[1] |
Bliss, G. A.,Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Illinois, 1946. · Zbl 0063.00459 |
[2] |
Breakwell, J. V., andHo, Y. C.,On the Conjugate Point Condition for the Control Problem, International Journal of Engineering Science, Vol. 2, pp. 565-579, 1965. · Zbl 0136.10005 · doi:10.1016/0020-7225(65)90037-6 |
[3] |
Bryson, A. E., andHo, Y. C.,Applied Optimal Control, Blaisdell, Waltham, Massachusetts, 1969. |
[4] |
Wood, L. J., andBryson, A. E.,Second-Order Optimality Conditions for Variable End-Time Terminal Control Problems, AIAA Journal, Vol. 11, pp. 1241-1246, 1973. · Zbl 0273.49013 · doi:10.2514/3.50573 |
[5] |
Hestenes, M.,Calculus of Variations and Optimal Control Theory, John Wiley, New York, New York, 1964. · Zbl 0143.12501 |
[6] |
Warga, J.,A Second-Order Lagrangian Condition for Restricted Control Problems, Journal of Optimization Theory and Applications, Vol. 24, pp. 475-483, 1978. · Zbl 0351.49003 · doi:10.1007/BF00932890 |
[7] |
Warga, J.,A Second-Order Condition that Strengthens Pontryagin’s Maximum Principle, Journal of Differential Equations, Vol. 28, pp. 284-307, 1979. · doi:10.1016/0022-0396(78)90073-6 |
[8] |
Warga, J.,A Hybrid Relaxed-Lagrangian Second-Order Condition for Minimum, Differential Games and Control Theory, Proceedings of Third Kingston Conference, Part A, Marcel Dekker, New York, New York, pp. 77-94, 1979. · Zbl 0414.49011 |
[9] |
Agrachev, A. A., andGamkrelidze, R. V.,A Second-Order Optimality Principle for a Time-Optimal Problem, Mathematics USSR Sbornik, Vol. 29, pp. 547-576, 1976. · Zbl 0377.49014 · doi:10.1070/SM1976v029n04ABEH003685 |
[10] |
Gabasov, R., andKirillova, F. M.,High Order Necessary Conditions for Optimality, SIAM Journal on Control, Vol. 10, pp. 127-168, 1972. · Zbl 0236.49005 · doi:10.1137/0310012 |
[11] |
Knobloch, H. W.,Higher Order Necessary Conditions in Optimal Control Theory, Springer-Verlag, New York, New York, 1981. · Zbl 0474.49001 |
[12] |
Krener, A. J.,The High Order Maximal Principle and Its Application to Singular Extremals, SIAM Journal on Control and Optimization, Vol. 15, pp. 256-293, 1977. · Zbl 0354.49008 · doi:10.1137/0315019 |
[13] |
Ben-Tal, A.,Second-Order and Related Extremality Conditions in Nonlinear Programming, Journal of Optimization Theory and Applications, Vol. 31, pp. 143-165, 1980. · Zbl 0416.90062 · doi:10.1007/BF00934107 |
[14] |
Ioffe, A. D.,Necessary and Sufficient Conditions for a Local Minimum 3: Second-Order Conditions and Augmented Duality, SIAM Journal on Control and Optimization, Vol. 17, pp. 266-288, 1979. · Zbl 0417.49029 · doi:10.1137/0317021 |
[15] |
Levitin, E. S., Miljutin, A. A., andOsmolovskii, N. P.,On Conditions for a Local Minimum in a Problem with Constraints, Mathematical Economics and Functional Analysis, Edited by B. S. Mitjagin, Nauka, Moscow, 1974 (in Russian). · Zbl 0292.49009 |
[16] |
Messerli, E. J., andPolak, E.,On Second-Order Necessary Conditions for Optimality, SIAM Journal on Control and Optimization, Vol. 7, pp. 272-291, 1969. · Zbl 0184.44501 · doi:10.1137/0307019 |
[17] |
Bernstein, D. S.,A Systematic Approach to Higher-Order Necessary Conditions in Optimization Theory, SIAM Journal on Control and Optimization (to appear). · Zbl 0552.90094 |
[18] |
Canon, M., Cullum, C., andPolak, E.,Theory of Optimal Control and Mathematical Programming, McGraw-Hill, New York, New York, 1970. · Zbl 0264.49001 |
[19] |
Brockett, R. W.,Finite-Dimensional Linear Systems, John Wiley, New York, New York, 1970. · Zbl 0216.27401 |
[20] |
Haas, V. B.,Normality and Controllability for the Problem of Bolza, International Journal on Control, Vol. 30, pp. 331-338, 1979. · Zbl 0416.49024 · doi:10.1080/00207177908922778 |
[21] |
Neustadt, L. W.,Optimization, A Theory of Necessary Conditions, Princeton University Press, Princeton, New Jersey, 1976. · Zbl 0353.49003 |
[22] |
Warga, J.,Optimal Control of Differential and Functional Equations, Academic Press, New York, New York, 1972. · Zbl 0253.49001 |