Coincidence criteria for maximal stable bridges in two game problems of approach
Tóm tắt
Từ khóa
Tài liệu tham khảo
N. N. Krasovskii, Game Problems on the Encounter of Motions (Nauka, Moscow, 1970) [in Russian].
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974); Engl. transl.: Game-Theoretical Control Problems (Springer, New York, 1988).
N. N. Krasovskii, “On the Problem of Unifying Differential Games,” Dokl. Akad. Nauk SSSR 226(6), 1260–1263 (1976) [Sov. Math., Dokl. 17, 269–273 (1976)].
N. N. Krasovskii, “Unification of Differential Games,” in Game Control Problems (Inst. Math. Mech., Ural Sci. Center, Acad. Sci. USSR, Sverdlovsk, 1977), Tr. Inst. Mat. Mekh., Ural. Nauchn. Tsentr, Akad. Nauk SSSR, Issue 24, pp. 32–45.
R. Isaacs, Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization (J. Wiley and Sons, New York, 1965; Mir, Moscow, 1967).
L. S. Pontryagin, “Linear Differential Games. I,” Dokl. Akad. Nauk SSSR 174(6), 1278–1280 (1967) [Sov. Math., Dokl. 8, 769–771 (1967)].
L. S. Pontryagin, “Linear Differential Games. II,” Dokl. Akad. Nauk SSSR 175(4), 764–766 (1967) [Sov. Math., Dokl. 8, 910–912 (1967)].
A. B. Kurzhanskii, “Pontryagin’s Alternated Integral in the Theory of Control Synthesis,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 224, 234–248 (1999) [Proc. Steklov Inst. Math. 224, 212–225 (1999)].
A. B. Kurzhanskii, “The Problem of Measurement Feedback Control,” Prikl. Mat. Mekh. 68(4), 547–563 (2004) [J. Appl. Math. Mech. 68, 487–501 (2004)].
A. V. Kryazhimskii and Yu. S. Osipov, “Differential-Difference Game of Encounter with a Functional Target Set,” Prikl. Mat. Mekh. 37(1), 3–13 (1973) [J. Appl. Math. Mech. 37, 1–10 (1973)].
A. I. Subbotin and A. G. Chentsov, Guarantee Optimization in Control Problems (Nauka, Moscow, 1981) [in Russian].
A. I. Subbotin, Generalized Solutions of First-Order PDEs: The Dynamical Optimization Perspective (Birkhäuser, Boston, 1995).
A. G. Chentsov, “On a Game Problem of Converging at a Given Instant of Time,” Mat. Sb. 99(3), 394–420 (1976) [Math. USSR, Sb. 28 (3), 353–376 (1976)].
B. N. Pshenichnyi, “The Structure of Differential Games,” Dokl. Akad. Nauk SSSR 84(2), 285–287 (1969) [Sov. Math., Dokl. 10, 70–72 (1969)].
V. I. Blagodatskikh and A. F. Filippov, “Differential Inclusions and Optimal Control,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 169, 194–252 (1985) [Proc. Steklov Inst. Math. 169, 199–259 (1986)].
M. S. Nikol’skii, “On the Alternating Integral of Pontryagin,” Mat. Sb. 116(1), 136–144 (1981) [Math. USSR, Sb. 44 (1), 125–132 (1983)].
E. A. Isakova, G. V. Logunova, and V. S. Patsko, “Construction of Stable Bridges in a Linear Differential Game with Fixed Termination Time,” in Algorithms and Programs for Solving Linear Differential Games (Inst. Math. Mech., Ural Sci. Center, Acad. Sci. USSR, Sverdlovsk, 1984), pp. 127–158 [in Russian].
V. N. Ushakov, “On the Stability in Differential Games,” in Positional Control with Guaranteed Result (Ural Branch Acad. Sci. USSR, Sverdlovsk, 1988), pp. 101–109 [in Russian].
V. N. Ushakov, “Construction of Stable Bridges in Differential Games,” Doctoral (Phys.-Math.) Dissertation (Inst. Math. Mech., Ural Branch Acad. Sci. USSR, Sverdlovsk, 1991).
H. G. Guseinov, A. I. Subbotin, and V. N. Ushakov, “Derivatives for Multivalued Mappings with Applications to Game-Theoretical Problems of Control,” Probl. Control Inf. Theory 14(3), 155–167 (1985).
A. M. Taras’yev, V. N. Ushakov, and A. P. Khripunov, “On a Computational Algorithm for Solving Game Control Problems,” Prikl. Mat. Mekh. 51(2), 216–222 (1987) [J. Appl. Math. Mech. 51, 167–172 (1987)].
A. M. Taras’ev and V. N. Ushakov, Construction of Stable Bridges in a Minimax Pursuit-Evasion Game, Available from VINITI, No. 2454–83 (Sverdlovsk, 1983).
V. N. Ushakov and A. P. Khripunov, “Approximate Construction of Solutions in Game-Theoretic Control Problems,” Prikl. Mat. Mekh. 61(3), 413–421 (1997) [J. Appl. Math. Mech. 61, 401–408 (1997)].
A. I. Panasyuk, “Equations of the Dynamics of Sets of Reachability in Problems of Optimization and Control under Conditions of Uncertainty,” Prikl. Mat. Mekh. 50(4), 531–543 (1986) [J. Appl. Math. Mech. 50, 405–415 (1986)].
J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis (J. Wiley and Sons, New York, 1984; Mir, Moscow, 1988).
V. F. Dem’yanov and A. M. Rubinov, Foundations of Nonsmooth Analysis, and Quasidifferential Calculus (Nauka, Moscow, 1990) [in Russian].