Ushakov, V. N.; Guseinov, Kh. G.; Latushkin, Ya. A.; Lebedev, P. D. 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 Keywords:conflict control system on a finite time interval; ordinary differential equation; feedback control; positional absorption sets Citations:Zbl 0298.90067 PDFBibTeX XMLCite \textit{V. N. Ushakov} et al., Dokl. Math. 85, No. 2, 186--190 (2012; Zbl 1264.93087); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 443, No. 1, 34--39 (2012) Full Text: DOI References: [1] N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974). [2] N. N. Krasovskii, Dokl. Akad. Nauk SSSR 226, 1260–1263 (1976). [3] N. N. Krasvoskii, Tr. Inst. Mat. Mekh. Ural. Nauchn. Tsentra Akad. Nauk SSSR 24, 32–45 (1977). [4] H. G. Guseinov, A. I. Subbotin, and V. N. Ushakov, Problems Control Inf. Theory 14, 405–419 (1985). [5] A. M. Taras’ev, V. N. Ushakov, and A. P. Khripunov, Prikl. Mat. Mekh. 51, 216–222 (1987). [6] V. N. Ushakov, Doctoral Dissertation in Mathematics and Physics (Inst. Mat. Mekh. Ural. Otd. Akad. Nauk SSSR, Sverdlovsk, 1991). [7] A. I. Subbotin and A. G. Chentsov, Optimization of Guaranteed Result in Control Problems (Nauka, Moscow, 1981) [in Russian]. · Zbl 0542.90106 [8] V. N. Ushakov, Kh. G. Guseinov, Ya. A. Latushkin, and P. D. Lebedev, Tr. Inst. Mat. Mekh. 15, 219–240 (2009). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.