COMPUTER SIMULATION OF THE SOLUTION OF THE PROBLEM OF PREDICTION AND MINIMAX ESTIMATION OF STATES OF A DISCRETE-TIME DYNAMICAL SYSTEM
The authors of the article consider the problem of predicting and estimating the state of a controlled dynamical object within the framework of a deterministic minimax approach. The dynamics of an object is described by a linear discrete-time controlled dynamical system in the presence of a phase constraint described in each time period by a corresponding joint system of linear algebraic equalities and inequalities. It is assumed that the values of the control action in each time period are constrained by the given polyhedra-compacts in the corresponding finite-dimensional vector space. The quality of the set of predicted phase states of the model of the object under consideration in a given time period, i.e. its predictive set (reachability set), is estimated using the corresponding minimax indicators - the Chebyshev center and the value of the Chebyshev radius of this set. Within the framework of the formed mathematical model, the formalization of the problem of predicting and guaranteed (minimax) estimation of the phase states of the object model under consideration in a given time period is presented. To solve the formulated problem, a technique is proposed for the formation and minimax estimation of a predictive set of phase states of an object model in a given time period, which is implemented as a finite sequence of solutions of only one-step operations that allow their algorithmization. Based on the proposed methodology, an appropriate numerical algorithm was developed and a software package was described that implements computer simulation of the solution of the problem under consideration.