01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
23.02.1959
E-mail:
Keywords:
dynamic systems; optimal control theory; viscosity solutions of Hamilton–Jacobi equations; differential games; mathematical economics.
Subject:
Grid schemes for constructing value functions and guaranteeing feedbacks are elaborated for optimal control problems. Finite difference operators based on constructions of nonsmooth analysis are proposed for approximation of generalized derivatives in Hamilton–Jacobi equations. Convergence results for approximation schemes are proved and estimates of convergence are indicated. Differential inequalities in terms of conjugate derivatives are obtaibed for characterization of stability properties of the value function in infinitesimal form. Regularity conditions for the function of programming maximin are derived in terms of conjugate variables. These results are applied to solution of a series of problems of mathematical economics: dynamic bimatrix games, models of optimal economic growth, problems of dynamic vector optimization, game interaction of investment projects, repeating games of auction type for searching optimal solutions of multicriteria problems.
Biography
Graduated from Faculty of Mathematics and Mechanics of Ural State University in 1981 (department of applied mathematics). Ph.D. thesis was defended in 1984. D.Sci. thesis was defended in 1996. A list of my works contains more than 100 titles. I have a part-time position in the Dynamic Systems project headed by A. V. Kryazhimskii at the International Institute for Applied Systems Analysis (IIASA, Laxenburg, Austria). I coordinate the program "Technology Innovation" organized at IIASA by the Committee of Systems Analysis of RAS.
In 1981 I was awarded the prize of the Ministry of Higher Education of Russian Federation for the masters's thesis devoted to algorithms for construction of resolving strategies in optimal control theory. In 1988 I received the prize of the Presidium of the Ural Branch of RAS and Sverdlovsk Komsomol organization for a series of papers on generalized solutions of Hamilton–Jacobi equations. In 1994 I won the Peccei prize of the International Institute for Applied Systems Analysis (IIASA, Laxenburg, Austria) for the research on dynamic bimatrix games.
Main publications:
Tarasyev A. M. Control Synthesis in Grid Schemes for Hamilton–Jacobi Equations. Annals of Operations Research, 1999, 88, 337–359.
Tarasyev A. M., Watanabe C. Optimal Dynamics of Innovation in Models of Economic Growth // Journal of Optimization Theory and Applications, 2001, 108(1), 175–203.
Tarasyev A. M., Watanabe C. Dynamic Optimality Principles and Sensitivity Analysis in Models of Economic Growth // Nonlinear Analysis, 2001, 47(4), 2309–2320.
Vladimir N. Ushakov, Alexander M. Tarasyev, “Game Problem of Target Approach for Nonlinear Control System”, Mat. Teor. Igr Pril., 15:2 (2023), 122–139
2022
2.
Anastasiia A. Usova, Alexander M. Tarasyev, “Analisys of a growth model with a production CES-function”, Mat. Teor. Igr Pril., 14:4 (2022), 96–114
2020
3.
Nikolay A. Krasovskii, Alexander M. Tarasyev, “Mechanism for shifting Nash equilibrium trajectories to cooperative Pareto solutions in dynamic bimatrix games”, Contributions to Game Theory and Management, 13 (2020), 218–243
4.
Alexander M. Tarasyev, Anastasiia A. Usova, “An estimate of a smooth approximation of the production function for integrtaing Hamiltonian systems”, Mat. Teor. Igr Pril., 12:1 (2020), 91–115; Autom. Remote Control, 82:5 (2021), 911–925
2019
5.
A. L. Bagno, A. M. Tarasyev, “Numerical methods for construction of value functions in optimal control problems on an infinite horizon”, Izv. IMI UdGU, 53 (2019), 15–26
6.
A. L. Bagno, A. M. Tarasyev, “Estimate for the Accuracy of a Backward Procedure for the Hamilton–Jacobi Equation in an Infinite-Horizon Optimal Control Problem”, Trudy Mat. Inst. Steklova, 304 (2019), 123–136; Proc. Steklov Inst. Math., 304 (2019), 110–123
A. L. Bagno, A. M. Tarasyev, “Discrete approximation of the Hamilton-Jacobi equation for the value function in an optimal control problem with infinite horizon”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:1 (2018), 27–39
A. L. Bagno, A. M. Tarasyev, “Asymptotics of value function in models of economic growth”, Tambov University Reports. Series: Natural and Technical Sciences, 23:124 (2018), 605–616
2017
9.
A. L. Bagno, A. M. Tarasyev, “Stability properties of the value function in an infinite horizon optimal control problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:1 (2017), 43–56; Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 1–14
N. A. Krasovskii, A. M. Tarasyev, “Asymptotic behavior of solutions in dynamical bimatrix games with discounted indices”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:2 (2017), 193–209
11.
A. A. Krasovskii, P. D. Lebedev, A. M. Tarasyev, “Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints”, Zh. Vychisl. Mat. Mat. Fiz., 57:5 (2017), 768–782; Comput. Math. Math. Phys., 57:5 (2017), 770–783
Alexandr M. Tarasyev, Anastasiya A. Usova, Yuliya V. Shmotina, “Predictive trajectories of economic development under structural changes”, Mat. Teor. Igr Pril., 8:3 (2016), 34–66
13.
Nikolay A. Krasovskii, Alexander M. Tarasyev, “Equilibrium trajectories in dynamical bimatrix games with average integral payoff functionals”, Mat. Teor. Igr Pril., 8:2 (2016), 58–90; Autom. Remote Control, 79:6 (2018), 1148–1167
A. A. Krasovskii, P. D. Lebedev, A. M. Tarasyev, “Some facts about the Ramsey model”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:3 (2016), 160–168; Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 123–131
15.
A. L. Bagno, A. M. Tarasyev, “Properties of the value function in optimal control problems with infinite horizon”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:1 (2016), 3–14
A. V. Kryazhimskiy, A. M. Tarasyev, “Optimal control for proportional economic growth”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:2 (2015), 115–133; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 101–119
17.
A. V. Kryazhimskiy, A. M. Tarasyev, A. A. Usova, W. Wang, “Proportional economic growth under conditions of limited natural resources”, Trudy Mat. Inst. Steklova, 291 (2015), 138–156; Proc. Steklov Inst. Math., 291 (2015), 127–145
A. M. Taras'ev, A. A. Usova, W. Wang, O. V. Russkikh, “Optimal trajectory construction by integration of Hamiltonian dynamics in models of economic growth under resource constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:4 (2014), 258–276
N. A. Krasovskiy, A. V. Kryazhimskiy, A. M. Tarasyev, “Hamilton–Jacobi equations in evolutionary games”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:3 (2014), 114–131
A. M. Tarasyev, A. A. Usova, “Stabilizing the Hamiltonian system for constructing optimal trajectories”, Trudy Mat. Inst. Steklova, 277 (2012), 257–274; Proc. Steklov Inst. Math., 277 (2012), 248–265
Nikolay A. Krasovskiy, Alexander M. Tarasyev, “Decomposition algorithm of searching equilibria in the dynamical game”, Mat. Teor. Igr Pril., 3:4 (2011), 49–88; Autom. Remote Control, 76:10 (2015), 1865–1893
A. M. Tarasyev, A. A. Usova, “Influence of production function parameters on the solution and value function in optimal control problem”, Mat. Teor. Igr Pril., 3:3 (2011), 85–115
2010
23.
A. M. Tarasyev, A. A. Usova, “Nonlinear stabilizer constructing for two-sector economic growth model”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:5 (2010), 297–307
24.
A. M. Tarasyev, A. A. Usova, “Construction of a regulator for the Hamiltonian system in a two-sector economic growth model”, Trudy Mat. Inst. Steklova, 271 (2010), 278–298; Proc. Steklov Inst. Math., 271 (2010), 265–285
N. A. Krasovskii, A. M. Tarasyev, “Search of maximum points for a vector criterion based on decomposition properties”, Trudy Inst. Mat. i Mekh. UrO RAN, 15:4 (2009), 167–182; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S174–S190
A. A. Krasovskii, A. M. Taras'ev, “Construction of nonlinear regulators in economic growth models”, Trudy Inst. Mat. i Mekh. UrO RAN, 15:3 (2009), 127–138; Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S143–S154
A. A. Krasovskii, A. M. Tarasyev, “Properties of Hamiltonian Systems in the Pontryagin Maximum Principle for Economic Growth Problems”, Trudy Mat. Inst. Steklova, 262 (2008), 127–145; Proc. Steklov Inst. Math., 262 (2008), 121–138
A. A. Krasovskii, A. M. Tarasyev, “Optimization of the stopping time in multilevel dynamic systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, no. 2, 63–64
2007
29.
A. A. Krasovskii, A. M. Tarasyev, “Dynamic optimization of investments in the economic growth models”, Avtomat. i Telemekh., 2007, no. 10, 38–52; Autom. Remote Control, 68:10 (2007), 1765–1777
S. M. Aseev, A. V. Kryazhimskii, A. M. Tarasyev, “The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval”, Trudy Mat. Inst. Steklova, 233 (2001), 71–88; Proc. Steklov Inst. Math., 233 (2001), 64–80
S. V. Grigor'eva, A. M. Tarasyev, A. A. Uspenskii, V. N. Ushakov, “Constructions of the differential game theory for solving the Hamilton–Jacobi equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 6:2 (2000), 320–336; Proc. Steklov Inst. Math. (Suppl.), 2000no. , suppl. 2, S38–S53
1999
32.
A. V. Kryazhimskii, A. Nentjes, S. V. Shibaev, A. M. Tarasyev, “A game model of negotiations and market equilibria”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 61 (1999), 15–32; J. Math. Sci. (New York), 100:6 (2000), 2601–2612
1992
33.
A. M. Tarasyev, V. N. Ushakov, A. P. Khripunov, “On construction of positional absorption set in conflict control problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 1 (1992), 160–177
Sergei M. Aseev, Alexander G. Chentsov, Alexey A. Davydov, Nikolai L. Grigorenko, Vyacheslav I. Maksimov, Elena A. Rovenskaya, Alexander M. Tarasiev, “In memory of Arkady Viktorovich Kryazhimskiy (1949-2014)”, Ural Math. J., 2:2 (2016), 3–15
Opening of the Conference N. L. Grigorenko, E. I. Moiseev, A. D. Gvishiani, E. A. Rovenskaya, S. M. Aseev, A. M. Tarasyev, A. A. Davydov, V. I. Maksimov, A. G. Chentsov International conference "Systems Analysis: Modeling and Control" in memory of Academician A. V. Kryazhimskiy May 31, 2018 09:30
Adaptive economic growth A. V. Kryazhimskiy, A. M. Tarasyev Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin September 25, 2013 17:20
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