BSU Bulletin. Mathematics, Informatics
Bibliographic description:
ON A CERTAIN PROCEDURE OF NON-LOCAL IMPROVEMENT OF CONTROLS IN QUADRIC-IN-STATE SYSTEMS WITH TERMINAL RESTRICTIONS // BSU Bulletin. Mathematics, Informatics. - 2018. №2. . - С. 42-49.
Title:
ON A CERTAIN PROCEDURE OF NON-LOCAL IMPROVEMENT OF CONTROLS IN QUADRIC-IN-STATE SYSTEMS WITH TERMINAL RESTRICTIONS
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In the article we propose an approach to nonlocal improvement of controls in the class of quadratic-in-state and linear problems of optimal control with a partially fixed right end based on the solution of a system of functional equations in the space of controls that determines the conditions for nonlocal management im- provement. To solve the system under consideration we use an iterative process, and the scalar equation is solved at each iteration. The procedure ensures the im- provement of permissible control without variation and with preservation of all terminal constraints and is used for solving a constrained problem using an itera- tive. Comparative efficiency of the method is illustrated on the model problem.
Keywords:
optimal control problem; terminal constraints; conditions for improving control; iterative process.
List of references:
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Buldaev A. S. Metody vozmushchenii v zadachakh uluchsheniya i optimizatsii upravlyaemykh sistem [Perturbation Methods in Problems of Improving and Optimiz- ing Controlled Systems]. Ulan-Ude: Buryat State University Publ., 2008. 260 p.
Vasil'ev O. V. Lektsii po metodam optimizatsii [Lectures on Optimization Meth- ods]. Irkutsk: Irkutsk State University Publ., 1994. 340 p.
Marchuk G. I. Matematicheskie modeli v immunologii. Vychislitel'nye metody i algoritmy [Mathematical Models in Immunology. Computational Methods and Algo- rithms]. Moscow: Nauka Publ., 1991. 304 p.
Samarskii A. A., Gulin A. V. Chislennye metody [Numerical Methods]. Mos- cow: Nauka Publ., Moscow: Nauka Publ., 1989. 432 p.
Trunin D. O. Ob odnom podkhode k nelokal'nomu uluchsheniyu upravlenii v kvadratichnykh po sostoyaniyu sistemakh s terminal'nymi ogranicheniyami [On a Cer- tain Approach to Nonlocal Improvement of Controls in Quadric-in-State Systems with Terminal Constraints]. Vestnik Buryatskogo gosudarstvennogo universiteta. Mate- matika, informatika — Bulletin of Buryat State University. Mathematics, Computer Science. 2017. No. 2. Pp. 40–45. DOI: 10.18101/2304-5728-2017-2-40-45.
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