References
A. I. Subbotin, “Control of the motion of a quasilinear system,” Differents. Uravneniya 3 (7), 1113–1118 (1967).
A. I. Subbotin, “On the problem of the game-interception of motions,” J. Appl. Math. Mech. 31 (5), 842–848 (1968).
A. I. Subbotin, “Regularization of a problem on the encounter of motions,” Differents. Uravneniya 4 (5), 779–784 (1968).
N. N. Krasovskii and A. I. Subbotin, “Optimal evasion in a differential game,” Differents. Uravneniya 4 (12), 2159–2165 (1968).
N. N. Krasovskii and A. I. Subbotin, “The problem of convergence of controlled objects,” J. Appl. Math. Mech. 32 (4), 597–586 (1968).
A. I. Subbotin, Encounter and Evasion Problems in Differential Games, Candidate’s Dissertation in Physics and Mathematics (Ural State Univ., Sverdlovsk, 1969).
A. I. Subbotin, Encounter and Evasion Problems in Differential Games, Abstract of Candidate’s Dissertation in Physics and Mathematics (Ural State Univ., Sverdlovsk, 1969).
N. N. Krasovskii and A. I. Subbotin, “Mixed control in a differential game,” Soviet Math. Dokl. 10 (5), 1180–1183 (1969).
N. N. Krasovskii and A. I. Subbotin, “Optimal strategies in a linear differential game,” J. Appl. Math. Mech. 33 (4), 675–682 (1969).
A. I. Subbotin and V. E. Tret’yakov, “Regularization of a pursuit problem,” in Proceedings of the Second Republican Conference of Belorussian Mathematicians, Minsk, USSR, 1969, pp. 219–221.
N. N. Krasovskii and A. I. Subbotin, “The structure of differential games,” Soviet Math. Dokl. 11 (3), 143–147 (1970).
A. I. Subbotin, “Differential games with constraints on phase states,” Soviet Math. Dokl. 11, 933–936 (1970).
N. N. Krasovskii and A. I. Subbotin, “A differential guidance game,” Differents. Uravneniya 6 (4), 579–591 (1970).
N. N. Barabanova and A. I. Subbotin, “On continuous evasion strategies in game problems on the encounter of motions,” J. Appl. Math. Mech. 34 (5), 765–772 (1970).
N. N. Krasovskii and A. I. Subbotin, “An alternative for the game problem of convergence,” J. Appl. Math. Mech. 34 (6), 948–965 (1970).
N. N. Krasovskii and A. I. Subbotin, “Extremal strategies in differential games,” Soviet Math. Dokl. 12, 98–102 (1971).
N. N. Krasovskii and A. I. Subbotin, “On the structure of game problems of dynamics,” J. Appl. Math. Mech. 35 (1), 81–91 (1971).
N. N. Barabanova and A. I. Subbotin, “On classes of strategies in differential games of evasion of contact,” J. Appl. Math. Mech. 35 (3), 349–356 (1971).
V. D. Batukhtin and A. I. Subbotin, “The regular case in a linear differential game,” Engrg. Cybernetics 9 (6), 978–982 (1972).
N. N. Krasovskii, A. I. Subbotin, and V. N. Ushakov, “A minimax differential game,” Soviet Math. Dokl. 13 (5), 1200–1204 (1972).
A. I. Subbotin, “Extremal strategies in differential games with perfect memory,” Soviet Math. Dokl. 13 (5), 1263–1267 (1972).
V. D. Batukhtin and A. I. Subbotin, “Conditions for terminating a pursuit game,” Engrg. Cybernetics, 10 (1), 1–5 (1972).
A. I. Subbotin, “Program and position absorption in differential games,” J. Appl. Math. Mech. 36 (4), 701–704 (1973).
N. N. Krasovskii and A. I. Subbotin, “The saddle point of a positional differential game,” Proc. Steklov Inst. Math. 128, 23–34 (1974).
A. I. Subbotin, Extremal Strategies in Differential Games, Doctoral Dissertation in Physics and Mathematics (Ural State Univ., Sverdlovsk, 1973).
A. I. Subbotin, Extremal Strategies in Differential Games, Abstract of Doctoral Dissertation in Physics and Mathematics (Ural State Univ., Sverdlovsk, 1973).
N. N. Krasovskii and A. I. Subbotin, “Approximation in a differential game,” J. Appl. Math. Mech. 37 (2), 185–192 (1973).
A. I. Subbotin, “Differential games with complete memory,” in Extremal Strategies in Positional Differential Games (UNTs AN SSSR, Sverdlovsk, 1974), issue 8, pp. 211–223 [in Russian].
A. I. Subbotin, “Control under conflict and uncertainty,” in Twenty Lectures Delivered at the International Congress of Mathematicians in Vancouver, 1974 (Amer. Math. Soc., Providence, RI, 1977), pp. 91–96.
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974) [in Russian]; Translated into French under the title Jeux Différentiels (Mir, Moscow, 1977).
N. N. Krasovskii and A. I. Subbotin, “Differential games with mixed strategies,” in Problems of Analytical Mechanics and the Theories of Stability and Control (Nauka, Moscow, 1975), pp. 11–18 [in Russian].
A. I. Subbotin, “Control under conflict and uncertainty,” in Proceedings of the International Congress of Mathematicians, Vancouver, Canada, 1974, Vol. 2, pp. 361–366.
N. N. Krasovskii, A. I. Subbotin, and V. F. Rossokhin, “Stochastic strategies in differential games,” Soviet Math. Dokl. 16 (1), 198–202 (1975).
A. I. Subbotin and V. N. Ushakov, “Alternative for an encounter–evasion differential game with integral constraints on the players’ controls,” J. Appl. Math. Mech. 39 (3), 367–375 (1976).
N. N. Subbotina and A. I. Subbotin, “Alternative for the encounter–evasion differential game with constraints on the momenta of the players’ controls,” J. Appl. Math. Mech. 39 (3), 376–385 (1976).
A. I. Subbotin, “A dynamical encounter–evasion game,” Soviet Math. Dokl. 18 (3), 683–687 (1977).
N. N. Subbotina and A. I. Subbotin, “A game problem of control in the case of incomplete information,” Engrg. Cybernetics 15 (5), 1–10 (1978).
A. I. Subbotin and N. N. Subbotina, “Necessary and sufficient conditions for a piecewise smooth value of a differential game,” Soviet Math. Dokl. 19 (6), 1447–1451 (1978).
M. Baibazarov and A. I. Subbotin, “Generalized potentials in a differential game with a fixed termination instant,” J. Appl. Math. Mech. 42 (2), 205–211 (1979).
A. A. Kreknin and A. I. Subbotin, “A game problem of pursuit under incomplete information on the states of the pursued system,” in Differential Control Systems (IMM UNTs AN SSSR, Sverdlovsk, 1979), issue 26, pp. 21–33 [in Russian].
M. S. Gabrielyan and A. I. Subbotin, “Game problems on encounter with m target sets,” J. Appl. Math. Mech. 43 (2), 222–226 (1980).
A. I. Subbotin, “A generalization of the basic equation of the theory of differential games,” Soviet Math. Dokl. 22 (2), 358–362 (1980).
A. I. Subbotin and A. G. Chentsov, Guarantee Optimization in Control Problems (Nauka, Moscow, 1981) [in Russian].
N. N. Subbotina and A. I. Subbotin, “Necessary and sufficient conditions for a nonsmooth value of a differential game,” in Problems of Dynamic Control (IMM UNTs AN SSSR, Sverdlovsk, 1981), pp. 73–81 [in Russian].
V. Ya. Dzhafarov and A. I. Subbotin, “The program maximin and the value of a positional differential game,” Soviet Math. Dokl. 23 (2), 452–456 (1981).
V M. Reshetov, A. I. Subbotin, and V. N. Ushakov, “Some problems of stability and stabilization in differential games,” in Stability of Motion. Analytical Mechanics. Control of Motion (Nauka, Moscow, 1981), pp. 238–251 [in Russian].
A. I. Subbotin, “On the isochronous and stroboscopic capture in differential games,” J. Optim. Theory Appl. 37 (1), 115–119 (1982).
V. F. Rossokhin and A. I. Subbotin, On Characteristic Properties of the Value Function in a Linear Differential Game (Kirov, 1982), Available from VINITI, No. 4320–82 [in Russian].
A. I. Subbotin and N. N. Subbotina, “The optimal result function in a control problem,” Soviet Math. Dokl. 26 (2), 336–340 (1982).
A. I. Subbotin and N. N. Subbotina, “Properties of a differential game’s potential,” J. Appl. Math. Mech. 46 (2), 150–155 (1983).
N. N. Subbotina and A. I. Subbotin, “Differentiability properties of the value function in a differential game with integral–terminal payoff,” Probl. Upravl. Teor. Inform. 12 (3), 153–166 (1983).
A. I. Subbotin and N. N. Subbotina, “The basis for the method of dynamic programming in optimal control problems,” Engrg. Cybernetics 21 (2), 16–23 (1984).
A. I. Subbotin, “Generalization of the main equation of differential game theory,” J. Optim. Theory Appl. 43 (1), 103–133 (1984).
M. Baibazarov and A. I. Subbotin, “Determination of the value of a differential game,” Differential Equations 20 (9), 1068–1073 (1984).
A. I. Subbotin and A. M. Taras’ev, Inequalities for Conjugate Derivatives of the Value Function of a Differential Game (Sverdlovsk, 1984), Available from VINITI, No. 6345–84 [in Russian].
H. G. Guseinov, A. I. Subbotin, and V. N. Ushakov, “Derivatives for multivalued mappings with applications to game-theoretical problems of control,” Probl. Control Inform. Theory 14 (3), 155–167 (1985).
A. I. Subbotin and A. M. Taras’ev, “Conjugate derivatives of the value function of a differential game,” Soviet Math. Dokl. 32 (1), 162–166 (1985).
N. N. Subbotina, A. I. Subbotin, and V. E. Tret’yakov, “Stochastic and deterministic control. Differential inequalities,” Probl. Control Inform. Theory 14 (6), 405–419 (1985).
H. G. Guseinov, A. I. Subbotin, and V. N. Ushakov, Derivatives of Stable Bridges in a Differential Game of Approach (Sverdlovsk, 1985), Available from VINITI, No. 840–85 [in Russian].
A. I. Subbotin and N. N. Subbotina, “Directional derivatives of the optimal result function,” in Problems of Analytical Mechanics and Motion Control (Nauka, Moscow, 1985), pp. 131–136 [in Russian].
A. I. Subbotin, “Conditions for optimality of a guaranteed outcome in game problems of control,” Proc. Steklov Inst. Math. 167, 291–304 (1986).
N. N. Subbotina, A. I. Subbotin, and V. E. Tret’yakov, “Stochastic and deterministic control. Differential inequalities,” Stochastic Optimization (Springer, Berlin, 1986), Ser. Lecture Notes in Control and Information Sciences, Vol. 81, pp. 728–737.
A. I. Subbotin and A. M. Taras’ev, “Stability properties of the value function of a differential game and viscosity solutions of Hamilton–Jacobi equations,” Probl. Control Inform. Theory 15 (6), 451–463 (1986).
I. Rozyev, A. I. Subbotin, and A. M. Taras’ev, On a Game Problem of Approach for Two Weakly Controlled Objects (Sverdlovsk, 1986), Available from VINITI, No. 8976–V86 [in Russian].
A. I. Subbotin, A. M. Taras’ev, and V. N. Ushakov, On the justification of the dynamic programming method in the theory of differential games, in Differential Equations and Applications: Proceedings of the International Conference, Ruse, Bulgaria, 1985 (Angel Kanchev Univ., Ruse, 1987), pp. 409–412.
A. I. Subbotin, “Calculation of the value in a differential game of approach of simple motions on a bounded time interval,” in Control with a Guaranteed Result (IMM UNTs AN SSSR, Sverdlovsk, 1987), pp. 71–76 [in Russian].
N. N. Krasovski and A. I. Subbotin, Game-Theoretical Control Problems (Springer, New York, 1988).
I. Rozyev and A. I. Subbotin, “Semicontinuous solutions of Hamilton–Jacobi equations,” J. Appl. Math. Mech. 52 (2), 141–146 (1988).
A. I. Subbotin, “Approximation of a guaranteed result in game control problems,” in Positional Control with Guaranteed Result (IMM UrO AN SSSR, Sverdlovsk, 1988), pp. 92–100 [in Russian].
A. I. Subbotin, “A piecewise linear value function for a differential game with simple motions,” Proc. Steklov Inst. Math. 185, 269–278 (1990).
R. A. Adiatullina and A. I. Subbotin, Minimax Solutions of Equations of the Form ∂φ/∂t+H(t, x, φ,ωxφ) = 0 (Sverdlovsk, 1989), Available from VINITI, No. 7651–V89 [in Russian].
A. I. Subbotin and L. G. Shagalova, Piecewise Linear Functions Used for the Construction of Solutions of Hamilton–Jacobi Equations (Sverdlovsk, 1990), Available from VINITI, No. 5627–V90 [in Russian].
A. I. Subbotin, “Existence and uniqueness results for Hamilton–Jacobi equations,” Nonlinear Anal. 16 (7–8), 683–699 (1991).
A. I. Subbotin, Minimax Inequalities and Hamilton–Jacobi Equations (Nauka, Moscow, 1991) [in Russian].
A. F. Kleimenov and A. I. Subbotin, “Positional differential games: Theory, applications, related topics,” in Proceedings of the International Conference on Game Theory, Florence, Italy, 1991, p. 15.
A. I. Subbotin, “On a property of the subdifferential,” Math. USSR Sb. 74 (1), 63–78 (1993).
I. Rozyev and A. I. Subbotin, “Discontinuous solutions of the Hamilton–Jacobi equation,” Differents. Uravneniya 28 (4), 727–729 (1992).
A. I. Subbotin, “Continuous and discontinuous solutions of boundary value problems for first-order partial differential equations,” Russian Acad. Sci. Dokl. Math. 45 (2), 257–261 (1993).
A. I. Subbotin and L. G. Shagalova, “Piecewise linear functions defined by structure matrices,” in Control Problems with Guaranteed Result (IMM UrO RAN, Yekaterinburg, 1992), pp. 73–87 [in Russian].
A. I. Subbotin, “Trajectories of differential inclusions that are monotone with respect to preorder,” Trudy Inst. Mat. Mekh. UrO RAN 1, 138–146 (1992).
R. A. Adiatullina and A. I. Subbotin, “Minimax solutions of equations of the form ∂φ/∂t+H(t,x,φ,ωxφ) = 0,” Differential Equations 28 (5), 643–649 (1992).
A. I. Subbotin and L. G. Shagalova, “A piecewise linear solution of the Cauchy problem for the Hamilton–Jacobi equation,” Russian Acad. Sci. Dokl. Math. 46 (1), 144–148 (1993).
A. I. Subbotin, “Discontinuous solutions of a Dirichlet-type boundary value problem for the first-order partial differential equation,” Russian J. Numer. Anal. Math. Modelling 8 (2), 145–164 (1993).
A. I. Subbotin, “A theory of generalized solutions to first-order PDEs with an emphasis on differential games,” in Advances in Nonlinear Dynamics and Control: A Report from Russia (Birkhäuser, Boston, 1993), Ser. Progress in Systems and Control Theory, Vol. 17, pp. 189–229.
A. I. Subbotin, Generalized Characteristics of First-Order Partial Differential Equations, Preprint No. CRM-1848 (Univ. Montreal, Montreal, 1993).
A. I. Subbotin and N. N. Subbotina, “Piecewise smooth solutions of first-order partial differential equations,” Russian Acad. Sci. Dokl. Math. 48 (3), 650–654 (1994).
A. I. Subbotin, A. M. Taras’ev, and V. N. Ushakov, “Generalized characteristics of Hamilton–Jacobi equations,” J. Comput. Systems Sci. Internat. 32 (2), 157–163 (1994).
G. G. Garnysheva and A. I. Subbotin, “Strategies of minimax aiming in the direction of the quasigradient,” J. Appl. Math. Mech. 58 (4), 575–581 (1994).
F. H. Clarke, Yu. S. Ledyaev, Subbotin, Universal Feedback via Proximal Aiming in Problems of Control and Differential Games, Preprint No. CRM-2386 (Univ. Montreal, Montreal, 1994).
A. I. Subbotin and N. N. Subbotina, “Nonsmooth and discontinuous solutions of first-order partial differential equations,” J. Comput. Systems Sci. Internat. 33 (6), 118–126 (1995).
A. I. Subbotin, Generalized Solutions of First-Order PDEs: The Dynamic Optimization Perspective (Birkhäuser, Boston, 1995).
G. G. Garnysheva and A. I. Subbotin, “Suboptimal universal strategies in an optimum-time game problem,” J. Appl. Math. Mech. 59 (5), 677–683 (1995).
A. I. Subbotin, “Generalized solutions of partial differential equations of the first order. The invariance of graphs relative to differential inclusions,” J. Math. Sci. 78 (5), 594–611 (1996).
A. I. Subbotin, “Minimax solutions of first-order partial differential equations,” Russ. Math. Surv. 51 (2), 283–313 (1996).
A. I. Subbotin, “M-solutions of first-order partial differential equations and their application to differential pursuit game,” in The Century of Radio: Collection of Papers (Izd. UrO RAN, Yekaterinburg, 1996), pp. 202–218 [in Russian].
A. I. Subbotin and A. G. Chentsov, “An iterative procedure for constructing minimax and viscosity solutions of the Hamilton–Jacobi equations,” Russian Acad. Sci. Dokl. Math. 53 (3), 416–419 (1996).
F. H. Clarke, Yu. S. Ledyaev, E. D. Sontag, and A. I. Subbotin, “Asymptotic controllability and feedback stabilization,” in Proceedings of the Conference on Information Sciences and Systems, Princeton, NJ, USA, 1996, pp. 1232–1237.
F. H. Clarke, Yu. S. Ledyaev, and A. I. Subbotin, “The synthesis of universal feedback pursuit strategies in differential games,” SIAM J. Control Optim. 35 (2), 552–561 (1997).
F. H. Clarke, Yu. S. Ledyaev, E. D. Sontag, and A. I. Subbotin, “Asymptotic controllability implies feedback stabilization,” IEEE Trans. Automat. Control 42 (10), 1394–1407 (1997).
A. S. Lakhtin and A. I. Subbotin, “Multivalued solutions of first-order partial differential equations,” Russian Akad. Sci. Sb. Math. 189 (6), 849–873 (1998).
A. S. Lakhtin and A. I. Subbotin, “Minimax and viscosity solutions to discontinuous first-order partial differential equations,” Russian Akad. Sci. Dokl. Math. 57 (2), 246–250 (1998).
A. S. Lakhtin and A. I. Subbotin, Generalized Solutions to Discontinuous First-Order Partial Differential Equations (Sverdlovsk, 1998), Available from VINITI, No. 267–V98 [in Russian].
A. I. Subbotin, “Constructive theory of positional differential games and generalized solutions to Hamilton–Jacobi equations,” in Stochastic and Differential Games: Theory and Numerical Methods, Ed. by M. Bardi, T. E. S. Raghavan, and T. Parthasarathy (Birkhäuser, Boston, 1999), Ser. Annals of the International Society of Dynamic Games, Vol. 4, pp. 3–67.
A. I. Subbotin and A. G. Chentsov, “An iterative procedure for constructing minimax and viscosity solutions to the Hamilton–Jacobi equations and its generalization,” Proc. Steklov Inst. Math. 224, 286–309 (1999).
A. I. Subbotin, “Minimax solutions to Hamilton–Jacobi equations,” in Results in Science and Engineering, Ser. Modern Mathematics and Its Applications (VINITI, Moscow, 1999), Vol. 64, pp. 222–231 [in Russian].
A. I. Subbotin, Generalized Solutions of First-Order Partial Differential Equations: The Dynamical Optimization Perspective (Inst. Komp. Issled., Moscow–Izhevsk, 2003) [in Russian].
A. I. Subbotin, “Superreachable domains,” Izv. Ural. Gos. Univ., No. 34, 14–31 (2005).
Additional information
Original Russian Text © A.M. Taras’ev, V.N. Ushakov, A.G.Chentsov, N.N. Subbotina, 2015, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Vol. 21, No. 2.
Rights and permissions
About this article
Cite this article
Taras’ev, A.M., Ushakov, V.N., Chentsov, A.G. et al. Andrei Izmailovich Subbotin (On the occasion of his 70th birthday). Proc. Steklov Inst. Math. 293 (Suppl 1), 1–16 (2016). https://doi.org/10.1134/S0081543816050011
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543816050011