Аннотация:We consider an optimal control problem with Volterra-type integral equations
on a nonfixed time interval subject to endpoint constraints,
mixed state-control constraints of equality and inequality type, and pure
state inequality constraints. The main assumption is the linear--positive
independence of the gradients of active mixed constraints with respect
to the control. We formulate first order necessary optimality conditions
for an extended weak minimum, the notion of which is a natural generalization
of the notion of weak minimum with account of variations of the time.
The presented conditions generalize the local maximum principle in optimal
control problems with ordinary differential equations.