Reference model of adaptive control system for unstable and deterministic chaotic processes in the catastrophe class hyperbolic umbilica

A method is proposed for solving the problem of synthesis of a self-organizing adaptive control system for unstable and deterministic chaotic processes in the catastrophe class hyperbolic umbilic for objects with m-inputs and n-outputs. The problem of synthesizing a self-organizing adaptive control system is solved by the velocity- gradient method of the Lyapunov vector function. From the boundary conditions of the aperiodic robust stability of the main contour and the generalized adjustable object, adjustable coefficients are calculated and the control goal is achieved. 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. At the same time, a self-organizing reference model with the desired dynamics is constructed in the class of catastrophes – a hyperbolic umbilic of a self-organizing system. But the aperiodic robust stability of a self-organizing reference model is studied using the Lyapunov vector function method. Collection of information about an object during operation, processing and its use to develop control impacts can improve the quality of management.A method is proposed for solving the problem of synthesizing the adaptation loop of a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophes “hyperbolic umbilic”. From the conditions of aperiodic robust stability of a generalized adjustable object, adjustable coefficients are calculated and the control goal is achieved.