Adaptive control of bifurcation modes in nonautonomous nonlinear systems

A new statement of the problem of adaptive control aimed at stabilizing the desired properties of bifurcation modes of nonlinear nonautonomous systems is put forward. An algorithm of control over measurements of the output is worked out for the class of Lurie systems, which affords the convergence of adjustable parameters to objective unknown values ensuring the desired properties of bifurcation modes of a system. The solution rests on the use of the theory of passive systems and adaptive observers. Examples of the analytical calculation and computational modeling are given, which illustrate the effectiveness and capacity of the obtained solution: a neuron integrator, excitation of a resonance mode for a pendulum, and an oscillatory system of the third order.