A multiple control system for a non-linear object with uncertainty

We propose an algebraic approach to constructing a multiple control system for nonlinear multidimensional objects with chaotic regimes. The purpose of control is to output an object to an analytically prescribed stable state. Two variants of the continuous and discrete description of control objects are considered. The controlled objects are presented as a system of ordinary non-linear differential or difference equations with chaotic behavior in the case of certain combinations of parameters. Part of the objects description may be unknown. The suggested control algorithm is realized on the basis of methods of nonlinear control on manifolds, Lyapunov functions and the algebraic approach to the synthesis of correct algorithms. Two applied problems of economic orientation with continuous and discrete models of description are considered. Numerical modeling was carried out on real data of small enterprises. The results of the paper are expected to be used in the system of economic decision-making support.