REGULAR MATHEMATICAL MODELS FOR SYSTEMS WITH MANAGEMENT: INVARIANCE, SYMMETRIES

Mathematical models for systems of "input - output" type, in particular systems with management and disturbed systems, are investigated in the paper aiming at the introduction of the notion of regularity for mathematical differential models, the comparison of dynamic processes and theoretical-grouping and finite models. During the investigation the general theory of differential equations, theory of local groups and algebra of Lie, grouping analysis of differential equations, differential-geometrical view of an object have been used. As a result the original determination of regularity has been introduced. The problem of the finding of the first integrals and the construction of invariant functionals has been solved on the base of this determination. Finite and theoretical-grouping models for systems of "input - output" type have been introduced and investigatedAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio