitative Ergebnisse zur Dehnung in der Tibia für diverse alltägliche Aktivitäten. Diese Ergebnisse sind, im Gegensatz zur bisherigen gängigen Methode, jedoch nicht auf einen singulären Messpunkt limitiert, sondern decken den kompletten rekonstruierten Bereich der Tibia ab. Dies führte zur Feststellung, dass die aktuell angenommenen Werte zu niedrig angesetzt sind. Hinzu kommt, dass die Analyse eine zeitliche und örtliche Varianz der Peak-Dehnungen im Knochen über den Ablauf einer Aktivität aufzeigt. Diese Ergebnisse verändern das bisherige Verständnis über die Knochenadaption und deren Regulierungsmechanismen

Biomechanical Spectrum of Human Sport Performance

Writing or managing a scientific book, as it is known today, depends on a series of major activities, such as regrouping researchers, reviewing chapters, informing and exchanging with contributors, and at the very least, motivating them to achieve the objective of publication. The idea of this book arose from many years of work in biomechanics, health disease, and rehabilitation. Through exchanges with authors from several countries, we learned much from each other, and we decided with the publisher to transfer this knowledge to readers interested in the current understanding of the impact of biomechanics in the analysis of movement and its optimization. The main objective is to provide some interesting articles that show the scope of biomechanical analysis and technologies in human behavior tasks. Engineers, researchers, and students from biomedical engineering and health sciences, as well as industrial professionals, can benefit from this compendium of knowledge about biomechanics applied to the human body