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On the coincidence of maximal stable bridges in two game problems. (English. Russian original) Zbl 1264.93087

Dokl. Math. 85, No. 2, 186-190 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 443, No. 1, 34-39 (2012).
From the text: We consider a conflict control system on a finite time interval governed by an ordinary differential equation. More specifically, we study and compare two game problems describing the system approaching a terminal set \(M\) in the state space of the system N. N. Krasovskiĭ and A. I. Subbotin [”Positional Differential Games”, Nauka, Moscow, (1974; Zbl 0298.90067)]. In one of these problems, the first player uses a feedback control to ensure that the state vector of the system reaches \(M\) at the terminal time. In the other problem, a feedback control is used to ensure that the state vector of the system reaches \(M\) no later than at the terminal time. In the approach proposed in [loc. cit.], the central elements of the solving construction in both problems are positional absorption sets, i.e., maximal \(u\)-stable bridges.
Necessary and sufficient conditions for the coincidence of maximal \(u\)-stable bridges for a time-invariant conflict control system are given.

MSC:

93C15 Control/observation systems governed by ordinary differential equations
91A10 Noncooperative games
49N70 Differential games and control
34H05 Control problems involving ordinary differential equations

Citations:

Zbl 0298.90067
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References:

[1] N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974).
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