Suboptimal control of distributed-parameter systems: Minimizing sequences and the value function (Q1974720)

The author considers elements of the suboptimal control theory of distributed-parameter systems with respect to an optimal control problem for a parabolic equation with weak solutions. In contrast to the traditional optimal control theory as the basic element is taken a suboptimal ordinary control and a minimizing sequence of ordinary controls rather than an optimal control. Necessary and sufficient conditions for elements of minimizing sequences are established. Differential properties of the value function considered as a function of perturbation of constraints are studied, and an expression for the generalized gradient of this function is presented.