This dissertation introduces novel methods for solving highly challenging model- ing and control problems, motivated by advanced aerospace systems. Adaptable, ro- bust and computationally effcient, multi-resolution approximation algorithms based on Radial Basis Function Network and Global-Local Orthogonal Mapping approaches are developed to address various problems associated with the design of large scale dynamical systems. The main feature of the Radial Basis Function Network approach is the unique direction dependent scaling and rotation of the radial basis function via a novel Directed Connectivity Graph approach. The learning of shaping and rota- tion parameters for the Radial Basis Functions led to a broadly useful approximation approach that leads to global approximations capable of good local approximation for many moderate dimensioned applications. However, even with these refinements, many applications with many high frequency local input/output variations and a high dimensional input space remain a challenge and motivate us to investigate an entirely new approach. The Global-Local Orthogonal Mapping method is based upon a novel averaging process that allows construction of a piecewise continuous global family of local least-squares approximations, while retaining the freedom to vary in a general way the resolution (e.g., degrees of freedom) of the local approximations. These approximation methodologies are compatible with a wide variety of disciplines such as continuous function approximation, dynamic system modeling, nonlinear sig-nal processing and time series prediction. Further, related methods are developed for the modeling of dynamical systems nominally described by nonlinear differential equations and to solve for static and dynamic response of Distributed Parameter Sys- tems in an effcient manner. Finally, a hierarchical control allocation algorithm is presented to solve the control allocation problem for highly over-actuated systems that might arise with the development of embedded systems. The control allocation algorithm makes use of the concept of distribution functions to keep in check the "curse of dimensionality". The studies in the dissertation focus on demonstrating, through analysis, simulation, and design, the applicability and feasibility of these ap- proximation algorithms to a variety of examples. The results from these studies are of direct utility in addressing the "curse of dimensionality" and frequent redundancy of neural network approximation.

The goal of this research is to build an experimental environment for the Simulation Interoperability Laboratory (SIL) of the University of Central Florida (UCF). The Simulation Interoperability Laboratory (SIL) is researching about multi-resolution modeling(MRM), with a focus on military field uses. This thesis proposes steps to develop an MRM federation system and build two different MRM systems using COTS simulations (SIMBox, VR-Forces, and MASA Sword). This report is written to provide the basis for a time-based MRM federation study in the Simulation Interoperability Laboratory. The report describes many definitions and notions related to Multi-Resolution Modeling(MRM) and discusses examples to make better understanding for further research. MRM is relatively new research, and there are high demands for integrating simulators running in military field purposes. Most military-related research is based on simulators currently being used in the military; this poses a problem for research because the data is classified, resulting in many limitations for outside researchers to see the military's process for building an MRM system or the results of the research. Therefore, development of the MRM federation using COTS simulations can provide many examples of MRM issues for future research.

Advanced modeling tools and methods are essential components for the analyses of congested conditions and advanced Intelligent Transportation Systems (ITS) strategies such as Managed Lanes (ML). A number of tools with different analysis resolution levels have been used to assess these strategies. These tools can be classified as sketch planning, macroscopic simulation, mesoscopic simulation, microscopic simulation, static traffic assignment, and dynamic traffic assignment tools. Due to the complexity of the managed lane modeling process, this dissertation investigated a Multi-Resolution Modeling (MRM) approach that combines a number of these tools for more efficient and accurate assessment of ML deployments. This study clearly demonstrated the differences in the accuracy of the results produced by the traffic flow models incorporated into different tools when compared with real-world measurements. This difference in the accuracy highlighted the importance of the selection of the appropriate analysis levels and tools that can better estimate ML and General Purpose Lanes (GPL) performance. The results also showed the importance of calibrating traffic flow model parameters, demand matrices, and assignment parameters based on real-world measurements to ensure accurate forecasts of real-world traffic conditions. In addition, the results indicated that the real-world utilization of ML by travelers can be best predicated with the use of dynamic traffic assignment modeling that incorporates travel time, toll, and travel time reliability of alternative paths in the assignment objective function. The replication of the specific dynamic pricing algorithm used in the real-world in the modeling process was also found to provide the better forecast of ML utilization. With regards to Connected Vehicle (CV) operations on ML, this study demonstrated the benefits of using results from tools with different modeling resolution to support each other’s analyses. In general, the results showed that providing toll incentives for Cooperative Adaptive Cruise Control (CACC)-equipped vehicles to use ML is not beneficial at lower market penetrations of CACC due to the small increase in capacity with these market penetrations. However, such incentives were found to be beneficial at higher market penetrations, particularly with higher demand levels.

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Cette thèse présente trois apports principaux dans le cadre de la modélisation et la simulation des systèmes physiologiques. Le premier apport est la formalisation des aspects qui concernent la modélisation multi-formalisme et multi-résolution. Le deuxième est la présentation et amélioration d'une librairie et un cadre général de modélisation et simulation qui intègre un ensemble d'outils pour aider la définition, l'analyse, l'utilisation et le partage des modèles mathématiques complexes. Le troisième apport est l'application du cadre de modélisation pour améliorer le diagnostic et les stratégies thérapeutiques des applications cliniques concernant le système cardiovasculaire, notamment l'insuffisance cardiaque associée à l'hypertension et les maladies coronariennes. Des applications potentielles associées à la thérapie de resynchronisation cardiaque et l'apnée-bradycardie du nouveau-né prématuré ont été aussi présentées. Ces cas d'étude incluent une intégration d'un cœur pulsatile dans un modèle globale du système cardiovasculaire qui prend en compte i) les mécanismes de régulation à long terme, ainsi que la représentation d'un type d'insuffisance cardiaque, ii) l'analyse de l'hémodynamique coronarienne et sa circulation collatérale pour des patients atteints d'une maladie tri-tronculaire et qui subissent une chirurgie de pontage aorto-coronarien, iii) l'intégration du système électrique cardiaque et son comportement mécanique pour l'optimisation du délai atrio-ventriculaire d'un stimulateur cardiaque, et iv) l'estimation basée sur modèles de l'activité des voies vagale et sympathique du baroreflèxe en période néonatale. / This thesis presents three main contributions in the context of modeling and simulation of physiological systems. The first one is a formalization of the methodology involved in multi-formalism and multi-resolution modeling. The second one is the presentation and improvement of a modeling and simulation framework integrating a range of tools that help the definition, analysis, usage and sharing of complex mathematical models. The third contribution is the application of this modeling framework to improve diagnostic and therapeutic strategies for clinical applications involving the cardiovascular system: hypertension-based heart failure (HF) and coronary artery disease (CAD). A prospective application in cardiac resynchronization therapy (CRT) is also presented, which also includes a model of the therapy. Finally, a final application is presented for the study of the baroreflex responses in the newborn lamb. These case studies include the integration of a pulsatile heart into a global cardiovascular model that captures the short and long term regulation of the cardiovascular system with the representation of heart failure, the analysis of coronary hemodynamics and collateral circulation of patients with triple-vessel disease enduring a coronary artery bypass graft surgery, the construction of a coupled electrical and mechanical cardiac model for the optimization of atrio ventricular and intraventricular delays of a biventricular pacemaker, and a model-based estimation of sympathetic and vagal responses of premature newborn lambs.

This thesis presents three main contributions in the context of modeling and simulation of physiological systems. The first one is a formalization of the methodology involved in multi-formalism and multi-resolution modeling. The second one is the presentation and improvement of a modeling and simulation framework integrating a range of tools that help the definition, analysis, usage and sharing of complex mathematical models. The third contribution is the application of this modeling framework to improve diagnostic and therapeutic strategies for clinical applications involving the cardiovascular system: hypertension-based heart failure (HF) and coronary artery disease (CAD). A prospective application in cardiac resynchronization therapy (CRT) is also presented, which also includes a model of the therapy. Finally, a final application is presented for the study of the baroreflex responses in the newborn lamb. These case studies include the integration of a pulsatile heart into a global cardiovascular model that captures the short and long term regulation of the cardiovascular system with the representation of heart failure, the analysis of coronary hemodynamics and collateral circulation of patients with triple-vessel disease enduring a coronary artery bypass graft surgery, the construction of a coupled electrical and mechanical cardiac model for the optimization of atrio ventricular and intraventricular delays of a biventricular pacemaker, and a model-based estimation of sympathetic and vagal responses of premature newborn lambs.