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In 1972 he graduated from the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University. In 1972 he graduated from the postgraduate school at this faculty and in 1976 he defended his thesis on geometric theory of differential equations.
In 1987 he defended his doctoral dissertation on management theory.
In 2011 he was elected a Corresponding Member of the Russian Academy of Sciences. |
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Was born on October 3, 1948 in Poltava, Doctor of Physical and Mathematical Sciences, Professor, Chief Research Scientist, Corresponding Member of the Russian Academy of Sciences, Russian scientist majoring in the field of nonlinear dynamical systems and control processes.
Since 1975 he has been working at Bauman Moscow State Technical University, he has been the Head of the Department of Mathematical Modeling since 1997. Alexandr Petrovich has also worked in Dorodnicyn Computing Centre of RAS and Institute for Systems Analysis of the Russian Academy of Sciences (ISA RAS).
Alexandr Petrovich's main scientific works are devoted to analysis of nonlinear dynamic systems, synthesis of control algorithms for nonlinear systems and developing the tools and methods of information technologies of mathematical modeling of nonlinear systems.
His main theoretical results were obtained on the basis of differential-geometric methods of analysis and information technologies of control algorithms synthesis for nonlinear systems.
In a set of multidimensional nonstationary affine systems Krishchenko A.P. identified systems of canonical and quasi-canonical forms, and proved a necessary and sufficient condition of their equivalence to the affine system. For affine systems, he developed a numerical and analytical method for constructing an equivalent system of canonical or quasi-canonical form. He proved the criteria of attainability and controllability for affine systems in the presence of states constraints, he proved the duality of controllability and observability properties in the case of affine systems, and obtained conditions for the separation principle for affine systems.
To stabilize software movements of nonlinear systems, he proposed methods of nonlinear stabilization and stabilization by finding virtual outputs in which the system is minimally phasic. He also suggested a method for constructing estimates of nonlinear systems stabilizability regions in the presence of control constraints.
He described the infinitesimal symmetries of affine systems and obtained conditions for their decomposition into subsystems.
Krishchenko A.P. proved the existence of the propagation property of solutions features of quasilinear partial differential equations and extended the concept of inverse dynamic problems in nonlinear systems with distributed parameters.
For nonlinear dynamical systems, Krischenko A.P. proposed a method for localizing the regions of periodic trajectories, domains with chaotic dynamics, and extended the method to construct estimates for all invariant compacts of nonlinear systems.
He proposed a method for suppressing chaotic dynamics of nonlinear systems trajectories with the help of arbitrarily small controls.
He proved the criteria for asymptotic stability and proposed a method for verifying them, covering a number of critical cases, for nonlinear systems, in particular for systems with chaotic dynamics, he identified the domains with trajectories' simple and complex behavior, and proposed a method for constructing Lyapunov functions.
Krishchenko A.P. developed methods for controlling the spatial motion of an aircraft without traction in the area of pre-landing maneuvering, and planning the trajectories of unmanned aerial vehicles.
Under his leadership, information modeling complexes have been created for mathematical simulation of the aircraft movement control.
He founded a scientific school "Nonlinear Dynamic Systems and Control Processes" and trained two Doctors of Sciences and nine Candidates of Sciences.
Krishchenko A.P. is a member of the editorial boards of the journals "Avtomatika i Telemekhanika" ("Automation and Telemechanics") and "Herald of the Bauman Moscow State Technical University. Series Natural Sciences"; the chairman of the Council for Mathematical Training at Bauman Moscow State Technical University. He is a member of the Expert Council of the Higher Attestation Commission, a member of RFBR (Russian Foundation for Basic Research) Scientific Council, a member of 2 dissertational councils, a member of the national committee of IFAC (International Federation for Automatic Control).
He is the author of 290 scientific works, including 2 monographs on management theory, 4 textbooks for universities, the editor of a series of textbooks "Mathematics in a Technical University."
Krishchenko A.P. is the prize-winner of the Government of the Russian Federation in the field of science and technology, he was awarded the medal "In memory of the 850th Moscow's anniversary" and the "Honored Worker of Higher Professional Education of the Russian Federation".
