A.S. Gorobtzov, E.N. Ryzhov, A.S. Churzina
The modern theory of synthesis of movement on the closed trajectories, systems of stabilization of movement in a direction of complication of geometry both trajectories, and qualitative methods of their research actively develops.
Fluctuations of biological systems carry relaxation character. In this connection the problem of construction of mechanisms of supervision over fluctuations and their registration is one of the primary goals of biomedical technologies. By the nature these oscillations will be nonlinear. The mechanism of nonlinear supervision over oscillations is considered, the nonlinear observer is received in article.
The approach to construction of mechanisms of supervision is based on the theory of synthesis integrated asymptotically stable manifolds in spaces of conditions: Construction of function of Lyapunov leads to synthesis of the observer which registers stabilization of system in a vicinity of border of area, gomeomorfied to S2n-1.
Time of an output of the observer for a self-oscillatory mode corresponds to time of an establishment of self-oscillations in a vicinity of manifold of Lame. The received control functions - polynoms of an odd degree also allow to raise self-oscillatory modes that attracts localization of movements in the limited areas of space of the conditions caused by occurrence of stable limit cycles. For example, in a radio engineering control of geometry of limit cycles is the basic problem at the decision of an extensive class of problems. Results of numerical modeling of processes of stabilization in spaces of conditions of the observer and observable system accordingly also are presented in the article.