Realization of sliding modes as generalized solutions to optimal control problems

Consideration is given to the problem of realization of generalized solutions of different nature in classes of admissible models traditional for applications for optimal control problems. The main attention is focused on sliding modes in systems with a bounded set of velocities (velocity hodograph). Constructive correction schemes for elements of the sequence converging to the sliding mode are specified so that they are strictly admissible. This defines the procedure for constructing a minimizing sequence the elements of which are approximate optimal practically realizable solutions to estimates of accuracy.