Abstract
This paper proposes a method for solving the problem of synthesizing the adaptation loop of a selforganizing control system for unstable and deterministic chaotic processes within the class of hyperbolic umbilic catastrophes for objects with m inputs and n outputs. The synthesis problem of the adaptation loop is solved using a gradient–velocity method based on vector Lyapunov functions. Considering the reference model and the main loop of the “generalized adjustable loop” of the adaptive control system as gradient systems, and Lyapunov functions as potential functions from catastrophe theory, makes it possible to propose a universal approach to constructing Lyapunov functions.