Abstract
The paper proposes a method for solving the problem of synthesis of an adaptive control system for unstable and deterministic chaotic processes in the class of ‘dovetail’ catastrophes for objects with m-inputs and n-outputs. The synthesis problem is solved by the gradient-velocity method of Lyapunov vector functions. From the conditions of the aperiodic robust stability of the etalon model with the desired dynamics of the main control loop and the generalised configurable object, the control goal is achieved. One of the most promising ways of solving the problem of managing unstable and deterministic chaotic processes is the synthesis of a control system in the class of ‘swallowtail’ catastrophes and the use of adaptation methods. Selecting and studying a reference model, and employing the gradient-velocity method for a generalised configurable control object ensure robust stability, utilise current information effectively, and achieve desired system quality and management goals.