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Optimal control of lumped sources in distributed-parameter systems on classes of impulse and Heaviside functions. (English. Russian original) Zbl 1288.49014

Cybern. Syst. Anal. 48, No. 5, 798-806 (2012); translation from Kibern. Sist. Anal. 2012, No. 5, 179-188 (2012).
Summary: Optimal control problems for distributed-parameter systems are considered. The controls are lumped sources and the control functions belong to such classes as impulse and Heaviside functions. Optimization problems for both the intensity and duration of impulse and Heaviside controls and the arrangement of lumped sources are solved. Analytical formulas for the gradient of the functional of the problems are obtained. They allow using numerical first-order optimization methods to solve the problems.

MSC:

49N25 Impulsive optimal control problems
34A37 Ordinary differential equations with impulses
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[1] A. G. Butkovskii and L. M. Pustyl’nikov, Theory of Mobile Control of Distributed-Parameter Systems [in Russian], Nauka, Moscow (1980).
[2] V. A. Dykhta, ”Optimization of dynamic systems with discontinuous paths and impulse controls,” Soros Educational Journal, No. 8, 110–115 (1999). · Zbl 0933.49022
[3] B. M. Miller, ”Optimality conditions in problems of generalized control. I. Necessary optimality conditions. II. Sufficient optimality conditions,” Avtom. Telemekh., No. 3, 50–58 (1992); No. 4, 39–48 (1992). · Zbl 0789.49014
[4] B. M. Miller and E. Ya. Rubinovich, Optimization of Dynamic Systems with Pulse Controls [in Russian], Nauka, Moscow (2005).
[5] G. A. Kolokol’nikova, ”Necessary second-order optimality conditions for special and impulse conditions,” Avtom. Telemekh., No. 6, 48–57 (1990).
[6] K. R. Aida-Zade and E. R. Ashrafova, ”Control of lumped-parameter systems on special classes of control functions,” Avtom. Vych. Tekhnika, No. 3, 47–56 (2009).
[7] K. R. Aida-Zade and A. B. Ragimov, ”Solving optimal-control problems on the class of piecewise constant functions,” Avtom. Vych. Tekhnika, No. 1, 27–36 (2007).
[8] K. R. Aida-Zade and A. G. Bagirov, On oil well spacing and control of their debits,” Avtom. Telemekh., No. 1, 52–61 (2006). · Zbl 1126.49326
[9] Yu. G. Evtushenko, Methods to Solve Extremum Problems and their Application in Optimization Systems [in Russian], Nauka, Moscow (1982).
[10] A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1966). · Zbl 0044.09302
[11] J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York (1971).
[12] F. P. Vasil’ev, Methods to Solve Extremum Problems [in Russian], Nauka, Moscow (1981).
[13] G. M. Fikhtengol’ts, A Course in Differential and Integral Calculus [in Russian], Vol. 2, Nauka, Moscow (1970).
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