ИСТИНА

We study a question on sign-definiteness of quadratic cost bounded by the system of linear integral equations and depending on the control linearly. The "classical" optimal control theory as in Pontryagin et al. (1962) is not applicable for it. However, applying some special transformations, one can get further conditions that are absent in case of non-degenerated functional. First, we consider a particular case when integral equations system might be reduced to ODE system. Then, we consider general case when such a reduction dows not seem to be possible. In the first case, we reduce original problem to a form which differs from the "classical" one only by parameter which defines endpoint value of a new control, by using Goh transformation (Goh (1966)). In general case, acting in a similar scheme, we also obtain necesasry conditions of the second order. Thus, a new class of problems with reduced cost is investigated and corresponding necessary optimality conditions are obtained.