zbMATH — the first resource for mathematics

Numerical investigation of attainability sets of nonlinear controlled differential systems. (English. Russian original) Zbl 1229.65106
Autom. Remote Control 72, No. 6, 1291-1300 (2011); translation from Avtom. Telemekh. 2011, No. 6, 160-170 (2011).
Summary: The paper is devoted to schemes of approximation of attainability sets of nonlinear controlled differential systems where the problem of program control optimization is an “elementary operation.” The results of numerical experiments are represented.

65K10 Numerical optimization and variational techniques
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI
[1] Chernous’ko, F.L., Otsenivanie fazovogo sostoyaniya dinamicheskikh sistem. Metod ellipsoidov (Estimation of a Phase State of Dynamical Systems. The Ellipsoid Method), Moscow: Nauka, 1988.
[2] Kurzhanskiy, A.A. and Varaiya, P., Ellipsoidal Toolbox, at http://code.google.com/p/ellipsoids/ .
[3] Gurman, V.I., Printsip rasshireniya v zadachakh upravleniya (The Extension Principle in Control Problems), Moscow: Fizmatlit, 1997. · Zbl 0905.49001
[4] Kurzhanskii, A.B., Differential Equations in Problems of Control Synthesis, Differ. Uravn., 2005, vol. 41, no. 1, pp. 12–22. · Zbl 1113.93004
[5] Kurzhanskii, A.B., The Comparison Principle for Equations of Hamilton-Jacobi Type in Control Theory, Tr. IMM UrO Ross. Akad. Nauk, 2006, vol. 12, no. 1, pp. 173–183. · Zbl 1129.49035
[6] Gurman, B.I. and Trushkova, E.A., Estimates of Attainability Sets of Controlled Systems, Differ. Uravn., 2009, vol. 45, no. 11, pp. 1601–1609.
[7] Mitchell, I.M., A Toolbox of Level Set Methods, at http://www.cs.ubc.ca/ mitchell/ . · Zbl 1203.65295
[8] Gornov, A.Yu., Vychislitel’nye tekhnologii resheniya zadach optimal’nogo upravleniya (Computational Technologies for Solving Optimal Control Problems), Novosibirsk: Nauka, 2009.
[9] Chernous’ko, F.L. and Kolmanovskii, V.B., Computational and Approximate Methods of Optimal Control, Itogi Nauki Tekhn., Mat. Analiz, Moscow: VINITI, 1977, vol. 14, pp. 101–166.
[10] Tyatyushkin, A.I., Chislennye metody i programmnye sredstva optimizatsii upravlyaemykh sistem (Numerical Methods and Software for Optimization of Controlled Systems), Novosibirsk: Nauka, 1992. · Zbl 0764.49018
[11] Tyatyushkin, A.I. and Morzhin, O.V., Constructive Methods of Control Optimization in Nonlinear Systems, Autom. Remote Control, 2009, no. 5, pp. 772–786. · Zbl 1180.93037
[12] Tyatyushkin, A.I. and Morzhin, O.V., Optimization Methods and a Program System for Solving Applied Problems of Optimal Control, Sovrem. Tekhn. Sistem. Analiz. Modelirov., 2009, no. 3, pp. 78–82. · Zbl 1180.93037
[13] Morzhin, O.V. and Tyatushkin, A.I., Approximation of Attainability and Solvability Sets of Nonlinear Controlled Differential Systems, Mekhatron. Avtomatiz. Upravlen., 2010, no. 2, pp. 16–23.
[14] Morzhin, O.V. and Tyatyushkin, A.I., An Algorithm of the Min-Cut Method and Software for Constucting Attainability Sets, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2008, no. 1, pp. 5–11.
[15] Morzhin, O.V. and Tyatyushkin, A.I., One Model Problem of Positional Control Optimization in an Attainability Tube, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2010, no. 5, pp. 60–69. · Zbl 1269.49052
[16] Morzhin, O.V., Nonlocal Improvement of Nonlinear Controlled Processes on the Basis of Sufficient Optimality Conditions, Autom. Remote Control, 2010, no. 8, pp. 1526–1539. · Zbl 1218.49033
[17] Gabasov, R. and Kirillova, F.M., Osobye optimal’nye upravleniya (Special Optimal Controls), Moscow: Nauka, 1973. · Zbl 0279.49003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.