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.
Subject:
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.
Biography
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.
V. A. Yakubovich, “Machines learning pattern recognition. II”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9:1 (2022), 94–112; Vestn. St. Petersbg. Univ., Math., 9:1 (2022), 71–86
2000
2.
V. A. Yakubovich, “The necessity for a quadratic criterion for absolute stability of systems with a periodically nonstationary linear part”, Avtomat. i Telemekh., 2000, no. 12, 62–74; Autom. Remote Control, 61:12 (2000), 1991–2002
A. S. Matveev, V. A. Yakubovich, “Nonconvex global optimization problems in control theory”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 60 (1998), 128–175; J. Math. Sci. (New York), 100:5 (2000), 2531–2563
A. L. Likhtarnikov, V. A. Yakubovich, “Dichotomy and stability of undetermined nonlinear systems in Hilbert spaces”, Algebra i Analiz, 9:6 (1997), 132–155; St. Petersburg Math. J., 9:6 (1998), 1129–1147
V. A. Yakubovich, “Universal Controllers in Stochastic Problems of Optimal Control of Linear Stationary Plants”, Avtomat. i Telemekh., 1997, no. 6, 170–182; Autom. Remote Control, 58:6 (1997), 1026–1036
A. S. Shiryaev, V. A. Yakubovich, “Optimal tracking of harmonic signals in linear systems with noise
in the measurements”, Dokl. Akad. Nauk, 353:1 (1997), 29–33
A. Lindquist, V. A. Yakubovich, “Universal controllers for the optimal damping of forced
oscillations in linear discrete systems”, Dokl. Akad. Nauk, 352:3 (1997), 314–317
V. A. Yakubovich, “A universal controller for the optimal damping of forced
oscillations in linear systems with delay”, Dokl. Akad. Nauk, 346:3 (1996), 319–323
V. A. Yakubovich, “A universal controller for optimal damping of forced stochastic
oscillations in a linear system”, Dokl. Akad. Nauk, 338:1 (1994), 19–24; Dokl. Math., 50:2 (1995), 192–199
V. A. Yakubovich, “The problem of optimal tracking of deterministic harmonic signals
with a known spectrum”, Dokl. Akad. Nauk, 337:4 (1994), 463–466; Dokl. Math., 39:10 (1994), 683–686
V. A. Yakubovich, “Optimal damping of forced oscillations with respect to the output
of a system”, Dokl. Akad. Nauk, 337:3 (1994), 323–327; Dokl. Math., 39:7 (1994), 477–481
V. A. Yakubovich, E. D. Yakubovich, “Optimal stabilization of a control system with constraints on the output variable”, Avtomat. i Telemekh., 1993, no. 9, 79–88; Autom. Remote Control, 54:9 (1993), 1368–1376
V. A. Yakubovich, “A linear-quadratic problem of optimal damping of forced
oscillations with unknown harmonic external action”, Dokl. Akad. Nauk, 333:2 (1993), 170–172; Dokl. Math., 38:11 (1993), 449–451
A. N. Savkin, V. A. Yakubovich, “Absolute stability of nonlinear systems with a nonstationary linear part”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, no. 4, 101–105; Russian Math. (Iz. VUZ), 37:4 (1993), 98–101
A. S. Matveev, V. A. Yakubovich, “Nonconvex problems of global optimization”, Algebra i Analiz, 4:6 (1992), 189–219; St. Petersburg Math. J., 4:6 (1993), 1217–1243
V. A. Yakubovich, “Functional identification of a linear infinite-dimensional object”, Dokl. Akad. Nauk, 327:4-6 (1992), 455–459; Dokl. Math., 37:12 (1992), 572–574
V. A. Yakubovich, “Nonoscillation of linear periodic Hamiltonian equations and related problems”, Algebra i Analiz, 3:5 (1991), 229–253; St. Petersburg Math. J., 3:5 (1992), 1165–1188
V. A. Yakubovich, “A linear-quadratic problem of optimization and the frequency theorem for periodic systems. II”, Sibirsk. Mat. Zh., 31:6 (1990), 176–191; Siberian Math. J., 31:6 (1990), 1027–1039
E. A. Tomberg, V. A. Yakubovich, “Conditions for auto-oscillations in nonlinear systems”, Sibirsk. Mat. Zh., 30:4 (1989), 180–194; Siberian Math. J., 30:4 (1989), 641–653
V. A. Yakubovich, “Adaptive stabilization of continuous linear processes”, Avtomat. i Telemekh., 1988, no. 4, 97–107; Autom. Remote Control, 49:4 (1988), 474–483
V. A. Yakubovich, “Absolute stability of nonlinear systems with a periodically
nonstationary linear part”, Dokl. Akad. Nauk SSSR, 298:2 (1988), 299–303; Dokl. Math., 33:1 (1988), 5–7
V. A. Yakubovich, “A linear-quadratic problem of optimization and the frequency theorem for periodic systems. I”, Sibirsk. Mat. Zh., 27:4 (1986), 181–200; Siberian Math. J., 27:4 (1986), 614–630
V. A. Yakubovich, “A singular problem of optimal control of a linear steady state system with a quadratic functional”, Sibirsk. Mat. Zh., 26:1 (1985), 189–200; Siberian Math. J., 26:1 (1985), 148–158
V. A. Yakubovich, “Optimization and invariance of linear stationary control systems”, Avtomat. i Telemekh., 1984, no. 8, 5–45; Autom. Remote Control, 45:8 (1984), 963–999
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, no. 7, 49–57; Autom. Remote Control, 45:7 (1984), 859–866
V. A. Yakubovich, E. D. Yakubovich, “Equivalent feedbacks in linear stationary control systems”, Avtomat. i Telemekh., 1984, no. 2, 54–65; Autom. Remote Control, 45:2 (1984), 188–198
V. A. Yakubovich, “Absolute stability of nonlinear systems with partial derivatives. I”, Avtomat. i Telemekh., 1983, no. 6, 53–61; Autom. Remote Control, 44:6 (1983), 729–736
V. A. Popov, V. A. Yakubovich, “An optimization problem with phase constraints at different times”, Avtomat. i Telemekh., 1983, no. 1, 50–59; Autom. Remote Control, 44:1 (1983), 39–47
V. A. Yakubovich, “Graphical criteria for absolute stability and absolute instability of nonlinear control systems”, Dokl. Akad. Nauk SSSR, 271:2 (1983), 307–310
A. L. Likhtarnikov, V. A. Yakubovich, “Abstract criteria for absolute stability of nonlinear systems with respect to the linear output and their application. II”, Sibirsk. Mat. Zh., 24:5 (1983), 129–148; Siberian Math. J., 24:5 (1983), 752–767
A. L. Likhtarnikov, V. A. Yakubovich, “Abstract criteria for absolute stability of nonlinear systems with respect to the linear output and their applications. I”, Sibirsk. Mat. Zh., 23:4 (1982), 103–121; Siberian Math. J., 23:4 (1982), 530–544
S. V. Gusev, V. A. Yakubovich, “An algorithm for adaptive control of a manipulator robot”, Avtomat. i Telemekh., 1980, no. 9, 101–111; Autom. Remote Control, 41:9 (1981), 1268–1277
N. E. Barabanov, V. A. Yakubovich, “Absolute stability of control systems having one hysteresis-like nonlinearity”, Avtomat. i Telemekh., 1979, no. 12, 5–12; Autom. Remote Control, 40:12 (1980), 1713–1719
A. M. Shvedov, A. A. Shmidt, V. A. Yakubovich, “Invariant systems of features in pattern recognition”, Avtomat. i Telemekh., 1979, no. 3, 131–142; Autom. Remote Control, 40:3 (1979), 430–441
A. A. Shmidt, V. A. Yakubovich, “Topic filtering algorithms and their use in recognition of complex images”, Avtomat. i Telemekh., 1978, no. 2, 161–176; Autom. Remote Control, 39:2 (1978), 289–301
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
A. L. Likhtarnikov, V. A. Yakubovich, “Frequency theorems and a stabilization theorem for unbounded
operators”, Uspekhi Mat. Nauk, 33:2(200) (1978), 195–196; Russian Math. Surveys, 33:2 (1978), 235–236
A. S. Matveev, V. A. Yakubovich, “Optimal control of certain systems with distributed parameters”, Sibirsk. Mat. Zh., 19:5 (1978), 1109–1140; Siberian Math. J., 19:5 (1978), 783–804
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; Math. USSR-Izv., 11:4 (1977), 849–864
A. L. Likhtarnikov, V. A. Yakubovich, “A frequency theorem for equations of evolution type”, Sibirsk. Mat. Zh., 17:5 (1976), 1069–1085; Siberian Math. J., 17:5 (1976), 790–803
V. A. Yakubovich, “Frequency conditions of oscillations in nonlinear control systems with one single-valued or hysteresis-type nonlinearity”, Avtomat. i Telemekh., 1975, no. 12, 51–64; Autom. Remote Control, 36:12 (1975), 1973–1985
V. A. Yakubovich, “The frequency theorem for the case in which the state space and the control space are Hilbert spaces, and its application in certain problems in the synthesis of optimal control. II”, Sibirsk. Mat. Zh., 16:5 (1975), 1081–1102; Siberian Math. J., 16:5 (1975), 828–845
I. M. Burkin, V. A. Yakubovich, “Frequency conditions for the existence of two almost periodic solutions of a nonlinear automatic control system”, Sibirsk. Mat. Zh., 16:5 (1975), 916–924; Siberian Math. J., 16:5 (1975), 699–705
R. P. Shepeleva, V. A. Yakubovich, “Critical frequencies of canonical fractional-periodic equations”, Sibirsk. Mat. Zh., 16:3 (1975), 612–622; Siberian Math. J., 16:3 (1975), 471–479
V. A. Yakubovich, “The frequency theorem for the case in which the state space and the control space are Hilbert spaces, and its application in certain problems in the synthesis of optimal control. I”, Sibirsk. Mat. Zh., 15:3 (1974), 639–668; Siberian Math. J., 15:3 (1974), 457–476
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
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
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
V. A. Yakubovich, “Frequency conditions for auto-oscillations in nonlinear systems with a certain stationary nonlinearity”, Sibirsk. Mat. Zh., 14:5 (1973), 1100–1129; Siberian Math. J., 14:5 (1973), 768–788
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
V. A. Yakubovich, “A theorem on the stability of a linear hamiltonian system with periodic coefficients”, Zap. Nauchn. Sem. LOMI, 27 (1972), 220–234
1971
63.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
A. L. Fradkov, V. A. Yakubovich, “Fourth leningrad symposium of theory of adaptive systems”, Avtomat. i Telemekh., 1981, no. 4, 186–192
1977
95.
D. P. Derevitskii, A. L. Fradkov, V. A. Yakubovich, “III Liningrad symposium on theory of adaptive systems”, Avtomat. i Telemekh., 1977, no. 12, 160–164
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
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
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
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