BSU bulletin
Mathematics, Informatics
LoginРУСENG

BSU bulletin. Mathematics, Informatics

Bibliographic description:
Shorikov A. F.
,
Bulaev V. V.
,
Goranov A. Y.
,
Kalev V. I.
APPROXIMATION OF ATTAINABILITY DOMAINS OF NONLINEAR DISCRETE-TIME CONTROLLED DYNAMICAL SYSTEMS // BSU bulletin. Mathematics, Informatics. - 2018. №1. . - С. 52-65.
Title:
APPROXIMATION OF ATTAINABILITY DOMAINS OF NONLINEAR DISCRETE-TIME CONTROLLED DYNAMICAL SYSTEMS
Financing:
Работа выполнена при финансовой поддержке РФФИ (проект № 17-01-00315; проект № 18-01-00544)
Codes:
DOI: 10.18101/2304-5728-2018-1-52-65UDK: 519.83; 519.6
Annotation:
The article deals with the problem of constructing and approximating the at- tainability 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 trajec- tory. 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 con- structing 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 discrete- time dynamical systems using the attainability domains of the corresponding linear discrete-time dynamical systems constructed with general and modified recurrent algebraic methods.
Keywords:
nonlinear discrete-time controlled dynamical system; approxi- mation of attainability domains; convex polyhedra; linear mathematical pro- gramming; simplex method.
List of references:
Krasovskii N. N. Teoriya upravleniya dvizheniem [Theory of Motion Control]. Moscow: Nauka Publ., 1968. 476 p.

Shorikov A. F. Minimaksnoe otsenivanie i upravlenie v diskretnykh di- namicheskikh sistemakh [Minimax Estimation and Control in Discrete Dy- namical Systems]. Ekaterinburg: Ural University Publ., 1997. 242 p.

Tyulyukin V. A., Shorikov A. F. Ob odnom algoritme postroeniya oblasti dostizhimosti lineinoi upravlyaemoi sistemy [About One Algorithm for Constructing the Attainability Domain of a Linear Controlled System]. Neglad- kie zadachi optimizatsii i upravlenie — Nonsmooth Optimization Problems and Control. Sverdlovsk: Ural Branch of USSR AS. 1988. Pp. 55–61.

Tyulyukin V. A., Shorikov A. F. Algoritm resheniya zadachi ter- minal'nogo upravleniya dlya lineinoi diskretnoi sistemy [Algorithm for Solving the Problem of Terminal Control for a Linear Discrete System]. Avtomatika i telemekhanika — Automation and Telemechanics. 1993. No. 4. Pp. 115–127.

Shorikov A. F., Goranov A. Yu. Metodika approksimatsii oblasti dostizhimosti nelineinoi upravlyaemoi dinamicheskoi sistemy [A Method for Approximating the Attainability Domain of a Nonlinear Controlled Dynamical System]. Prikladnaya matematika i voprosy upravleniya — Applied Mathemat- ics and Control Problems. 2017. No. 2. Pp. 112–121.

Bulaev V. V. Ob ispol'zovanii simpleks-metoda dlya approksi-matsii vypuklykh mnogogrannikov [About Use of Simplex Method for Approximating Convex Polyhedra]. Proc. 2nd Scientific and Technical Conference of Young Scientists of Ural Energy Institute. Ekaterinburg: Ural Federal University Publ., 2017. Pp. 397–399.

Chernikov S. N. Lineinye neravenstva [Linear Inequalities]. Moscow: Nauka Publ., 1968. 488 p.

Yudin D. B., Gol'shtein E. G. Zadachi i metody lineinogo pro- grammirovaniya [Problems and Methods of Linear Programming]. Moscow: Sovetskoe radio Publ., 1964. 736 p.