Differential-geometric methods in control theory and differential equations.
Main publications:
Krishchenko A. P. On Structure of Singularities of Solution of Quasi-linear Equations // Uspekhi Matematicheskih nauk, 1976, N 3, p. 219–220 (in Russian).
Zevnin A. A., Krishchenko A. P. Controllability of Nonlinear Systems and synthesis of control algorithms // Dokl. Akad. Nauk SSSR, 1981, V. 258, N 4. P. 805–809 (in Russian).
Krishchenko A. P. Optimal Control of Nonlinear Systems // Avtomat. Telemekh., 1982, N 11. P. 48–56 (in Russian).
Krishchenko A. P. An Investigation of Controllability and Reachability sets of Nonlinear Control Systems // Avtomat. Telemekh., 1984, N 6. P. 30–36 (in Russian).
Krishchenko A. P. Stabilization of programmed motion of nonlinear systems // Izv. Akad. Nauk SSSR, Tekhn. kibernetika, 1985, N 6. P. 108–112 (in Russian).
Kanatnikov A. N., Krishchenko A. P. Symmetries and decomposition of nonlinear systems // Differentsialnye Uravneniya, 30, N 11, 1994, 1880–1891 (in Russian).
Krishchenko A. P. Stabilization of equilibrium points of chaotic systems // Phys. Lett. A, 1995, v. 203, P. 350–356.
Krishchenko A. P. Localization of limit cycles // Differentsialnye Uravneniya, v. 31, N 11, 1995, p. 1858–1865 (in Russian).
Krishchenko A. P. Domains of Existences of Cycles // Dokl. Akad. Nauk, 1997, V. 353, N 1, P. 17–19 (in Russian).
Krishchenko A. P. Estimations of domains with cycles // Computers & Mathematics with Applications, 1997, Vol. 34, No. 2-4, pp. 325–332.
Ermoshina O. V., Krishchenko A. P. Synthesis of Programmed Control of Spacecraft Orientation by the Method of Inverse Problem of Dynamics // Izv. Akad. Nauk, Teoriya i Sistemy Upravleniya, 2000, N 2, P. 155–162 (in Russian).
Golubev A. E., Krishchenko A. P., Tkachev S. B. Separation principle for a class of nonlinear systems // Differentsialnye Uravneniya, 2001, V. 37, N 11, p. 1468–1475 (in Russian).
Krishchenko A. P., Panfilov D. U., Tkachev S. B. Global stabilization of affine systems using virtual outputs // Differentsialnye Uravneniya, 2003. V. 39. N 11. p. 1503–1510 (in Russian).
Krishchenko A. P., Kavinov A. V. Suppression of chaotic dynamics // Differentsialnye Uravneniya, 2004, V. 40, N 12, p. 1629–1635 (in Russian).
Starkov K. E., Krishchenko A. P. Location of Periodic Orbits of Polynomial Systems by Ellipsoidal Estimates // Chaos, Solitons & Fractals, 2005, v. 23, P. 981–988.
Krasnoshchechenko V. I., Krishchenko A. P. Nonlinear systems: geometrical methods of analysis and synthesis Moscow: Izd-vo BMSTU, 2005, 520 p. (in Russian).
Golubev A. E., Krishchenko A. P., Tkachev S. B. Stabilization of nonlinear dynmic systems using the system state estimates made by the asymptotic observe // Avtomat. Telemekh., 2005. N 7. p. 3–18 (in Russian).
Krishchenko A. P. Localization of invariant compact sets dynamical systems // Differentsialnye Uravneniya, 2005, V. 41, N 12, p. 1597–1604 (in Russian).
Krishchenko A. P., Starkov K. E. Localization of compact invariant sets of the Lorenz system // Phys. Lett. A, 2006, V. 353, N 6, P. 383–388.
Krishchenko A. P., Starkov K. E. Localization of compact invariant sets of nonlinear systems with application to the Lanford systems // Int. J. of Bifurcation and Chaos, 2006, N 11, p. 3249–3256.
Krishchenko A. P., Starkov K. E. Estimation of the domain containing all compact invariant sets of a system modelling the amplitude of a plasma instability // Phys. Lett. A, 2007, V. 367, N 1, P. 65–72.
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