Abstract:
The general optimal control problem subject to irregular constraints is considered for which the factor of the objective functional in Pontryagin’s function may vanish. It turns out that, in the case of $p$-regular constraints, this drawback can be overcome and a constructive version of the $p$-order maximum principle can be formulated.
Key words:singular optimal control problem, $p$-regular Pontryagin’s maximum principle, generalized Lyusternik theory, $p$-order implicit function theorem.