Top

Journal of Dynamical and Control Systems

Published in:

07-11-2019

Time Optimality for Systems with Multidimensional Control and Vector Moment Min-Problem

Author: V. I. Korobov

Published in: Journal of Dynamical and Control Systems | Issue 3/2020

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The linear time-optimal problem for some classes of linear systems with a multidimensional control is considered. The general position condition, which guarantees the uniqueness of the optimal control, is not assumed to be satisfied. We introduce a vector moment min-problem, which is a further development of the moment min-problem proposed by V.I. Korobov and G.M. Sklyar in 1987 for solving linear time-optimal problems with a one-dimensional control. In the paper the case of the time-optimal problem for linear systems with two-dimensional control is thoroughly studied by use of the vector moment min-problem.

previous article Global Existence, Extinction, and Non-Extinction of Solutions to a Fast Diffusion p-Laplace Evolution Equation with Singular Potential

next article Integrable Weak Saddles for Trigonometric Liénard Systems

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Pontryagin L S, Boltyanskii V G, Gamkrelidze R V, Mishchenko E F. 1962. The mathematical theory of optimal processes. Moskva Nauka 1961, Engl. transl.: Interscience Publishers John Wiley & Sons, Inc., New York-London.

Feldbaum A A. Basis of optimal automatic systems theory (Russian). Nauka: Moskva; 1966.

Gamkrelidze R V. On the theory of optimal processes in linear systems (Russian). Dokl Akad Nauk SSSR (N.S.) 1957;116:9–11.MathSciNetMATH

Gamkrelidze R V. Theory of processes in linear systems which are optimal with respect to rapidity of action (Russian). Izv Akad Nauk SSSR Ser Mat 1958;22(4):449–474.MathSciNet

Gamkrelidze R V, Vol. 7. Principles of optimal control theory (Russian). Izd-vo Tbilisskogo un-ta, Tbilisi (1977); Engl transl.: Mathematical Concepts and Methods in Science and Engineering. New York: Plenum Press; 1978.

Tchebichef P. Sur les valeurs limites des integrales. Journal de mathematiques pures et appliquees 2e serie 1874;19:157–160.MATH

Krein M G, Nudel’man A A. 1977. The Markov moment problem and extremal problems. Ideas and problems of P.L. Čebyšev and A.A. Markov and their further development. Moskva, Nauka (1973); Engl. transl.: Translations of Mathematical Monographs, 50, AMS, Providence R. I.

Karlin S, Stadden W. 1966. Tchebycheff systems: With applications in analysis and statistics. New York: Interscience Publishers John Wiley & Sons, v Pure and Applied Mathematics XV. Wiley.

Korobov V I, Sklyar G M. 1991. The Markov moment min-problem and time optimality (Russian) Sibirsk. Mat. Zh., 32, 60–71 (1991); Engl. transl, in: Siberian Math. J., 32, 46–55.

10.

Korobov V I, Sklyar G M. 1990. The Markov moment problem on a minimally possible segment (Russian), Dokl. Akad. Nauk SSSR, 308, 525–528 (1989); Engl. transl, in: Soviet Math. Dokl., 40, 334–337.

11.

Korobov V I, Sklyar G M. 1989. Time-optimality and the power moment problem (Russian), Mat. Sb. (N.S.), 134(176), 186–206 (1987); Engl. transl. in: Math. USSR-Sb., 62, 185–206.

12.

Korobov V I, Sklyar G M. 1990. Time-optimality and the trigonometric moment problem (Russian), Izv. Akad. Nauk SSSR Ser. Mat., 53, 868–885 (1989); Engl. transl. in: Math. USSR-Izv., 35, 203–220.

13.

Korobov V I, Sklyar G M. 1988. Exact solution of an n-dimensional time-optimality problem (Russian), Dokl. Akad. Nauk SSSR, 298, 1304–1308 (1988); Engl. transl. in: Soviet Math. Dokl., 37, 247–250.

14.

Korobov V I, Sklyar G M. Markov power min-problem with periodic gaps. J Math Sci 1996;80(1):1559–1581.MathSciNetCrossRef

15.

Korobov V I, Sklyar G M. 1992. The generating function method in the problem of moments with periodic gaps (Russian), Dokl. Akad. Nauk SSSR, 318(1), 32–35 (1991); Engl. transl. in: Soviet Math. Dokl., 43(3), 657–660.

16.

Korobov V I, Bugaevskaya A N. The solution of time-optimal problem on the basis of the Markov moment min-problem with even gaps. Mat Fiz Anal Geom 2003;10: 505–523.MathSciNetMATH

17.

Korobov V I, Bugaevskaya A N. Almost power sum systems. Math Comp 2016; 85:717–736.MathSciNetCrossRef

18.

Krein M G. 1962. L-moment problem in the abstract linear normed space, in N.I. Akhiezer, M.G. Krein, Some questions in the theory of moments (Russian), Kharkov, Nauchno-Tekhnich. Izdat. Ukrainy, 1938; Engl. transl. in: Translations of Mathematical Monographs 2. AMS, Providence, R.I.

19.

Krasovsky N N. Theory of control of motion (Russian). Nauka: Moskva; 1968.

20.

Butkovsky A G. Methods of controlling the distributed parameter systems (Russian). Nauka: Moskva; 1975.

21.

Boltyansky V G. Mathematical methods of optimal control (Russian). Nauka: Moskva; 1969.

22.

Korobov V I, Sklyar G M, Florinskii V V. A polynomial of minimal degree for determining all switching moments in a time optimal problem (Russian). Mat Fiz Anal Geom 2000;7(3):308–320.MathSciNetMATH

23.

Korobov V I, Sklyar G M, Florinskii V V. 2002. A minimal polynomial for finding the switching times and the support vector to the controllability domain (Russian), Differ. Uravn., 38(1), 16–19 (2002); Engl. transl. in: Differ. Equ., 38(1), 15–18.

24.

Korobov V I, Sklyar G M, Ignatovich SYU. Solving of the polynomial systems arising in the linear time-optimal control problem. Commun Math Anal conference, Conf 2011;3:153–171.MathSciNetMATH

25.

Luenberger D. Canonical forms for linear multivariable systems. IEEE Trans Autom Cont 1967;12(3):290–293.MathSciNetCrossRef

Title: Time Optimality for Systems with Multidimensional Control and Vector Moment Min-Problem
Author: V. I. Korobov
Publication date: 07-11-2019
Publisher: Springer US
Published in: Journal of Dynamical and Control Systems / Issue 3/2020
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-019-09465-2

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 3/2020

Standing Waves for Nonautonomous Klein-Gordon-Maxwell Systems

On Foliations by Curves with Singularities of Positive Dimension

Periodic Trajectory Tracking for Control-Affine Driftless Systems on Compact Lie Groups

Integrable Weak Saddles for Trigonometric Liénard Systems

Global Existence, Extinction, and Non-Extinction of Solutions to a Fast Diffusion p-Laplace Evolution Equation with Singular Potential

Existence and Uniqueness Results for Quasilinear Parabolic Systems in Orlicz Spaces

Premium Partners