Abstract
In the paper, we study a problem of minimization of degenerate integral quadratic functional of special delayed structure (a subintegral function contains items concentrated at the moment and items with delay in phase coordinates) on trajectories of a linear system of differential equations with time delay in phase coordinates considered on a finite period of time. Sufficient conditions for the existence of optimal program control in space of generalized functions of the lth order of singularity are established and an optimal control is obtained. A special feature of the problem is that the optimal program contains pulse components concentrated at the ends of the control gap.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Gurman, V.I., Printsip rasshireniya v zadachakh upravleniya (The Extension Principle in Problems of Control), Moscow: Nauka, 1985.
Zavalishchin, S.T. and Sesekin, A.N., Special Solutions in Problems of Optimization of Dynamic Systems with Quadratic Criterion of quality, Diff. Uravn., 1975, no. 4, pp. 665–671.
Zavalishchin, S.T., Sesekin, A.N., and Drozdenko, S.E., Dinamicheskie sistemy s impul’snoi strukturoi (Dynamic Systems Pulse Structure), Sverdlovsk: Sredne-Ural’skoe Knizh. Izd., 1983.
Sesekin, A.N. and Fetisova, Yu.V., Degenerate Linear-Quadratic Optimization Problem for Systems with Time Delay, Trudy IX Mezhdunarodnoi Chetaevskoi konferentsii “Analiticheskaya mekhanika, ustoichivost’ i upravlenie dvizheniem,” posvyashchennoi 105-letiyu N.G. Chetaeva (Proc. IX Int. Chetaev Conf. “Analytical Mechanics, Stability, and Motion Control” Devoted to the 105th Annivers. of N.G. Chetaev), Irkutsk, 2007, vol. 3, pp. 197–205.
Fetisova, J.V. and Sesekin, A.N., Singular Linear—Quadratic Problem for Distributed Delay Systems, Proc. 3 Int. IEEE Sci. Conf. Physics and Control (PhysCon2007), http://lib.physcon.ru/?item=1192.
Sesekin, A.N., On the Singularity Order of Optimal Controls in Linear-Quadratic Optimization Problems for Systems with Time Delay, Funct. Diff. Equat., 1998, vol. 5, no. 3, pp. 243–251.
Kolmanovskii, V.B. and Maizenberg, T.L., Optimal Estimates of System State and Some Problems of Control of Equations with Time Delay, Prikl. Mat. Mekh., 1977, vol. 41, no. 3, pp. 446–456.
Yanushevsky, R.T., Upravlenie ob”ektami s zapazdyvaniem (Control of Delayed Objects), Moscow: Nauka, 1978.
Vladimirov, V.S., Obobshchennye funktsii v matematicheskoi fizike (Generalized Functions in Mathematical Physics), Moscow: Nauka, 1976.
Author information
Authors and Affiliations
Additional information
Original Russian Text © A.N. Sesekin, Yu.V. Fetisova, 2009, published in Avtomatika i Telemekhanika, 2009, No. 4, pp. 31–40.
This work was supported by the Russian Foundation for Basic Research, project no. 06-01-00445.
Rights and permissions
About this article
Cite this article
Sesekin, A.N., Fetisova, Y.V. The order of singularity of pulse optimal controls in degenerate linear-quadratic optimization problems with time delay. Autom Remote Control 70, 589–597 (2009). https://doi.org/10.1134/S0005117909040055
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117909040055