Integral estimates for ordinary differential equations and their application to nonsmooth optimal control problems. (Russian) Zbl 0762.34015

Dokuchaev, N. G.

Differ. Uravn. 27, No. 10, 1679-1691 (1991).

Two integral estimates are derived for the solution of the ordinary differential equation \(\dot y(t)=f(y(t),t)\), \(t\in[0,T]\). The estimates are utilized in the problem of nonsmooth optimal control with a random initial state \(y(0)=a\). Existence theorems for optimal control solutions are derived.

Reviewer: J.Ramik (Ostrava)

MSC:

34C11	Growth and boundedness of solutions to ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems, general theory
49J15	Existence theories for optimal control problems involving ordinary differential equations

Keywords:

existence theorems; integral estimates; ordinary differential equation; nonsmooth optimal control; random initial state