An urgent problem in the conditions of uncertainty of the parameters of the control object and external influences, for the control of unstable and deterministic chaotic processes, is the use of adaptation methods. In this case, the reference model with the desired dynamics and the main control loop of the adaptive system are constructed in the catastrophe class “hyperbolic umbilic”, and the aperiodic robust stability of the reference model with the desired dynamics and the main control loop of the self-organizing adaptive system with an increased potential for robust stability is studied by the gradient-velocity method of the vector function Lyapunov.