Speciality:
01.01.11 (System analisys)
Birth date:
26.02.1949
E-mail: ,
Keywords: dynamical systems; integral manifolds; singular perturbations; dynamics of multibody and gyroscopic systems; mathematical modelling; automatic control; chemical kinetics.
Subject:
Theorems on existence and properties of weakly attractive slow integral mamifolds were proved and, as consequence, the known problem on mathematical justification of the precession theory of gyroscopic systems was solved and some paradoxes of this theory were explained. A notion of a fast integral manifold was proposed and the possibility to reduce singularly perturbed systems to a block triagular form was stated. This permits to develop a new method of decomposition of control systems this slow and fast variables and to apply this method to solution of some control theory problems. Such approach was developed on continuous and discrete systems with several time scales (with N. V. Voropaeva), stochastic systems (with E. Ya. Gorelova), periodic control systems (with E. N. Zharikova), time delay systems (with E. Fridman), distributed parameter systems (with S. V. Ozerskii). The slow integral manifolds theory was extended to systems in the events that the usual conditions of known Tikhonov theorem are violated. The slow integral manifolds branching problems were studied with K. Schneider. A new approach to investigation of so called canard-trajectories, which is based on an idea of glueing of attractive and reppelent slow integral manifolds, was proposed. A notion of black swan (multidimensional analogy of a canard) was proposed and theorem on existence and properties of such integral surface were stated (with E. A. Shchepakina). Jointly with G. N. Gorelov a canard-trajectory was found at first in parabolic systems and used to solve the chemical kinetics problems (critical condition of thermal explosion in the case of autocatalytic combustion were obtained). Jointly with V. M. Gol'dshtein a detailed algorithm of chemical kinetics systems, based on a combined using of integral manifolds method and Mishchenko–Rozov asymptotic formulae, was worked out. Two monographs and number of papers (with V. I. Babushok, V. M. Gol'dshtein, G. N. Gorelov, A. Ziniviev, E. A. Shchepakina, G. S. Yablonslii et al) are devoted to investigation of chemical kinetics problems. Jointly with K. Scneider and E. A. Shchepakina a new type of combustion travelling waves is described (canard travelling wave). Jointly with V. V. Strygin some problems of dynamics and stability of rigid bodies systems and satellites were solved.
Main publications:
Mortell M.P., O'Malley R.E., Pokrovskii A., Sobolev V. Singular perturbations and hysteresis. SIAM, 2005.
Shchepakina E., Sobolev V., Mortell M.P. Singular perturbations: Introduction to system order reduction methods with applications. Springer, 2014.
