Numerical solution methods for differential game problems

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2009

Author dc:creator

• Johnson, Philip A. (Philip Arthur)

Advisor dc:contributor.advisor

• Steven R. Hall and Russell Smith.

• Aeronautics and Astronautics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/50600

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/50600