Hamilton-jacobi type equation for problems of control of functional differential systems

摘要

For control problems under lack of information, which are formalized as differential games of systems with aftereffect, an equation of Hamilton-Jacobi type is obtained for the value functional. A definition of its minimax solution (MS) is given. The existence, uniqueness,a nd well-posedness of MS are proved. A method of constructing extremal to MS strategies is developed. It is shown that they are optimal for the control problem considered, and the value functional coincides with MS.