Tuesday, 15:15 - 15:40 h, Room: H 2035


Aram Arutyunov
The R.V. Gamkrelidze's maximum principle for state constrained optimal control problem: Revisited

Coauthors: Dmitry Karamzin, Fernando Lobo Pereira


We study necessary conditions of optimality for optimal control problem with state constraints in the form of the Pontryagin's maximum principle (for short MP). For problems with state constraints these conditions were first obtained by R.V. Gamkrelidze in 1959 and subsequently published in the classic monograph by the four authors. This MP was obtained under a certain regularity assumption on the optimal trajectory. Somewhat later, in 1963, A.Ya. Dubovitskii and A.A. Milyutin proved another MP for problems with state constraints. In contrast with the MP of R.V. Gamkrelidze, this MP was obtained without a priori regularity assumptions, but it degenerates in many cases of interest what was dicovered and studied later. Here, we suggest a MP in the form proposed by R.V. Gamkrelidze without any a priori regularity assumptions on the optimal trajectory. However, without a priori regularity assumptions, this MP may degenerate. Therefore, we prove that, under certain additional conditions of controllability relatively to the state constraints at the end-points, or regularity of the control process, degeneracy will not occur, since a stronger non-triviality condition will be satisfied.


Talk 1 of the invited session Tue.3.H 2035
"Control and optimization of impulsive systems II" [...]
Cluster 24
"Variational analysis" [...]


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