Differential games for neutral-type systems: An approximation model

N. Yu. Lukoyanov ; A. R. Plaksin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 291 (2015), pp. 202-214

Résumé

For a conflict-controlled dynamical system whose motion is described by neutral-type functional differential equations in Hale's form and for a quality index that evaluates the motion history realized up to the terminal instant of time, we consider a differential game in the class of control-with-guide strategies. We construct an approximating differential game in the class of pure positional strategies in which the motion of a conflict-controlled system is described by ordinary differential equations and the quality index is terminal. We show that the value of the approximating game gives the value of the original game in the limit, and that the optimal strategies in the original game can be constructed by using the optimal motions of the approximating game as guides.