Application of the averaging method to the problems of optimal control of the impulse systems

Abstract

The problem of optimal control at finite time interval for a system of differential equations with impulse action at fixed moments of time as well as the corresponding averaged system of ordinary differential equations are considered. It is proved the existence of optimal control of exact and averaged problems. Also, it is established that optimal control of averaged problem realize the approximate optimal synthesis of exact problem. The main result of the article is a theorem, where it is proved that optimal contol of an averaged problem is almost optimal for exact problem. Substantiation of proximity of solutions of exact and averaged problems is obtained.

Keywords

• optimal control problem
• optimal control
• exact problem
• averaged problem
• valid control
• averaging condition
• weak convergence
• compactness
• semi-continuity
• quality criterion
• minimizing sequence