A Differential Game Approach to Optimal Strategies in a Ballistic Missile War

摘要

A ballistic missile war between two countries is modeled by four nonlinear differential equations. The dynamic model defines the changes in missile stocks and sustained casualties for both countries, and includes the effects of initial missile stocks, missile firing strategies, and missile countervalue and counterforce effectiveness. Termination conditions are imposed, so that the war terminates when either country has suffered intolerable causualties or missile losses. The problem for each country of selecting optimal missile firing strategies is formulated as a two-person zero-sum continuous-time differential game. Firing strategies are defined for each country by its missile firing rate and counterforce proportion targeting variable, and necessary conditions for the selection of these control variables are determined through application of the Minimax Principle. The satisfaction of these necessary conditions is seen to depend on the solution of a two-point boundary-value problem involving the model differential equations and a fourth-order dynamic costate system. An interative steepest-descent search procedure is used for the solution of this problem, and a FORTRAN-4 digital computer program is written for its implementation. (Author)