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On the maximum principle when the endpoints of the optimal trajectory lie on the state boundary

Dmitruk Andrei V., Osmolovskii Nikolai P.

Control and Cybernetics

2024

Vol. 53, No. 1

77--107

We consider an optimal control problem in the Mayer form with an autonomous control system, a bounded control set U, endpoint equality constraints, and one pointwise state inequality constraint. We analyze the case when the starting point of the optimal trajectory belongs to the state boundary. A nontrivial maximum principle was obtained for this case by A.Ya. Dubovitskii and V.A. Dubovitskii about 40 years ago, but the proof was written in an extremely condensed form. Here we offer a new proof of their result.