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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2014. Vol. 8

Projection Perturbation Methods in Optimization Problems of Controlled Systems

Author(s)
A. S. Buldaev
Abstract

Perturbation methods are used to implement the conditions of nonlocal improvement of controls, constructed in the form of special boundary value problems in space of phase and conjugate variables and in the form of special tasks of a fixed point of definite operator in the space of controls. Terms improvement of controls are determined by the operation of projection onto the set of admissible control values. Methods are characterized by a lack of operations of convex or needle variation of controls and principal possibility to improve suboptimal controls satisfying the maximum principle.

Keywords
controlled system, conditions of control improvement, projection operators, perturbation methods
UDC
518.517
References

1. Buldaev A.S. Perturbation Methods in Improvement and Optimization Problems for Controllable Systems(in Russian). Ulan-Ude, Buryat. Gos. Univ., 2008, 260 p.

2. Buldaev A.S., Morzhin O.V. Control Improvement in Nonlinear Systems Based on Boundary Problems(in Russian). Izv. Irkut. Gos. Univ., Mat., 2009, vol. 2, no. 1, pp. 94-107.

3. Buldaev A.S., Morzhin O.V. A Modification of the Projection Method for Improving Nonlinear Controls (in Russian). Vest. Buryat. Gos. Univ., Vypusk 9 «Mat., Informat.», 2010, pp. 10-17.

4. Buldaev A.S. A Boundary Improvement Problem for Linearly Controlled Processes. Automation and Remote Control, 2011, vol. 72, no. 6, pp. 1221-1228.

5. Buldaev A.S., Khishektueva I.-Kh.D. The Fixed Point Method in Parametric Optimization Problems for Systems. Automation and Remote Control, 2013, vol. 74, no. 12, pp. 1927-1934.

6. Buldaev A.S., Trunin D.O. Methods of perturbations in quadratic problems of optimal control. Automation and Remote Control, 2008, vol. 69, no. 3, pp. 472-482.

7. Buldaev A.S., Trunin D.O. Nonlocal improvement of controls in state-linear systems with terminal constraints, Automation and Remote Control, 2009, vol. 70, no. 5, pp. 743-749.

8. Srochko V.A. Iteration Methods for the Solution of Optimal Control Problems (in Russian). Moscow, Fizmatlit, 2000, 160 p.

9. Trunin D.O. An approach to the optimization of nonlinear control systems with terminal constraints (in Russian). Vest. Buryat. Gos. Univ. Mat., Informat., 2013, no. 1, pp. 15-20.


Full text (russian)