The article discusses the application of the theory of optimal control for solving Hamilton-Jacob equations with phase constraints.
A method for constructing generalized solutions using optimal control problems is proposed. The results and analysis of numerical experiments, conditions for the existence of equilibrium situations in noncooperative differential games of several persons, namely the conditions for the existence of equilibrium situations in noncooperative differential games of several persons, defining the action according to Hamilton, are stated. Necessary conditions in the form of Hamilton-Jacobi equations are obtained.
Game theory as an applied mathematical theory is used to understand and explain the mechanisms that are used when people make decisions. The theory contributes to the functioning of the logic of strategic planning and the relationship between individuals. Game theory as a method of applied mathematics is used for behavioral studies in various conditions, and helps understand the behavior of economic agents.
The theory has many applications and can be used in different areas such as: strategy games, administration, economics and artificial intelligence research. The article describes a mathematical method for studying optimal situations in game theory.
Keywords: Differential game; dynamic systems; equilibrium situation; equilibrium trajectory; Hamilton-Jacobi function; Euler-Lagrange equations; Weierstrass-Erdmann conditions.
