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.

Small and medium-sized enterprises (SMEs) have emerged as a vital force in the economic development of our country, significantly influencing national economic growth, employment rates, market competition, and innovation. Consequently, the ability of SMEs to achieve stable performance growth is crucial for socio-economic development. Previous research has identified factors such as political connections, cash flow, capital, and information technology as significant contributors to business growth. However, SMEs often lack these resources or cannot control them, making existing research inadequate for guiding the performance growth of SMEs.To address this issue, this study is grounded in the resource-based view and constructs a theoretical model on the impact of SME strategic completeness on performance growth. This model is based on literature research and in-depth interviews. It highlights the mediating roles of market adaptability, operational agility, and employee proactivity. Additionally, the model examines the moderating effects of competitive intensity, strategic implementation capability, and management digitalization. The study collected 203 valid SME samples for analysis and hypothesis testing, yielding the following conclusions: (1)The more comprehensive the business strategy, the better the adaptability to external markets, the higher the operational agility, and the stronger the initiative of employees. (2)Better market adaptability leads to faster performance growth. (3)Higher operational agility accelerates performance growth. (4)Greater employee initiative enhances performance growth. (5)The stronger the external competitive intensity faced by a business, the more effective a well-developed strategy is in improving market adaptability, operational agility, and employee initiative. (6)Stronger strategic implementation capabilities further enhance the effectiveness of a well-developed strategy in improving market adaptability and employee initiative. (7)A higher level of management digitalization enhances the effects of market adaptability, operational agility, and employee initiative, thereby boosting business performance. This study offers theoretical and practical value by clarifying the paths, mechanisms, and boundary conditions through which strategic completeness promotes business performance growth, enriching the theoretical system of SME performance growth. Furthermore, by integrating the cutting-edge concept of management digitalization into the research on strategic completeness and performance growth, this study contributes to the development and refinement of the research framework. Practically, it provides strategic recommendations for SMEs on how to enhance business performance growth through strategic completeness.

Modular multilevel converters (MMCs) have become an attractive technology for high power applications. One of the main challenges associated with control and operation of the MMC-based systems is to smoothly precharge submodule (SM) capacitors to the nominal voltage during the startup process. The existing closed-loop methods require additional effort to analyze the small-signal model of MMC and tune control parameters. The existing open-loop methods require auxiliary voltage sources to charge SM capacitors, which add to the system complexity and cost. A generalized precharging strategy is proposed in this thesis.

For large-scale MMC-embedded power systems, it is required to investigate dynamic performance, fault characteristics, and stability. Modeling of the MMC is one of the challenges associated with the study of large-scale MMC-based power systems. The existing models of MMC did not consider the various configurations of SMs and different operating conditions. An improved equivalent circuit model is proposed in this thesis.

The solid state transformer (SST) has been investigated for the distribution systems to reduce the volume and weight of power transformer. Recently, the MMC is employed into the SST due to its salient features. For design and control of the MMC-based SST, its operational principles are comprehensively analyzed. Based on the analysis, its mathematical model is developed for evaluating steady-state performances. For optimal design of the MMC-based SST, the mathematical model is modified by considering circuit parameters.

One of the challenges of the MMC-based SST is the balancing of capacitor voltages. The performances of various voltage balancing algorithms and different modulation methods have not been comprehensively evaluated. In this thesis, the performances of different voltage-balancing algorithms and modulation methods are analyzed and evaluated. Based on the analysis, two improved voltage-balancing algorithms are proposed in this thesis.

For design of the MMC-based SST, existing references only focus on optimal design of medium-frequency transformer (MFT). In this thesis, an optimal design procedure is developed for the MMC under medium-frequency operation based on the mathematical model of the MMC-based SST. The design performance of MMC is comprehensively evaluated based on free system parameters.

he accurate simulation of many-body quantum systems is a challenge for computational physics. Quantum Monte Carlo methods are a class of algorithms that can be used to solve the many-body problem. I study many-body quantum systems with Path Integral Monte Carlo techniques in three related areas of semiconductor physics: (1) the role of correlation in exchange coupling of spins in double quantum dots, (2) the degree of correlation and hyperpolarizability in Stark shifts in InGaAs/GaAs dots, and (3) van der Waals interactions between 1-D metallic quantum wires at finite temperature. The two-site model is one of the simplest quantum problems, yet the quantitative mapping from a three-dimensional model of a quantum double dot to an effective two-site model has many subtleties requiring careful treatment of exchange and correlation. I calculate exchange coupling of a pair of spins in a double dot from the permutations in a bosonic path integral, using Monte Carlo method. I also map this problem to a Hubbard model and find that exchange and correlation renormalizes the model parameters, dramatically decreasing the effective on-site repulsion at larger separations. Next, I investigated the energy, dipole moment, polarizability and hyperpolarizability of excitonic system in InGaAs/GaAs quantum dots of different shapes and successfully give the photoluminescence spectra for different dots with electric fields in both the growth and transverse direction. I also showed that my method can deal with the higher-order hyperpolarizability, which is most relevant for fields directed in the lateral direction of large dots. Finally, I show how van der Waals interactions between two metallic quantum wires change with respect to the distance between them. Comparing the results from quantum Monte Carlo and the random phase approximation, I find similar power law dependance. My results for the calculation in quasi-1D and exact 1D wires include the effect of temperature, which has not previously been studied.