MS, University of Cincinnati, 2024, Engineering and Applied Science: Aerospace Engineering

The integration of AI in autonomous vehicles has been rapidly expanding and has the potential to raise concerns about non-compliant or malicious actors. Predicting movements or strategies of these actors could provide a substantial advantage in the mitigation of such threats. In a simulated asteroids style game, capture of these actors closely resembles pursuit evasion problems in differential games. In this work, multiple evader control methods are mapped by an adaptable fuzzy modified potential field avoidance method trained via genetic algorithm. Evader routes are integrated and optimal interception points are determined by numerical methods or a fuzzy logic approach. Time delayed mines are then placed at the interception point to eliminate the evader. The fuzzy modified potential field has also been separately trained to produce highly effective avoidance within congested asteroid environments.

Committee: Kelly Cohen Ph.D. (Committee Chair); Anoop Sathyan Ph.D. (Committee Member); Donghoon Kim Ph.D. (Committee Member); Manish Kumar Ph.D. (Committee Member) Subjects: Aerospace Engineering

PhD, University of Cincinnati, 2022, Engineering and Applied Science: Electrical Engineering

Supremacy in armed conflict comes not merely from superiority in capability or numbers but from how assets are used, down to the maneuvers of individual vehicles and munitions. This document outlines a research plan focused on skirmish-level tactics to militarily relevant scenarios. Skirmish-level refers to both the size of the adversarial engagement -- generally one vs. one, two vs. one, and/or one vs. two -- as well as the fact that the goal or objective of each team is well-established. The problem areas include pursuit-evasion and target guarding, either of which may be considered as sub-problems within military missions such as air-to-air combat, suppression/defense of ground-based assets, etc. In most cases, the tactics considered are comprised of the control policy of the agents (i.e., their spatial maneuvers), but may also include role assignment (e.g, whether to act as a decoy or striker) as well as discrete decisions (e.g., whether to engage or retreat). Skirmish-level tactics are important because they can provide insight into how to approach larger scale conflicts (many vs. many, many objectives, many decisions). Machine learning approaches such as reinforcement learning and neural networks have been demonstrated to be capable of developing controllers for large teams of agents. However, the performance of these controllers compared to the optimal (or equilibrium) policies is generally unknown. Differential Game Theory provides the means to obtain a rigorous solution to relevant scenarios in the form of saddle-point equilibrium control policies and the min/max (or max/min) cost / reward in the case of zero-sum games. When the equilibrium control policies can be obtained analytically, they are suitable for onboard / real-time implementation. Some challenges associated with the classical Differential Game Theory approach are explored herein. These challenges arise mainly due to the presence of singularities, which may appear in even the simplest differenti (open full item for complete abstract)

Committee: Zachariah Fuchs Ph.D. (Committee Member); David Casbeer Ph.D. (Committee Member); Dieter Vanderelst Ph.D. (Committee Member); Meir Pachter Ph.D. (Committee Member); John Gallagher Ph.D. (Committee Member) Subjects: Electrical Engineering

Master of Science (MS), Ohio University, 2020, Electrical Engineering & Computer Science (Engineering and Technology)

Deep reinforcement learning was used to train an agent within the framework of a Markov Decision Process (MDP) to pursue a target, while avoiding a defender, for the Target-Attacker-Defender (TAD) differential game of pursuit and evasion. The aim of this work was to explore the games where the previous attacking guidance methods found in literature failed to capture the Target. The reward function of the MDP presented by this work allowed for an attacking agent to learn a policy that expanded the number of cases where the target is captured beyond the former limit of success through the application of the Twin Delayed Deep Deterministic Policy Gradient algorithm (TD3). The strategy developed using artificial intelligence expands the target capture guidance approach to consider the long-term goal, rather than an instantaneous optimal heading. Initial Target positions within a limited set were considered with fixed values for agent velocities and Attacker and Defender initial positions to evaluate the Attacker's learned behavior in comparison with the optimal point capture guidance laws for target capture in the TAD game.

Committee: Jay Wilhelm PhD. (Advisor) Subjects: Computer Science

MS, University of Cincinnati, 2020, Engineering and Applied Science: Electrical Engineering

Differential games provide a framework for solving dynamic systems of two competing interests. One family of differential games focuses on two competing agents. Another family of differential games has competing teams of agents known as teaming games. Solutions to teaming games have inherit challenges due to the number of agents. By increasing the number of agents on each team, the dimension of the state space increases and additional termination cases are created. Singularities are a challenge in the majority of differential games and increasing the number of agents compounds that difficulty. This study aimed to overcome the challenges presented in solving teaming differential games by solving corresponding optimal control problems. The teaming game in question is a single pursuer, dual evader pursuit-evasion differential game. By fixing the control strategy of the pursuer, the teaming differential game is transformed into an optimal control problem for the team of evaders. Conversely, fixing the control strategies of the evaders results in an optimal control problem for the pursuer. For both problems, the optimal control strategy for the team in question is determined along with any singularities present within the control strategies. The teaming game is then reconsidered. Similarities between the optimal control problems and differential game allow for a simplified development of the solution to teaming game. The work concludes by demonstrating how solving the corresponding optimal control problems helps to overcome the inherit challenges of solving a teaming differential game.

Committee: Zachariah Fuchs Ph.D. (Committee Chair); David Casbeer Ph.D. (Committee Member); Ali Minai Ph.D. (Committee Member); Dieter Vanderelst Ph.D. (Committee Member) Subjects: Electrical Engineering

Doctor of Philosophy, The Ohio State University, 1983, Graduate School

Committee: Not Provided (Other) Subjects: Business Administration

Doctor of Philosophy, The Ohio State University, 1974, Graduate School

Committee: Not Provided (Other) Subjects: Engineering

Doctor of Philosophy, The Ohio State University, 2006, Electrical Engineering

The increasing use of autonomous assets in modern military operations has led to renewed interest in (multi-player) Pursuit-Evasion (PE) differential games. However, the current differential game theory in the literature is inadequate for dealing with this newly emerging situation. The purpose of this dissertation is to study general PE differential games with multiple pursuers and multiple evaders in continuous time. The current differential game theory is not applicable mainly because the terminal states of a multi-player PE game are difficult to specify. To circumvent this difficulty, we solve a deterministic problem by an indirect approach starting with a suboptimal solution based on “structured” controls of the pursuers. If the structure is set-time-consistent, the resulting suboptimal solution can be improved by the optimization based on limited look-ahead. When the performance enhancement is applied iteratively, an optimal solution can be approached in the limit. We provide a hierarchical method that can determine a valid initial point for this iterative process. The method is also extended to the stochastic game case. For a problem where uncertainties only appear in the players' dynamics and the states are perfectly measured, the iterative method is largely valid. For a more general problem where the players's measurement is not perfect, only a special case is studied and a suboptimal approach based on one-step look-ahead is discussed. In addition to the numerical justification of the iterative method, the theoretical soundness of the method is addressed for deterministic PE games under the framework of viscosity solution theory for Hamilton-Jacobi equations. Conditions are derived for the existence of solutions of a multi-player game. Some issues on capturability are also discussed for the stochastic game case. The fundamental idea behind the iterative approach is attractive for complicated problems. When a direct solution is difficult, an alternative appro (open full item for complete abstract)

Committee: Jose Cruz (Advisor) Subjects:

Doctor of Philosophy, Case Western Reserve University, 2009, Operations

This dissertation is comprised of three essays. The first, “Optimal Marketing Strategies for Competing New Ventures in a Nascent Industry” has been originally accepted for publication in the International Journal of Entrepreneurship and Innovation Management. It considers new ventures that are pioneering a nascent industry. Just as their established counterparts do, these ventures strive to increase profit by acquiring sales of rival new ventures. However, new ventures can also grow by attracting unrealized sales. The essay investigates the resulting tradeoff in marketing expenditures via a differential game between two competing new ventures. Extensive numerical analysis suggests that an increase in a new venture's unit profit margin, effectiveness in gaining new sales, or initial sales level, but a decrease in sales decay, may cause a positive spillover for its rival. The second essay, “Integrating Customer Preferences with Technology Adoption and Product Redesign in a Duopoly” focuses on a firm's decision to add a technology that changes how customers interact with the firm's product. We formulate a two-stage game-theoretic framework to investigate the conditions under which two competing firms should add a technology, and how a firm that adopts technology should redesign its product to incorporate technology. We investigate how prospective and existing customers' preferences for the technology and the product-technology fit should affect the firm's adoption and product redesign decisions. We articulate conditions for the existence of a Nash equilibrium where both firms add technology, and demonstrate that customer preferences for technology standardization may actually impede standardization. The third essay, “New Product Positioning for a Segmented Market” focuses on how competing firms should set price and quality for a new technologically-advanced product. The targeted market is comprised of two customer segments that differ in innovativeness. We analyze a c (open full item for complete abstract)

Committee: Moren Levesque (Advisor); Lisa Maillart (Committee Member); Bo Carlsson (Committee Member); Danny Solow (Committee Member) Subjects: Management; Operations Research; Technology