Synthesis of the Control System for a Second Order Non-Linear Object with an Incomplete Description

Abstract

We consider the control problem for a poorly formalizable object (in terms of L.A. Rastrigin) defined as a system of ordinary second-order differential (difference) equations with a nonlinear right-hand side in a general form. We analyze the conditions for the application of the method of nonlinear adaptation on manifolds as generalizations of the algorithm of analytic design of aggregated regulators for such an object under perturbations along a controlled coordinate with an unknown description. We consider examples of the use of thus algorithm for different cases of analytic descriptions of the target manifold.