Numerical solution methods for differential game problems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2009.Includes bibliographical references (p. 95-98).Differential game theory provides a potential means for the parametric analysis of combat engagement scenarios. To determine its viability for this type of analysis, three frameworks for solving differential game problems are evaluated. Each method solves zero-sum, pursuit-evasion games in which two players have opposing goals. A solution to the saddle-point equilibrium problem is sought in which one player minimizes the value of the game while the other player maximizes it. The boundary value method is an indirect method that makes use of the analytical necessary conditions of optimality and is solved using a conventional optimal control framework. This method provides a high accuracy solution but has a limited convergence space that requires a good initial guess for both the state and less intuitive costate. The decomposition method in which optimal trajectories for each player are iteratively calculated is a direct method that bypasses the need for costate information. Because a linearized cost gradient is used to update the evader's strategy the initial conditions can heavily influence the convergence of the problem. The new method of neural networks involves the use of neural networks to govern the control policy for each player. An optimization tool adjusts the weights and biases of the network to form the control policy that results in the best final value of the game. An automatic differentiation engine provides gradient information for the sensitivity of each weight to the final cost.(cont.) The final weights define the control policy's response to a range of initial conditions dependent upon the breadth of the state-space used to train each neural network. The neural nets are initialized with a normal distribution of weights so that no information regarding the state, costate, or switching structure of the controller is required. In its current form this method often converges to a sub-optimal solution. Also, creative techniques are required when dealing with boundary conditions and free end-time problems.by Philip A. Johnson.S.M

Optimal Strategy Imitation Learning from Differential Games

The ability of a vehicle to navigate safely through any environment relies on its driver having an accurate sense of the future positions and goals of other vehicles on the road. A driver does not navigate around where an agent is, but where it is going to be. To avoid collisions, autonomous vehicles should be equipped with the ability to to derive appropriate controls using future estimations for other vehicles, pedestrians, or otherwise intentionally moving agents in a manner similar to or better than human drivers. Differential game theory provides one approach to generate a control strategy by modeling two players with opposing goals. Environments faced by autonomous vehicles, such as merging onto a freeway, are complex, but they can be modeled and solved as a differential game using discrete approximations; these games yield an optimal control policy for both players and can be used to model adversarial driving scenarios rather than average ones, so that autonomous vehicles will be safer on the road in more situations. Further, discrete approximations of solutions to complex games that are computationally tractable and provably asymptotically optimal have been developed, but may not produce usable results in an online fashion. To retrieve an efficient, continuous control policy, we use deep imitation learning to model the discrete approximation of a differential game solution. We successfully learn the policy generated for two games of different complexity, a fence escape and merging game, and show that the imitated policy generates control inputs faster than the differential game generated policy

The BG News February 13, 1987

The BGSU campus student newspaper February 13, 1987. Volume 69 - Issue 80https://scholarworks.bgsu.edu/bg-news/5619/thumbnail.jp

Air Force Institute of Technology Research Report 2017

This Research Report presents the FY18 research statistics and contributions of the Graduate School of Engineering and Management (EN) at AFIT. AFIT research interests and faculty expertise cover a broad spectrum of technical areas related to USAF needs, as reflected by the range of topics addressed in the faculty and student publications listed in this report. In most cases, the research work reported herein is directly sponsored by one or more USAF or DOD agencies. AFIT welcomes the opportunity to conduct research on additional topics of interest to the USAF, DOD, and other federal organizations when adequate manpower and financial resources are available and/or provided by a sponsor. In addition, AFIT provides research collaboration and technology transfer benefits to the public through Cooperative Research and Development Agreements (CRADAs)

Air Force Institute of Technology Research Report 2019

This Research Report presents the FY19 research statistics and contributions of the Graduate School of Engineering and Management (EN) at AFIT. AFIT research interests and faculty expertise cover a broad spectrum of technical areas related to USAF needs, as reflected by the range of topics addressed in the faculty and student publications listed in this report. In most cases, the research work reported herein is directly sponsored by one or more USAF or DOD agencies. AFIT welcomes the opportunity to conduct research on additional topics of interest to the USAF, DOD, and other federal organizations when adequate manpower and financial resources are available and/or provided by a sponsor. In addition, AFIT provides research collaboration and technology transfer benefits to the public through Cooperative Research and Development Agreements (CRADAs). Interested individuals may discuss ideas for new research collaborations, potential CRADAs, or research proposals with individual faculty using the contact information in this document

Air Force Institute of Technology Research Report 2020

This Research Report presents the FY20 research statistics and contributions of the Graduate School of Engineering and Management (EN) at AFIT. AFIT research interests and faculty expertise cover a broad spectrum of technical areas related to USAF needs, as reflected by the range of topics addressed in the faculty and student publications listed in this report. In most cases, the research work reported herein is directly sponsored by one or more USAF or DOD agencies. AFIT welcomes the opportunity to conduct research on additional topics of interest to the USAF, DOD, and other federal organizations when adequate manpower and financial resources are available and/or provided by a sponsor. In addition, AFIT provides research collaboration and technology transfer benefits to the public through Cooperative Research and Development Agreements (CRADAs). Interested individuals may discuss ideas for new research collaborations, potential CRADAs, or research proposals with individual faculty using the contact information in this document

2009 Abstract Booklet

Complete Schedule of Events for the 11th Annual Undergraduate Research Conference at Minnesota State University, Mankato

Air Force Institute of Technology Research Report 2018

This Research Report presents the FY18 research statistics and contributions of the Graduate School of Engineering and Management (EN) at AFIT. AFIT research interests and faculty expertise cover a broad spectrum of technical areas related to USAF needs, as reflected by the range of topics addressed in the faculty and student publications listed in this report. In most cases, the research work reported herein is directly sponsored by one or more USAF or DOD agencies. AFIT welcomes the opportunity to conduct research on additional topics of interest to the USAF, DOD, and other federal organizations when adequate manpower and financial resources are available and/or provided by a sponsor. In addition, AFIT provides research collaboration and technology transfer benefits to the public through Cooperative Research and Development Agreements (CRADAs). Interested individuals may discuss ideas for new research collaborations, potential CRADAs, or research proposals with individual faculty using the contact information in this document