L. Alkhazishvili

I. Javakhishvili Tbilisi State University Tbilisi, Georgia

OPTIMAL PROBLEMS WITH INCOMMENSURABLE DELAYS AND WITH CONTINUOUS AND DISCONTINUOUS INITIAL CONDITIONS

Optimal problems for a non-linear controlled differential equation with variable delays in phase coordinates and controls, non-fixed initial moment and discontinuous and continuous initial conditions are considered. Necessary conditions of optimality of initial function and control in the form of linearized integral maximum principle and necessary conditions of optimality of initial moment in the form of equality and inequality are obtained.