Human-robot interactions can often be formulated as general-sum differential games where the equilibrial policies are governed by Hamilton-Jacobi-Isaacs (HJI) equations. Solving HJI PDEs faces the curse of dimensionality (CoD). While physics-informed neural networks (PINNs) alleviate CoD in solving PDEs with smooth solutions, they fall short in learning discontinuous solutions due to their sampling nature. This causes PINNs to have poor safety performance when they are applied to approximate values that are discontinuous due to state constraints. This dissertation aims to improve the safety performance of PINN-based value and policy models. The first contribution of the dissertation is to develop learning methods to approximate discontinuous values. Specifically, three solutions are developed: (1) hybrid learning uses both supervisory and PDE losses, (2) value-hardening solves HJIs with increasing Lipschitz constant on the constraint violation penalty, and (3) the epigraphical technique lifts the value to a higher-dimensional state space where it becomes continuous. Evaluations through 5D and 9D vehicle and 13D drone simulations reveal that the hybrid method outperforms others in terms of generalization and safety performance. The second contribution is a learning-theoretical analysis of PINN for value and policy approximation. Specifically, by extending the neural tangent kernel (NTK) framework, this dissertation explores why the choice of activation function significantly affects the PINN generalization performance, and why the inclusion of supervisory costate data improves the safety performance. The last contribution is a series of extensions of the hybrid PINN method to address real-time parameter estimation problems in incomplete-information games. Specifically, a Pontryagin-mode PINN is developed to avoid costly computation for supervisory data. The key idea is the introduction of a costate loss, which is cheap to compute yet effectively enables the learning of important value changes and policies in space-time. Building upon this, a Pontryagin-mode neural operator is developed to achieve state-of-the-art (SOTA) safety performance across a set of differential games with parametric state constraints. This dissertation demonstrates the utility of the resultant neural operator in estimating player constraint parameters during incomplete-information games.

Least squares fitting in 3D is applied to produce higher level geometric parameters that describe the optimum location of a line-profile through many nodal points that are derived from Finite Element Analysis (FEA) simulations of elastic spring-back of features both on stamped sheet metal components after they have been plasticly deformed in a press and released, and on simple assemblies made from them. Although the traditional Moore-Penrose inverse was used to solve the superabundant linear equations, the formulation of these equations was distinct and based on virtual work and statics applied to parallel-actuated robots in order to allow for both more complex profiles and a change in profile size. The output, a small displacement torsor (SDT) is used to describe the displacement of the profile from its nominal location. It may be regarded as a generalization of the slope and intercept parameters of a line which result from a Gauss-Markov regression fit of points in a plane. Additionally, minimum zone-magnitudes were computed that just capture the points along the profile. And finally, algorithms were created to compute simple parameters for cross-sectional shapes of components were also computed from sprung-back data points according to the protocol of simulations and benchmark experiments conducted by the metal forming community 30 years ago, although it was necessary to modify their protocol for some geometries that differed from the benchmark.

National Airspace Systems (NAS) are complex cyber-physical systems that require swift air traffic management (ATM) to ensure flight safety and efficiency. With the surging demand for air travel and the increasing intricacy of aviation systems, the need for advanced technologies to support air traffic management and air traffic control (ATC) service has become more crucial than ever. Data-driven models or artificial intelligence (AI) have been conceptually investigated by various parties and shown immense potential, especially when provided with a vast volume of real-world data. These data include traffic information, weather contours, operational reports, terrain information, flight procedures, and aviation regulations. Data-driven models learn from historical experiences and observations and provide expeditious recommendations and decision support for various operation tasks, directly contributing to the digital transformation in aviation. This dissertation reports several research studies covering different aspects of air traffic management and ATC service utilizing data-driven modeling, which are validated using real-world big data (flight tracks, flight events, convective weather, workload probes). These studies encompass a range of topics, including trajectory recommendations, weather studies, landing operations, and aviation human factors. Specifically, the topics explored are (i) trajectory recommendations under weather conditions, which examine the impact of convective weather on last on-file flight plans and provide calibrated trajectories based on convective weather; (ii) multi-aircraft trajectory predictions, which study the intention of multiple mid-air aircraft in the near-terminal airspace and provide trajectory predictions; (iii) flight scheduling operations, which involve probabilistic machine learning-enhanced optimization algorithms for robust and efficient aircraft landing sequencing; (iv) aviation human factors, which predict air traffic controller workload level from flight traffic data with conformalized graph neural network. The uncertainties associated with these studies are given special attention and addressed through Bayesian/probabilistic machine learning. Finally, discussions on high-level AI-enabled ATM research directions are provided, hoping to extend the proposed studies in the future. This dissertation demonstrates that data-driven modeling has great potential for aviation digital twins, revolutionizing the aviation decision-making process and enhancing the safety and efficiency of ATM. Moreover, these research directions are not merely add-ons to existing aviation practices but also contribute to the future of transportation, particularly in the development of autonomous systems.

Advanced driving assistance systems (ADAS) are one of the latest automotive technologies for improving vehicle safety. An efficient method to ensure vehicle safety is to limit vehicle states always within a predefined stability region. Hence, this thesis aims at designing a model predictive control (MPC) with non-overshooting constraints that always confine vehicle states in a predefined lateral stability region. To consider the feasibility and stability of MPC, terminal cost and constraints are investigated to guarantee the stability and recursive feasibility of the proposed non-overshooting MPC. The proposed non-overshooting MPC is first verified by using numerical examples of linear and nonlinear systems. Finally, the non-overshooting MPC is applied to guarantee vehicle lateral stability based on a nonlinear vehicle model for a cornering maneuver. The simulation results are presented and discussed through co-simulation of CarSim® and MATLAB/Simulink.

The distribution and transport of mercury in the human body are poorly constrained. For instance, the long-term persistence and intra-individual distribution of mercury in bones from dental amalgams or environmental exposure have not been studied. A robust method validated for accuracy and precision specifically for mercury in human bones would facilitate studies of mercury in anthropological, forensic, and medical studies. I present a highly precise, accurate mercury concentration analytical method targeted to human bone samples. This method uses commercially commonly available and reliable instruments that are not limited to elemental Hg analysis. This method requires significantly lower sample amounts than existing methods because it has a much lower limit of detection compared to the best mercury analyzers on the market and other analytical methods. With the low limit of detection achieved, this mercury concentration protocol is an excellent fit for studies with a limited amount of samples for destructive analysis. I then use this method to analyze the mercury concentration distribution in modern skeletal collections provided by three U.S. anthropological research facilities. Mercury concentration and distribution were analyzed from 35 donors’ skeletons with 18 different skeletal elements (bones) per donor to evaluate both the intra-individual and inter-individual variation in mercury concentration. Considered factors include geological differences in decomposition sites and the presence of dental amalgam filling. Geological differences in decomposition sites did not statistically affect the mercury concentration in the donor’s skeleton. The presence of dental amalgam significantly affected the inter-individual and intra-individual mercury concentration variation in donors’ skeletal samples. Individuals who had dental amalgam had significantly higher mercury concentration in their skeleton compared to individuals who did not have dental amalgam (p-value <0.01). Mercury concentration in the mandible, occipital bone, patella, and proximal phalanx (foot) was significantly affected by the presence of dental amalgam.

The need for autonomous cars has never been more vital, and for a vehicle to be completely autonomous, multiple components must work together, one of which is the capacity to park at the end of a mission. This thesis project aims to design and execute an automated parking assist system (APAS). Traditional Automated parking assist systems (APAS) may not be effective in some constrained urban parking environments because of the parking space dimension. The thesis proposes a novel four-wheel steering (4-WS) vehicle for automated parallel parking to overcome this kind of challenge. Then, benefiting from the maneuverability enabled by the 4WS system, the feasible initial parking area is vastly expanded from those for the conventional 2WS vehicles. In addition, the expanded initial area is divided into four areas where different paths are planned correspondingly. In the proposed novel APAS first, a suitable parking space is identified through ultra-sonic sensors, which are mounted around the vehicle, and then depending upon the vehicle's initial position, various compact and smooth parallel parking paths are generated. An optimization function is built to get the smoothest (i.e., the smallest steering angle change and the shortest path) parallel parking path. With the full utilization of the 4WS system, the proposed path planning algorithm can allow a larger initial parking area that can be easily tracked by the 4WS vehicles. The proposed APAS for 4WS vehicles makes the automatic parking process in restricted spaces efficient. To verify the feasibility and effectiveness of the proposed APAS, a 4WS vehicle prototype is applied for validation through both simulation and experiment results.

The increasing availability of data and advances in computation have spurred the development of data-driven approaches for modeling complex dynamical systems. These approaches are based on the idea that the underlying structure of a complex system can be discovered from data using mathematical and computational techniques. They also show promise for addressing the challenges of modeling high-dimensional, nonlinear systems with limited data. In this research expository, the state of the art in data-driven approaches for modeling complex dynamical systems is surveyed in a systemic way. First the general formulation of data-driven modeling of dynamical systems is discussed. Then several representative methods in feature engineering and system identification/prediction are reviewed, including recent advances and key challenges.

Autonomous systems inevitably must interact with other surrounding systems; thus, algorithms for intention/behavior estimation are of great interest. This thesis dissertation focuses on developing passive and active model discrimination algorithms (PMD and AMD) with applications to set-valued intention identification and fault detection for uncertain/bounded-error dynamical systems. PMD uses the obtained input-output data to invalidate the models, while AMD designs an auxiliary input to assist the discrimination process. First, PMD algorithms are proposed for noisy switched nonlinear systems constrained by metric/signal temporal logic specifications, including systems with lossy data modeled by (m,k)-firm constraints. Specifically, optimization-based algorithms are introduced for analyzing the detectability/distinguishability of models and for ruling out models that are inconsistent with observations at run time. On the other hand, two AMD approaches are designed for noisy switched nonlinear models and piecewise affine inclusion models, which involve bilevel optimization with integer variables/constraints in the inner/lower level. The first approach solves the inner problem using mixed-integer parametric optimization, whose solution is included when solving the outer problem/higher level, while the second approach moves the integer variables/constraints to the outer problem in a manner that retains feasibility and recasts the problem as a tractable mixed-integer linear programming (MILP). Furthermore, AMD algorithms are proposed for noisy discrete-time affine time-invariant systems constrained by disjunctive and coupled safety constraints. To overcome the issues associated with generalized semi-infinite constraints due to state-dependent input constraints and disjunctive safety constraints, several constraint reformulations are proposed to recast the AMD problems as tractable MILPs. Finally, partition-based AMD approaches are proposed for noisy discrete-time affine time-invariant models with model-independent parameters and output measurement that are revealed at run time. Specifically, algorithms with fixed and adaptive partitions are proposed, where the latter improves on the performance of the former by allowing the partitions to be optimized. By partitioning the operation region, the problem is solved offline, and partition trees are constructed which can be used as a `look-up table' to determine the optimal input depending on revealed information at run time.

Deep neural network-based methods have been proved to achieve outstanding performance on object detection and classification tasks. Deep neural networks follow the ``deeper model with deeper confidence'' belief to gain a higher recognition accuracy. However, reducing these networks' computational costs remains a challenge, which impedes their deployment on embedded devices. For instance, the intersection management of Connected Autonomous Vehicles (CAVs) requires running computationally intensive object recognition algorithms on low-power traffic cameras. This dissertation aims to study the effect of a dynamic hardware and software approach to address this issue. Characteristics of real-world applications can facilitate this dynamic adjustment and reduce the computation. Specifically, this dissertation starts with a dynamic hardware approach that adjusts itself based on the toughness of input and extracts deeper features if needed. Next, an adaptive learning mechanism has been studied that use extracted feature from previous inputs to improve system performance. Finally, a system (ARGOS) was proposed and evaluated that can be run on embedded systems while maintaining the desired accuracy. This system adopts shallow features at inference time, but it can switch to deep features if the system desires a higher accuracy. To improve the performance, ARGOS distills the temporal knowledge from deep features to the shallow system. Moreover, ARGOS reduces the computation furthermore by focusing on regions of interest. The response time and mean average precision are adopted for the performance evaluation to evaluate the proposed ARGOS system.