ABSTRACT
In the paper, optimal control problems with discontinuous right-hand side are considered. The main attention is paid to situations when there are intervals where optimal trajectory lies on a switching surface. It is shown that for such a situation the known optimality conditions degenerate: they are satisfied for any feasible control. Hence such conditions are not informative. New non-degenerate necessary optimality conditions in a form of Maximum principle are formulated and proved. Comparison of the obtained optimality conditions with ones known from the literature is presented.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 Such partitioning is not unique. Further we consider the partitioning of the set with minimal number
.