We present a framework for space partitioning, where the Regions of Influence (ROIs) of the agents are defined based on proximity metrics derived from the cost of optimal control problems. Efficient space partitioning in multi-agent systems, particularly in Unmanned Aerial Vehicle (UAV) operations, is critical for coverage, load balancing, and task allocation. However, traditional methods, such as the standard Voronoi Diagrams (VDs) based solely on distances, often fail to account for the dynamic behavior and capabilities of UAV s. We generalize the VD concept by replacing distance-based metrics with transition costs obtained from optimal control formulations. This allows the resulting partitions to incorporate UAV dynamics, including initial states and control effort, in defining regions where one agent is more suitable than another for a given task. We show that for a broad class of problems with second-order optimal costs, the boundaries between ROIs are given by either hyperplanes or quadratic surfaces. This includes, as special cases, classical VDs based on distance, minimum-time problems for single integrators, the fixed-final-state (FFS) optimal transfer problem, and Linear Quadratic Regulators (LQR). Overall, the proposed framework bridges geometric and control-theoretic space partitioning, enabling dynamic and context-aware task allocation in multi-agent systems.

In this paper we introduce the Adversarial Voronoi Regions (AVR) as a way of evaluating and updating the states of opposing teams. While many multi-agent problems focus on cooperative tasks like search and rescue, task allocation, or distributed sensing, there are also adversarial settings where teams compete to maximize their own outcomes, often at the expense of the opposing team. Such scenarios include zero-sum games, various team sports, pursuit-evasion problems, and business competition.We show how the AVR concept can be used to formulate an optimization problem that captures the utility of the positions of agents in adversarial scenarios, such as competing business locations, team sport tactics, and security agents handling potential threats. We also derive the analytical gradient of the AVR utility and show how this can be used to dynamically control the team over time, or to find locally optimal configurations. Then we show that for an agent with a single adversarial neighbor, the gradient drives the agent closer to its neighbor and toward the center of mass of the edge separating them. Finally, we illustrate the approach with practical examples, demonstrating its adaptability in dynamic and competitive scenarios.

Beyond Visual Range (BVR) air combat is an essential part of modern aerial warfare, relying on advanced radar, missile systems, and decision-support technologies. This survey provides a comprehensive overview of how simulation and Machine Learning (ML) tools have been used to analyze BVR combat, covering key methodologies, applications, and challenges. We examine how ML enables adaptive tactics to improve behavior recognition and threat assessment to enhance situational awareness. The paper also traces the historical evolution of BVR combat, outlining key engagement phases such as detection, missile launch, and post-engagement assessment. A key focus is on the role of simulation environments in modeling realistic combat scenarios, supporting pilot training, and validating AI-driven decision-making strategies. We analyze state-of-the-art simulation tools, comparing their capabilities and limitations for studying multi-agent coordination and real-time adaptability. This survey's main contributions include descriptions of ML applications in BVR air combat, evaluations of simulation tools, identifications of research gaps, and insights into future research directions. This work provides an overview of how traditional simulation approaches merge with artificial intelligence to enable advanced, effective human and autonomous decision-making systems in dynamic and contested environments.

Tactical decisions in air combat are typically evaluated using experience as a basis. Pilots undergo frequent training in various air combat processes to enhance their combat proficiency and evaluation skills. Having the Situational Awareness (SA) necessary to evaluate the effects of multiple missile threats can often be challenging. This study provides a new method for calculating an aircraft fleet's maneuver flexibility in a Beyond-Visual-Range (BVR) setting. Sustaining a high degree of flexibility is necessary to adapt to unforeseen circumstances in BVR air combat. To do that, we employ Deep Neural Networks (DNN) to capture the result of a highperformance aircraft model in the presence of adversarial BVR missiles. We then modify our approach to calculate the aircraft's maneuverability concerning an opposing fleet, looking at the advantages and disadvantages of several flight formations. Finally, we consider the anticipated threat from an incoming opponent formation and optimize the counter-formation. This methodology offers a more sophisticated comprehension of aircraft maneuver flexibility within a BVR framework and aids in developing flexible and efficient decision-making techniques for air combat.