Approximation of attainability domains of nonlinear discrete-time controlled dynamical systems

The article deals with the problem of constructing and approximating the attainability domains of a nonlinear discrete controlled dynamical system. The object of study is the class of controlled dynamical systems described by vector nonlinear recurrent equations. The initial nonlinear discrete-time model is transformed to a discrete linear form with respect to the reference phase trajectory. It is assumed that the phase vector of the system and the control parameter are constrained by convex, closed and bounded polyhedral sets with a finite number of vertices in the corresponding finite-dimensional vector spaces. We have given a description of the general recurrent algebraic method for constructing domains of attainability and its modification. In conclusion the article describes the results of computer simulation and comparative analysis of the attainability domains of approximation accuracy for specific nonlinear discretetime dynamical systems using the attainability domains of the corresponding linear discrete-time dynamical systems constructed with general and modified recurrent algebraic methods.