Yakubovich, Vladimir Andreevich

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Total publications: 69
Scientific articles: 63

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Corresponding member of RAS
Doctor of physico-mathematical sciences
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 21.10.1926
Keywords: parametric rezonance; linear periodic Hamiltonian systems; frequency methods; nonlinear systems; periodic, almost periodic solutions; dissipativity; dichotomy; convergence; absolute stability; adaptive systems; finite conve rgent algorithms for the solutions of infinite systems of inequalities; optimal control; abstract maximum principle; linear quadratic optimization problems; nonconvex optimization problems; differencial games, universal controllers.


The parametric resonance theory and new approaches to the stability theory of nonlinear systems and to the optimization theory were developed. Among the contributions there are the quadratic criterion for absolute stabi lity, "Frequency theorem", the method of "recursive aim inequalities" in adaptive control and an abstract theory of optimal control, extending the Pontrjagin maximum principle to many new cases. Lemma Kalman-Yakubovich permits to connect two methods of control theory: frequency method and Liapu nov method. It is also of importance in stochastic realization theory. These theoretic investigations finds an application in many applied problems including robotic, mechanical engineering and electric energetics. The main results in recent years concern new aspects of linear-quadratic optimization problems.


Graduated from Faculty of Mathematics and Mechanics of Moscow State University in 1949 (differential equations and functional analysis chairs). Ph.D. thesis was defended in 1952. D.Sci. thesis was defended in 1959. The author of more than 300 papers and coauthor of seven books in different areas of applied mathematics and control theory.

Member of Russian Academy of Nature Sciences from 1992 and a member of Russian Academy of Nonlinear Sciences from 1997. I was awarded a Premium for the pedagogical art by the Sankt Petersburg University (1986). I was awarded the Norbert Wiener Prize (1991), a Premium by the international editorial company "Nauka" for best publication in its journals (1995), and the IEEE Control Systems Award "For pioneering and fundamental contributions to stability analysis and optimal control"(1996). My result on the solution of certain special matrix inequalities published in Doklady AN SSSR in 1962 is included in a millennium volume "Twenty-Five Seminal Papers in Control" containing the papers that have had a major impact on the field.

Main publications:
  • Yakubovich V. A. Nonconvex optimization problem: The infinite-horizon lin ear quadratic control problem with quadratic constraints // Systems and Control Letters, 1992, 19, 13–22.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. V. A. Yakubovich, “The necessity for a quadratic criterion for absolute stability of systems with a periodically nonstationary linear part”, Avtomat. i Telemekh., 2000, 12,  62–74  mathnet  mathscinet  zmath; Autom. Remote Control, 61:12 (2000), 1991–2002
2. E. A. Tomberg, V. A. Yakubovich, “On one problem of Smale”, Sibirsk. Mat. Zh., 41:4 (2000),  926–928  mathnet  mathscinet  zmath; Siberian Math. J., 41:4 (2000), 771–773  isi
3. A. S. Matveev, V. A. Yakubovich, “Nonconvex global optimization problems in control theory”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 60 (1998),  128–175  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 100:5 (2000), 2531–2563
4. A. L. Likhtarnikov, V. A. Yakubovich, “Dichotomy and stability of undetermined nonlinear systems in Hilbert spaces”, Algebra i Analiz, 9:6 (1997),  132–155  mathnet  mathscinet  zmath; St. Petersburg Math. J., 9:6 (1998), 1129–1147
5. V. A. Yakubovich, “Universal Controllers in Stochastic Problems of Optimal Control of Linear Stationary Plants”, Avtomat. i Telemekh., 1997, 6,  170–182  mathnet  mathscinet  zmath; Autom. Remote Control, 58:6 (1997), 1026–1036
6. V. A. Yakubovich, E. D. Yakubovich, “Optimal stabilization of a control system with constraints on the output variable”, Avtomat. i Telemekh., 1993, 9,  79–88  mathnet  mathscinet  zmath; Autom. Remote Control, 54:9 (1993), 1368–1376
7. A. N. Savkin, V. A. Yakubovich, “Absolute stability of nonlinear systems with a nonstationary linear part”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, 4,  101–105  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 37:4 (1993), 98–101
8. A. S. Matveev, V. A. Yakubovich, “Nonconvex problems of global optimization”, Algebra i Analiz, 4:6 (1992),  189–219  mathnet  mathscinet  zmath; St. Petersburg Math. J., 4:6 (1993), 1217–1243
9. V. A. Yakubovich, “Nonoscillation of linear periodic Hamiltonian equations and related problems”, Algebra i Analiz, 3:5 (1991),  229–253  mathnet  mathscinet  zmath; St. Petersburg Math. J., 3:5 (1992), 1165–1188
10. V. A. Yakubovich, “Adaptive stabilization of continuous linear processes”, Avtomat. i Telemekh., 1988, 4,  97–107  mathnet  mathscinet  zmath; Autom. Remote Control, 49:4 (1988), 474–483
11. V. A. Yakubovich, “A frequency theorem for periodic systems”, Dokl. Akad. Nauk SSSR, 287:1 (1986),  70–73  mathnet  mathscinet  zmath
12. V. A. Yakubovich, “Optimization and invariance of linear stationary control systems”, Avtomat. i Telemekh., 1984, 8,  5–45  mathnet  mathscinet  zmath; Autom. Remote Control, 45:8 (1984), 963–999
13. N. G. Dokuchaev, V. A. Yakubovich, “Optimal programmed control of a stochastic plant with constraints on the state for every time instant”, Avtomat. i Telemekh., 1984, 7,  49–57  mathnet  mathscinet  zmath; Autom. Remote Control, 45:7 (1984), 859–866
14. V. A. Yakubovich, E. D. Yakubovich, “Equivalent feedbacks in linear stationary control systems”, Avtomat. i Telemekh., 1984, 2,  54–65  mathnet  mathscinet  zmath; Autom. Remote Control, 45:2 (1984), 188–198
15. V. A. Yakubovich, “Absolute stability of nonlinear systems with partial derivatives. I”, Avtomat. i Telemekh., 1983, 6,  53–61  mathnet  mathscinet  zmath; Autom. Remote Control, 44:6 (1983), 729–736
16. V. A. Popov, V. A. Yakubovich, “An optimization problem with phase constraints at different times”, Avtomat. i Telemekh., 1983, 1,  50–59  mathnet  mathscinet  zmath; Autom. Remote Control, 44:1 (1983), 39–47
17. V. A. Yakubovich, “Graphical criteria for absolute stability and absolute instability of nonlinear control systems”, Dokl. Akad. Nauk SSSR, 271:2 (1983),  307–310  mathnet  mathscinet
18. S. V. Gusev, V. A. Yakubovich, “An algorithm for adaptive control of a manipulator robot”, Avtomat. i Telemekh., 1980, 9,  101–111  mathnet  zmath; Autom. Remote Control, 41:9 (1981), 1268–1277
19. N. E. Barabanov, V. A. Yakubovich, “Absolute stability of control systems having one hysteresis-like nonlinearity”, Avtomat. i Telemekh., 1979, 12,  5–12  mathnet  zmath; Autom. Remote Control, 40:12 (1980), 1713–1719
20. A. M. Shvedov, A. A. Shmidt, V. A. Yakubovich, “Invariant systems of features in pattern recognition”, Avtomat. i Telemekh., 1979, 3,  131–142  mathnet  zmath; Autom. Remote Control, 40:3 (1979), 430–441
21. A. A. Shmidt, V. A. Yakubovich, “Topic filtering algorithms and their use in recognition of complex images”, Avtomat. i Telemekh., 1978, 2,  161–176  mathnet  zmath; Autom. Remote Control, 39:2 (1978), 289–301
22. V. A. Yakubovich, “Frequency criteria for invariance up to $\varepsilon$ of control systems with one nonlinear block”, Dokl. Akad. Nauk SSSR, 240:2 (1978),  283–286  mathnet  mathscinet  zmath
23. A. L. Likhtarnikov, V. A. Yakubovich, “Frequency theorems and a stabilization theorem for unbounded operators”, Uspekhi Mat. Nauk, 33:2(200) (1978),  195–196  mathnet  mathscinet  zmath; Russian Math. Surveys, 33:2 (1978), 235–236
24. A. L. Likhtarnikov, V. A. Yakubovich, “The frequency theorem for continuous one-parameter semigroups”, Izv. Akad. Nauk SSSR Ser. Mat., 41:4 (1977),  895–911  mathnet  mathscinet  zmath; Math. USSR-Izv., 11:4 (1977), 849–864
25. V. A. Yakubovich, “Some variants of the abstract maximum principle”, Dokl. Akad. Nauk SSSR, 229:4 (1976),  816–819  mathnet  mathscinet  zmath
26. V. A. Yakubovich, “Frequency conditions of oscillations in nonlinear control systems with one single-valued or hysteresis-type nonlinearity”, Avtomat. i Telemekh., 1975, 12,  51–64  mathnet  mathscinet  zmath; Autom. Remote Control, 36:12 (1975), 1973–1985
27. V. A. Yakubovich, “An a priori estimate of the decrease of decreasing solutions of nonlinear systems”, Uspekhi Mat. Nauk, 29:3(177) (1974),  239–240  mathnet  mathscinet  zmath
28. A. L. Fradkov, V. A. Yakubovich, “Necessary and sufficient conditions for absolute stability in classes of systems with two integral quadratic relations”, Dokl. Akad. Nauk SSSR, 213:4 (1973),  798–801  mathnet  mathscinet  zmath
29. V. A. Yakubovich, “Minimization of quadratic functionals under quadratic constraints and the necessity of a frequency condition in the quadratic criterion for absolute stability of nonlinear control systems”, Dokl. Akad. Nauk SSSR, 209:5 (1973),  1039–1042  mathnet  mathscinet  zmath
30. V. A. Yakubovich, “Necessary and sufficient conditions for absolute stability under certain types of quadratic constraints”, Dokl. Akad. Nauk SSSR, 209:2 (1973),  312–315  mathnet  mathscinet  zmath
31. V. A. Andreev, Yu. F. Kazarinov, V. A. Yakubovich, “Synthesis of optimal controls for linear nonhomogeneous systems in the problem of minimizing the mean value of a quadratic functional”, Dokl. Akad. Nauk SSSR, 202:6 (1972),  1247–1250  mathnet  mathscinet  zmath
32. V. A. Yakubovich, “A theorem on the stability of a linear hamiltonian system with periodic coefficients”, Zap. Nauchn. Sem. LOMI, 27 (1972),  220–234  mathnet  mathscinet  zmath
33. V. A. Yakubovich, “On the synthesis of optimal controls in a linear differential game on a finite time interval with quadratic payoff functional”, Dokl. Akad. Nauk SSSR, 200:3 (1971),  548–551  mathnet  mathscinet  zmath
34. V. A. Andreev, Yu. F. Kazarinov, V. A. Yakubovich, “Synthesis of optimal controls for linear inhomogeneous systems in problems of quadratic functional minimization”, Dokl. Akad. Nauk SSSR, 199:2 (1971),  258–261  mathnet  mathscinet  zmath
35. G. D. Penev, V. A. Yakubovich, “Certain problems in adaptive control”, Dokl. Akad. Nauk SSSR, 198:4 (1971),  787–790  mathnet  mathscinet  zmath
36. V. A. Yakubovich, “The synthesis of optimal controls in a linear differential game with a quadratic payoff functional”, Dokl. Akad. Nauk SSSR, 195:2 (1970),  296–299  mathnet  mathscinet  zmath
37. V. A. Yakubovich, “Factorization of symmetric matrix polynomials”, Dokl. Akad. Nauk SSSR, 194:3 (1970),  532–535  mathnet  mathscinet  zmath
38. V. A. Yakubovich, “Solution of a certain algebra problem that arises in control theory”, Dokl. Akad. Nauk SSSR, 193:1 (1970),  57–60  mathnet  mathscinet  zmath
39. V. A. Yakubovich, “Frequency conditions for certain topological types of behavior “in the large” of solutions of nonlinear differential equation”, Uspekhi Mat. Nauk, 25:6(156) (1970),  233–234  mathnet  mathscinet  zmath
40. V. A. Yakubovich, “Finitely convergent algorithms for the solution of countable systems of inequalities, and their application in problems of the synthesis of adaptive systems”, Dokl. Akad. Nauk SSSR, 189:3 (1969),  495–498  mathnet  mathscinet  zmath
41. V. A. Yakubovich, “A certain class of nonlinear differential equations for which stability in the large and instability questions can be solved effectively”, Dokl. Akad. Nauk SSSR, 186:5 (1969),  1027–1030  mathnet  mathscinet  zmath
42. V. A. Yakubovich, “Adaptive systems with multistep goal conditions”, Dokl. Akad. Nauk SSSR, 183:2 (1968),  303–306  mathnet  mathscinet  zmath
43. V. A. Yakubovich, “Theory of adaptive systems”, Dokl. Akad. Nauk SSSR, 182:3 (1968),  518–521  mathnet  mathscinet  zmath
44. V. A. Yakubovich, “Impulse control systems with width modulation”, Dokl. Akad. Nauk SSSR, 180:2 (1968),  290–293  mathnet  mathscinet  zmath
45. V. A. Yakubovich, “Periodic and almost periodic limiting states of control systems with several, in general discontinuous, nonlinear terms”, Dokl. Akad. Nauk SSSR, 171:3 (1966),  533–536  mathnet  mathscinet  zmath
46. B. N. Kozinets, R. M. Lantsman, V. A. Yakubovich, “The use of electron computers in criminalistics for differentiation between very similar handwritings”, Dokl. Akad. Nauk SSSR, 167:5 (1966),  1008–1011  mathnet
47. V. A. Yakubovich, “Recurrent finitely convergent algorithms for solving systems of inequalities”, Dokl. Akad. Nauk SSSR, 166:6 (1966),  1308–1311  mathnet  mathscinet
48. V. A. Yakubovich, “Frequency conditions for absolute stability and dissipativeness of control systems with one differentiable nonlinearity”, Dokl. Akad. Nauk SSSR, 160:2 (1965),  298–301  mathnet  mathscinet  zmath
49. V. A. Yakubovich, “Solution of certain matrix inequalities encountered in non-linear control theory”, Dokl. Akad. Nauk SSSR, 156:2 (1964),  278–281  mathnet  mathscinet  zmath
50. V. I. Derguzov, V. A. Yakubovich, “Existence of solutions of linear Hamiltonian equations with unbounded operator coefficients”, Dokl. Akad. Nauk SSSR, 151:6 (1963),  1264–1267  mathnet  mathscinet  zmath
51. V. A. Yakubovich, “Frequency conditions for absolute stability of control systems with hysteresis-like non-linearities”, Dokl. Akad. Nauk SSSR, 149:2 (1963),  288–291  mathnet  mathscinet  zmath
52. V. A. Yakubovich, “The solution of some matrix inequalities encountered in automatic control theory”, Dokl. Akad. Nauk SSSR, 143:6 (1962),  1304–1307  mathnet  mathscinet  zmath
53. V. A. Yakubovich, “Oscillatory properties of solutions of canonical equations”, Mat. Sb. (N.S.), 56(98):1 (1962),  3–42  mathnet  mathscinet  zmath
54. V. A. Yakubovich, “The structure of the functional space of complex canonical equations with periodic coefficients”, Dokl. Akad. Nauk SSSR, 139:1 (1961),  54–57  mathnet  mathscinet  zmath
55. V. A. Yakubovich, “Systems of standard linear differential equations with periodic coefficients (summary of the doctor's Thesis)”, Uspekhi Mat. Nauk, 16:1(97) (1961),  223–234  mathnet  zmath
56. V. A. Yakubovich, “Arguments on the group of symplectic matrices”, Mat. Sb. (N.S.), 55(97):3 (1961),  255–280  mathnet  mathscinet  zmath
57. V. A. Yakubovich, “Stability conditions in the large for some non-linear differential equations of automatic control”, Dokl. Akad. Nauk SSSR, 135:1 (1960),  26–29  mathnet  mathscinet  zmath
58. V. A. Yakubovich, “On the boundedness and stability in the whole of the solutions of some non-linear differential equations”, Dokl. Akad. Nauk SSSR, 121:6 (1958),  984–986  mathnet  zmath
59. V. A. Yakubovich, “On the dynamic stability of elastic systems”, Dokl. Akad. Nauk SSSR, 121:4 (1958),  602–605  mathnet  mathscinet  zmath
60. V. A. Yakubovich, “Structure of the group of symplectic matrices and of the set of unstable canonical systems with periodic coefficients”, Mat. Sb. (N.S.), 44(86):3 (1958),  313–352  mathnet  mathscinet  zmath
61. V. A. Yakubovich, “On a class of non-linear differential equations”, Dokl. Akad. Nauk SSSR, 117:1 (1957),  44–46  mathnet  mathscinet  zmath
62. V. A. Yakubovich, “Questions of the stability of solutions of a system of two linear differential equations of canonical form with periodic coefficients”, Mat. Sb. (N.S.), 37(79):1 (1955),  21–68  mathnet  mathscinet  zmath
63. V. A. Yakubovich, “On the asymptotic behavior of the solutions of a system of differential equations”, Mat. Sb. (N.S.), 28(70):1 (1951),  217–240  mathnet  mathscinet  zmath

64. A. L. Fradkov, V. A. Yakubovich, “Fourth leningrad symposium of theory of adaptive systems”, Avtomat. i Telemekh., 1981, 4,  186–192  mathnet
65. D. P. Derevitskii, A. L. Fradkov, V. A. Yakubovich, “III Liningrad symposium on theory of adaptive systems”, Avtomat. i Telemekh., 1977, 12,  160–164  mathnet
66. V. G. Antonov, V. A. Yakubovich, “The special representation of Hermitian forms that are encountered in game theory”, Uspekhi Mat. Nauk, 30:5(185) (1975),  199–200  mathnet  mathscinet  zmath
67. A. N. Andrianov, A. I. Vinogradov, Yu. V. Linnik, A. V. Malyshev, D. K. Faddeev, N. G. Chudakov, V. A. Yakubovich, “On book of N. I. Gavrilov, The Riemann problem on the distribution of the roots of the zeta function”, Uspekhi Mat. Nauk, 26:3(159) (1971),  238–247  mathnet  mathscinet
68. A. O. Gel'fond, Yu. V. Linnik, N. G. Chudakov, V. A. Yakubovich, “On an erroneous paper of N. I. Gavrilov”, Uspekhi Mat. Nauk, 17:1(103) (1962),  265–267  mathnet  mathscinet
69. Yu. V. Linnik, E. S. Lyapin, V. A. Yakubovich, “Vladimir Abramovich Tartakovskii (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 16:5(101) (1961),  225–230  mathnet  mathscinet  zmath

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