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On the existence of solutions in problems of optimization under vector- valued criteria. (English) Zbl 0258.49001


MSC:

49J99 Existence theories in calculus of variations and optimal control
49K99 Optimality conditions
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[1] Letov, A. M.,Some Nondecided Problems in Control Theory (in Russian), Differential Equations, Vol. 6, No. 4, 1970.
[2] Letov, A. M.,Optimal Control Theory, Paper Presented at the 2nd IFAC Congress, Basel, Switzerland. 1963. · Zbl 0123.06404
[3] Pareto, V.,Cours d’Economie Politique, Rouge, Lausanne, Switzerland, 1896.
[4] Zadeh, L. A.,Optimality and Non-Scalar-Valued Performance Criteria, IEEE Transactions on Automatic Control, Vol. AC-8, No. 1, 1963.
[5] Salukvadze, M. E.,Concerning Optimization of Vector Functionals. I. Programming of Optimal Trajectories (in Russian), Automatics and Telemechanics, No. 8, 1971. · Zbl 0236.49019
[6] Salukvadze, M. E.,Concerning Optimization of Vector Functionals. II. Analytic Design of Optimal Regulators (in Russian), Automatics and Telemechanics, No. 9, 1971. · Zbl 0236.49020
[7] Salukvadze, M. E.,On Optimization of Control Systems According to Vector-Valued Performance Criteria, Paper Presented at the 5th IFAC Congress, Paris, France, 1972.
[8] Salukvadze, M. E.,On a Linear Programming Problem with a Vector-Valued Control Criterion (in Russian), Automatics and Telemechanics, No. 5, 1972. · Zbl 0252.90039
[9] Salama, A. I. A., andGourishankar, V.,Optimal Control of Systems with a Single Control and Several Cost Functions, International Journal of Control, Vol. 14, No. 4, 1971. · Zbl 0226.49008
[10] Huang, S. C.,Note on the Mean-Square Strategy for Vector-Valued Objective Functions, Journal of Optimization Theory and Applications, Vol. 9, No. 5, 1972. · Zbl 0222.49004
[11] Letov, A. M.,Flight Dynamics and Control, Nauka, Moscow, USSR, 1969.
[12] Athans, M., andFalb, P. L.,Optimal Control, McGraw-Hill Book Company, New York, New York, 1966. · Zbl 0196.46303
[13] Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., andMischenko, E. F.,The Mathematical Theory of Optimal Processes, John Wiley and Sons (Interscience Publishers), New York, New York, 1962.
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