Necessary conditions for optimality of generalized control. I

The paper is concerned with optimal control of dynamic systems whereby the control signal is an element of the space of generalized functions. For such problems the class of generalized feasible controls is defined and functional analysis methods lead to the necessary conditions of control optimality in this class. The first part of the paper is concerned with optimization of a system with a free right-hand end of the path. In the second part the necessary optimality conditions are formulated for boundary conditions of a more general type.