On transformations of degenerate optimal control problems

We consider practical algorithms for transforming a system with unbounded controls to a new model regular from the point of view of known general optimal control methods. In addition to a transformation to a certain derivative system on the entire time interval, which is traditional for degenerate problems, we consider a family of such transformations, choosing a specific one at every moment of time. As a result we get a controllable system which is in a certain sense equivalent to the original one, and one can operate with it like a regular system. Its solution is realized in the original class as an impulse sliding mode.