Abstract
Neighboring extremals of dynamic optimization problems with path equality constraints and with an unknown parameter vector are considered in this paper. With some simplifications, the problem is reduced to solving a linear, time-varying two-point boundary-value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Two example problems are solved to illustrate the validity and usefulness of the solution technique.
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Miele, A., Damoulakis, N., Cloutier, J. R., andTietze, J. L.,Sequential Gradient-Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints, Journal of Optimization Theory and Applications, Vol. 13, No. 2, pp. 218–255, 1974.
Jacobson, D. H., andLele, M. M.,A Transformation Technique for Optimal Control Problems with a State Variable Inequality Constraint, IEEE Transactions on Automatic Control, Vol. AC-14, No. 5, pp. 457–464, 1969.
Breakwell, J. V., Speyer, J. L., andBryson, A. E., Jr.,Optimization and Control of Nonlinear Systems Using the Second Variation, SIAM Journal on Control, Series A, Vol. 1, No. 2, pp. 193–217, 1963.
Bryson, A. E., Jr., andHo, Y. C.,Applied Optimal Control, Hemisphere, Washington, DC, 1975.
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Communicated by A. Miele
This research was supported in part by the National Aeronautics and Space Administration under NASA Grant No. NCC-2-106.
The author is indebted to Professor A. E. Bryson, Jr., Department of Aeronautics and Astronautics, Stanford University, for many stimulating discussions.
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Lee, A.Y. Neighboring extremals of dynamic optimization problems with path equality constraints. J Optim Theory Appl 57, 519–536 (1988). https://doi.org/10.1007/BF02346169
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DOI: https://doi.org/10.1007/BF02346169