A Remarkable Property of the Dynamic Optimization Extremals

摘要: We give conditions under which a function F (t;x;u;ˆ0;ˆ) satisfles the relation dF dt = @F @t + @x ¢ @H @ˆ i along Pontryagin extremals (x(¢);u(¢);ˆ0;ˆ(¢)) of an optimal control problem, where H is corresponding Hamiltonian. The generalizes well known fact that equality dH holds and in autonomous case · constant. As applications new relation, methods for obtaining conserved quantities characterizing problems possessing given constants motion are obtained.