ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Ordinary Differential Equations and Control Systems – Comparative Group Analysis


G. N. Yakovenko

Depatment of Theoretical Mechanics,
Moskow Institute of Physics & Technology,
Institutsky str., 9,
Moskow Region,


The system of the ordinary differential equations derives one-parametrical group of shifts along the decisions and admits set of transformations of symmetry, which is not put in finiteparametric group. Control system has, as a rule, inverse picture: the set of transformations of shifts along the decisions has functional power, and unique transformation of symmetry is identical. The class of group systems is discussed, for which despite of functional power of the decisions, transformations of shifts belong finiteparametric group. The subclass of group systems – L-systems is discussed also. L-system admits group of transformations the quantity of parameters at which coincides with dimension of state space. The work is executed at finacial support of the Russian Foundations for Basic Researches (code of the project 02–01–00697) and of the Programs Coucil of support of Leading Scientific Schools (grant 00–15–96137).

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