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**A problem of dynamic optimization in the presence of dangerous factors.**
*(English)*
Zbl 1452.49012

Tarasyev, Alexander (ed.) et al., Stability, control and differential games. Proceedings of the international conference on stability, control and differential games (SCDG2019), Yekaterinburg, Russia, September 16–20, 2019. Cham: Springer. Lect. Notes Control Inf. Sci. – Proc., 273-281 (2020).

An optimal control problem with a mixed functional and free stopping time is considered. Dynamics of the system is given by means of a differential inclusion. The integral term of the functional contains the characteristic function of a given open set \(M \subset\mathbb{R}^n\) which can be interpreted as a “risk” or “dangerous” zone. The statement of the problem (Problem P) can be treated as a weakening of the statement of the classical optimal control problem with state constraints. The goal of the present paper is to study relationships between Problem P and the optimal control problem for differential inclusion with state constraints. The main result states that, under suitable controllability assumptions, Problem P can provide an exact penalization of the corresponding problem with state constraints. An illustrative example is also provided.

For the entire collection see [Zbl 1444.93003].

For the entire collection see [Zbl 1444.93003].

Reviewer: Andrej V. Plotnikov (Odessa)

### MSC:

49K21 | Optimality conditions for problems involving relations other than differential equations |

34A60 | Ordinary differential inclusions |

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\textit{S. M. Aseev}, in: Stability, control and differential games. Proceedings of the international conference on stability, control and differential games (SCDG2019), Yekaterinburg, Russia, September 16--20, 2019. Cham: Springer. 273--281 (2020; Zbl 1452.49012)

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