An extension of Ascoli's theorem and its applications to the theory of optimal control

Author:
S. S. L. Chang

Journal:
Trans. Amer. Math. Soc. **115** (1965), 445-470

MSC:
Primary 93.40

DOI:
https://doi.org/10.1090/S0002-9947-1965-0195612-0

MathSciNet review:
0195612

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References | Similar Articles | Additional Information

**[1]**R. V. Gamkrelidze,*Optimal control processes with restricted phase coordinates*, Izv. Akad. Nauk SSSR Ser. Mat.**24**(1960), 315-356. Translated by L. W. Neustadt, Space Technology Laboratories Report, March, 1961. MR**0120438 (22:11192)****[2]**S. S. L. Chang,*Minimal time control with multiple saturation limits*, IEEE Trans. Automatic Control**AC-8**(1963), 35-42.**[3]**V. G. Boltjanskiĭ, R. V. Gamkrelidze, and L. S. Pontryagin,*The theory of optimal**processes*. I.*Maximum principle*, Izv. Akad. Nauk SSSR Ser. Mat.**24**(1960), no. 1. Translated by L. W. Neustadt, Space Technology Laboratories, Report No. 9810. 32-01, October, 1960. MR**0120437 (22:11191)****[4]**R. V. Gamkrelidze,*The theory of time optimal process in linear systems*, Izv. Akad. Nauk SSSR**2**(1958), 449-474. Translated by members of the staffs of the University of California and Space Technology Laboratories, January, 1961. MR**0097571 (20:4039)****[5]**E. B. Lee and L. Markus,*On the existence of optimal controls*, Preprint ASME-61-JAC-2, Amer. Soc. Mechanical Engineers, Chicago, Ill., MR**0133564 (24:A3395)****[6]**L. M. Graves,*The theory of functions of real variables*, McGraw-Hill, New York, 1956; Theorem 23, p. 66. MR**0075256 (17:717f)****[7]**M. E. Munroe,*Introduction to measure and integration*, Addison-Wesley, Reading, Mass., 1959, p. 225. MR**0053186 (14:734a)****[8]**-,*Introduction to measure and integration*, Addison-Wesley, Reading, Mass., 1959; p. 222.**[9]**L. M. Graves,*The theory of functions of real variables*, McGraw-Hill, New York, 1956; Theorem 2, p. 100 and Theorem 25, p. 121. MR**0075256 (17:717f)****[10]**-,*The theory of functions of real variables*, McGraw-Hill, New York, 1956; Theorem 23, p. 66. MR**0075256 (17:717f)**

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DOI:
https://doi.org/10.1090/S0002-9947-1965-0195612-0

Article copyright:
© Copyright 1965
American Mathematical Society