Gorobtzov A.S., Ryzhov E.N.

The geometrical principals of synthesis of chemical excitation for auto-oscillation systems for medical cybernetics is presented. The principals are founded on the stability manifold theory of V.I. Zybov. Key value is allocated to synthesis of systems with invariant set in problems of regulated movements. Such sets partition phase space into domains in which localization of movements under condition of existence and uniqueness of the solution of initial-value problem takes place. In the present paper the following principles of analytical feedback control design are formulated on which algorithms of stable auto-oscillatory regime design are based: 1) synthesis of invariant ellipsoid in phase space; 2) support of synthesized ellipsoid stability; 3) an opportunity of regulation of the size of border of asymptotically stability domain by ellipsoid axes. The first principle leads to localization of the processes beginning on domain bounded by ellipsoid, according to theorems of invariant sets of dynamic systems, i.e. phase trajectories of system at initial data on these sets, cannot leave them at . The second principle provides an approach to the given regime. The third principle allows to regulate the amplitude of oscillations i.e. the size of domain of stability at the initial data inside the area with invariant ellipsoid as a border. In particular, sufficient conditions at which the problem of synthesis satisfies three analytical principles are formulated and proved. Properties of ellipsoid surface, conditions of its invariance and stability define the character of nonlinear friction as control in the form of vector- polynoms of the third degree synthesized in dynamic systems. The chemical excitation is described by the kinetics equations of the substance. The example of the numerical modeling processes stabilization of the oscillation in the neighborhood of orbital stable circle is investigated. Theorems of synthesis are received. Scheme of synthesis for problems of amplitude correction of oscillations by the chemical excitation is biosystems is presented. The time of transient processes fine is estimated numerically