Abstract
The research of the last century revealed a wide variety of dynamics of nonlinear systems and led to one of the most important discoveries of the twentieth century in nonlinear dynamical systems – deterministic chaos and a strange attractor. An urgent problem in the conditions of uncertainty of the parameters of the control object and external influences, for the management of unstable and deterministic chaotic processes is the use of adaptation methods. At the same time, the reference model with the desired dynamics and the main control loop of the adaptive system are constructed in the class of «Dovetail» catastrophes, and the aperiodic robust stability of the reference model with the desired dynamics and the main control loop of the adaptive system with an increased potential for robust stability is investigated by the gradient-velocity method of the Lyapunov vector functions. From the conditions of aperiodic robust stability of a generalized tunable object, the tunable coefficients are calculated and the control goal is achieved. The solution of the problem of synthesis of the main contour of the adaptive control system of unstable and deterministic chaotic processes with m – inputs and n – outputs in the class of «Dovetail» catastrophes is proposed