Yuri Ledyaev's main research interests lie in control theory (in particular, stabilization, optimal control, differential games), theory of differential inclusions, nonlinear functional and nonsmooth analysis (in particular, nonsmooth analysis' applications in control theory).
He received his Ph.D. degree from Moscow Institute for Physics and Technology in 1980 and his Dr.Sc. degree from Steklov Institute of Mathematics in 1990. He was with Department of Mathematics of Moscow Institute for Physics and Technology during 1980–1984, since 1984 he has been with Steklov Institute of Mathematics of Russian Academy of Sciences where he is a Principal Researcher at the Department of Differential Equations founded by L. S. Pontryagin. He is a Full Professor at the Department of Mathematics, Western Michigan University since 2000.
He authored about 40 papers in above mentioned areas. He is a coauthor with F. H. Clarke, R. J. Stern and P. R. Wolenski of the textbook "Nonsmooth Analysis and Control Theory" published by Springer-Verlag in 1998.
He is a member of the Editorial Boards of "Journal of Dynamical and Control Systems" and "Nonlinear Analysis". His most recently supervised Ph.D. students have been: M. Radulescu (1996, Math, Universite de Montreal) and E. Devdariani (1996, Math, Queen's University, Kingston, Canada).
Main publications:
Ledyaev Yu. S. and Zhu Q. J., “Multidirectional mean value inequalities and weak monotonicity”, J. London Math. Soc. (2), 71:1 (2005), 187–202
Ledyaev Yu. S., “On an infinite-dimensional variant of the Rashevskii-Chow theorem”, Dokl. Akad. Nauk, 398:6 (2004), 735–737
Ledyaev Yu. S. and Zhu Qiji J., “Techniques for nonsmooth analysis on smooth manifolds. II. Deformations and flows”, Optimal control, stabilization and nonsmooth analysis, Lecture Notes in Control and Inform. Sci., 301, Springer, Berlin, 2004, 299–311
Ledyaev Yu. S. and Zhu Qiji J., “Techniques for nonsmooth analysis on smooth manifolds. I. Local problems”, Optimal control, stabilization and nonsmooth analysis, Lecture Notes in Control and Inform. Sci., 301, Springer, Berlin, 2004, 283–297
Ledyaev Yuri S., “On generic existence and uniqueness in nonconvex optimal control problems”, Set-Valued Anal., 12:1-2 (2004), 147–162
Yu. S. Ledyaev, “Wilcox Formula for Vector Fields on Banach Manifolds”, Tr. IMM UrO RAN, 27, no. 3, 2021, 271–285;
2.
Yu. S. Ledyaev, “Criteria for Convexity of Closed Sets in Banach Spaces”, Proc. Steklov Inst. Math., 304 (2019), 190–204
3.
Yu. S. Ledyaev, J. S. Treiman, “Sub- and supergradients of envelopes, semicontinuous closures, and limits of sequences of functions”, Russian Math. Surveys, 67:2 (2012), 345–373
4.
Yuri S. Ledyaev, “On analytical solutions of matrix Riccati equations”, Proc. Steklov Inst. Math., 273 (2011), 214–228
5.
F. Clarke, Yu. Ledyaev, M. d. R. de Pinhoário, “An extension of the Schwarzkopf multiplier rule in optimal control”, SIAM J. Control Optim., 49:2 (2011), 599–610
Yuri S. Ledyaev, Richard B. Vinter, “Discontinuous feedback in nonlinear control: Stabilization under persistent disturbances”, Proc. Steklov Inst. Math., 268 (2010), 222–241
Ledyaev Yu. S., “On an infinite-dimensional variant of the Rashevskiĭ-Chow theorem”, Dokl. Akad. Nauk, 398:6 (2004), 735–737
11.
Ledyaev Yu. S., Zhu Qiji J., “Techniques for nonsmooth analysis on smooth manifolds. II. Deformations and flows”, Optimal control, stabilization and nonsmooth analysis, Lecture Notes in Control and Inform. Sci., 301, Springer, Berlin, 2004, 299–311
Ledyaev Yu. S., Zhu Qiji J., “Techniques for nonsmooth analysis on smooth manifolds. I. Local problems”, Optimal control, stabilization and nonsmooth analysis, Lecture Notes in Control and Inform. Sci., 301, Springer, Berlin, 2004, 283–297
Bessis D. N., Ledyaev Yu. S., Vinter R. B., “Dualization of the Euler and Hamiltonian inclusions”, Nonlinear Anal., 43:7, Ser. A: Theory Methods (2001), 861–882
Proc. Inst. Math. Mech., 2000no. , suppl. 1, S72–S89
16.
Clarke F. H., Ledyaev Yu. S., Rifford L., Stern R. J., “Feedback stabilization and Lyapunov functions”, SIAM J. Control Optim., 39:1 (2000), 25–48 (electronic)
F. Clarke, Yu. S. Ledyaev, A. I. Subbotin, “Universal Feedback Control via Proximal Aiming in Problems of Control under Disturbance and Differential Games”, Proc. Steklov Inst. Math., 224 (1999), 149–168
23.
Clarke F. H., Ledyaev Yu. S., Stern R. J., “Proximal techniques of feedback construction”, Dynamical systems and differential equations, Vol. I (Springfield, MO, 1996), Discrete Contin. Dynam. Systems, 1998, no. Added Volume I, 177–194
24.
Clarke F. H., Hiriart-Urruty J.-B., Ledyaev Yu. S., “On global optimality conditions for nonlinear optimal control problems”, J. Global Optim., 13:2 (1998), 109–122
Clarke F. H., Ledyaev Y., Vinter R. B., “Addendum to: “Regularity properties of solutions to linear quadratic optimal control problems with state constraints” [Systems Control Lett. 30 (1997), no. 5, 265–272; MR1453840 (98d:49047)]”, Systems Control Lett., 33:2 (1998), 139
Clarke F. H., Ledyaev Yu. S., Stern R. J., Wolenski P. R., Nonsmooth analysis and control theory, Graduate Texts in Mathematics, 178, Springer-Verlag, New York, 1998 , xiv+276 pp.
28.
Clarke F. H., Ledyaev Yu. S., Stern R. J., “Complements, approximations, smoothings and invariance properties”, J. Convex Anal., 4:2 (1997), 189–219
29.
Clarke F. H., Ledyaev Yu. S., Radulescu M. L., “Approximate invariance and differential inclusions in Hilbert spaces”, J. Dynam. Control Systems, 3:4 (1997), 493–518
30.
Clarke Francis H., Ledyaev Yuri S., Sontag Eduardo D., Subbotin Andrei I., “Asymptotic controllability implies feedback stabilization”, IEEE Trans. Automat. Control, 42:10 (1997), 1394–1407
Clarke F. H., Ledyaev Y., Vinter R. B., “Regularity properties of solutions to linear quadratic optimal control problems with state constraints”, Systems Control Lett., 30:5 (1997), 265–272
Clarke F. H., Ledyaev Yu. S., Stern R. J., “Fixed point theory via nonsmooth analysis”, Recent developments in optimization theory and nonlinear analysis (1995, Jerusalem), Contemp. Math., 204, Amer. Math. Soc., Providence, RI, 1997, 93–106
Clarke F. H., Ledyaev Yu. S., Subbotin A. I., “The synthesis of universal feedback pursuit strategies in differential games”, SIAM J. Control Optim., 35:2 (1997), 552–561
Ledyaev Yu. S., Sontag E. D., “A notion of discontinuous feedback”, Control using logic-based switching (1995, Block Island, RI), Lecture Notes in Control and Inform. Sci., 222, Springer, London, 1997, 97–103
35.
Clarke F. H., Ledyaev Yu. S., Hiriart-Urruty J.-B., “Global optimality in the calculus of variations”, Nonlinear Anal., 28:7 (1997), 1187–1192
Hiriart-Urruty J.-B., Ledyaev Yuri S., “A note on the characterization of the global maxima of a (tangentially) convex function over a convex set”, J. Convex Anal., 3:1 (1996), 55–61
37.
Devdariani E. N., Ledyaev Yu. S., “Optimality conditions for implicit controlled systems”, Dynamical systems, 2, J. Math. Sci., 80:1 (1996), 1519–1532
Clarke F. H., Ledyaev Yu. S., Stern R. J., Wolenski P. R., “Qualitative properties of trajectories of control systems: a survey”, J. Dynam. Control Systems, 1:1 (1995), 1–48
Ledyaev Yu. S., “Criteria for viability of trajectories of nonautonomous differential inclusions and their applications”, J. Math. Anal. Appl., 182:1 (1994), 165–188
Yu. S. Ledyaev, E. F. Mishchenko, “Extremal problems in the theory of differential games”, Proc. Steklov Inst. Math., 185 (1990), 165–190
48.
Ledyaev Yu. S., Mishchenko E. F., “Conditions for the optimality of strategies in differential games of fixed duration”, Differentsial'nye Uravneniya, 23:2 (1987), 244–255, 364
49.
Ledyaev Yu. S., Mishchenko E. F., “Optimal strategies in differential games with fixed duration”, Dokl. Akad. Nauk SSSR, 286:2 (1986), 284–287
Yu. S. Ledyaev, “Regular differential games with mixed constraints on the controls”, Proc. Steklov Inst. Math., 167 (1986), 233–242
51.
Ledyaev Yu. S., “Theorems on an implicitly given set-valued mapping”, Dokl. Akad. Nauk SSSR, 276:3 (1984), 543–546
52.
R. P. Ivanov, Yu. S. Ledyaev, “Time optimality for the pursuit of several objects with simple motion in a differential game”, Proc. Steklov Inst. Math., 158 (1983), 93–103
53.
Ledyaev Yu. S., Pokotilo V. G., “A differential game with information delay”, Differentsial'nye Uravneniya, 16:8 (1980), 1385–1391, 1532
54.
Gusiatnikov P. B., Lediaev Iu. S., Mezentsev A. V., “Differential escape games with information lag”, J. Appl. Math. Mech., 43:2 (1979), 213–221 (1980)
55.
Gusjatnikov P. B., Ledjaev Ju. S., “A small parameter in a differential evasion game”, Differentsial'nye Uravneniya, 14:9 (1978), 1566–1575, 1721–1722
Program-predictive control for differential games Yu. S. Ledyaev International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin December 14, 2018 10:30
Optimal Control of Systems with Evolving Dynamics Yu. S. Ledyaev International Conference "Mathematical Theory of Optimal Control"
dedicated to the 90th birthday of Academician R. V. Gamkrelidze June 2, 2017 11:50
Memoirs about L. S. Pontryagin Yu. S. Ledyaev, R. V. Gamkrelidze Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin September 24, 2013 18:00
10.
Differential games as nonsmooth extremal problems Yu. S. Ledyaev Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin September 24, 2013 15:20
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