Sufficient optimality conditions for extremal controls based on functional increment formulas

Abstract

Optimal control problem without phase and terminal constraints is considered. Conceptions of strongly extremal controls are introduced on the basis of nonstandard functional increment formulas. Such controls are optimal in linear and quadratic problems. In general case optimality property is guaranteed by concavity condition of the Pontryagin function with respect to phase variables. 2010 Mathematics Subject Classification. 49K15.