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Optimal control with a functional averaged along the trajectory. (English. Russian original) Zbl 0614.49015
J. Appl. Math. Mech. 49, 404-413 (1985); translation from Prikl. Mat. Mekh. 49, 524-535 (1985).
Consider a control problem in which the differential equation relating the state and control functions, as well as the integrand in the performance criterion, are not explicitely time-dependent. A set of infinite optimal trajectories (IOT) is defined. It is shown that in an arbitrary fixed-time interval any optimal trajectory can be uniformly approximated to some IOT with a desired accuracy, provided that the control time is fairly large.
Reviewer: J.Rubio

MSC:
49K15 Optimality conditions for problems involving ordinary differential equations
34H05 Control problems involving ordinary differential equations
49M05 Numerical methods based on necessary conditions
93C15 Control/observation systems governed by ordinary differential equations
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References:
[1] Panasyuk, A.I.; Panasyuk, V.I., On the asymptotic form of the trajectories of a class of problems of optimization, Avtomatika i telemekhanika, No.8, (1975) · Zbl 0613.49003
[2] Panasyuk, A.I.; Panasyuk, V.I., The asymptotic optimization of non-linear control systems, (1977), Izd. Belorusskogo Univ Minsk · Zbl 0362.49005
[3] Panasyuk, A.I.; Panasyuk, V.I., On the behaviour of infinite optimal trajectories of a class of continuous dynamic systems, Differents. uravneniya, 6, (1982) · Zbl 0613.49003
[4] Panasjuk, A.; Panasjuk, V., Die wichtigsten leitsätze der magiatralen asymptotischen theorie der optimalen steuerung, (), 5, Ilmenau
[5] Romanovskii, I.V., Algorithms for solving extremal problems, (1977), Nauka Moscow
[6] Gusev, D.E.; Yakubovich, V.A., The main line theorem in the problem of continuous optimization, Vestn. LGU. ser. matem., mekhan., astron., 1, (1983) · Zbl 0524.49029
[7] Dukel’skii, M.S.; Tsirlin, A.M., Conditions of unsteadiness of the optimal steady mode of a controlled object, Avtomatika i telemekhanika, 9, (1977)
[8] Chernous’ko, F.L.; Akulenko, L.D.; Sokolov, B.N., Control of oscillations, (1980), Nauka Moscow · Zbl 0574.49001
[9] Anisovich, V.V.; Kryukov, B.I., On the optimization of almost-periodic oscillations, Avtomatika i telemekhanika, 12, (1981) · Zbl 0512.65045
[10] Vasil’eva, A.B.; Dimitriev, M.G., Singular perturbations in problems of optimal control, () · Zbl 0542.49014
[11] Plotnikov, V.A., The asymptotic investigation of equations of controlled motion, () · Zbl 0591.49026
[12] Panasyuk, V.I., The problems of main trajectories in discrete problems of optimal control, Avtomatika i telemekhanika, 8, (1981) · Zbl 0489.93036
[13] Panasyuk, V.I., Main periodic trajectories in discrete problems of optimal control, Avtomatika i telemekhanika, 9, (1983) · Zbl 0562.93055
[14] Fleming, W.; Rischel, R., Optimal control of determinate and stochastic systems, (1978), Mir Moscow
[15] Kelly, J.L., General topology, (1981), Nauka Moscow
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