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Baillieul, J.

Geometric methods for nonlinear optimal control problems. (English) Zbl 0368.49013

J. Optimization Theory Appl. 25, 519-548 (1978).
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Cited in 28 Documents

MSC:

49K27 Optimality conditions for problems in abstract spaces
93C10 Nonlinear systems in control theory
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References:

[1] Brockett, R. W.,Lie Theory and Control Systems Defined on Spheres, SIAM Journal on Applied Mathematics, Vol. 25, No. 2, 1973. · Zbl 0272.93003
[2] Baillieul, J.,Optimal Control on Lie Groups, Proceedings of the 1974 Allerton Conference on Circuit and System Theory, Urbana, Illinois, 1974.
[3] Baillieul, J.,Some Optimization Problems in Geometric Control Theory, Harvard University, PhD Thesis, 1975.
[4] Jacobson, D. H.,On the Optimal Control of Systems of Quadratic and Bilinear Differential Equations, Proceedings of IFAC World Conference, Boston, Massachusetts, 1975.
[5] Samelson, H.,Notes on Lie Algebras, Van Nostrand Reinhold Company, New York, New York, 1969. · Zbl 0209.06601
[6] Warner, F.,Foundations of Differentiable Manifolds and Lie Groups, Scott, Foresman, and Company, Glenview, Illinois, 1971. · Zbl 0241.58001
[7] Hermann, R.,Differential Geometry and the Calculus of Variations, Academic Press, New York, New York, 1968. · Zbl 0219.49023
[8] Brockett, R. W.,System Theory on Group Manifolds and Coset Spaces, SIAM Journal on Control, Vol. 10, No. 2, 1972. · Zbl 0238.93001
[9] Cesari, L.,Existence Theorems for Weak and Usual Optimal Solutions in Lagrange Problems with Unilateral Constraints, Transactions of the American Mathematical Society, Vol. 124, pp. 369-412, 1966. · Zbl 0145.12501 · doi:10.1090/S0002-9947-1966-0203542-1
[10] Hermann, R.,Geodesics and Classical Mechanics on Lie Groups, Journal of Mathematical Physics, Vol. 13, No. 4, 1972. · Zbl 0235.53026
[11] Krener, A. J.,The High Order Maximal Principle and Its Application to Singular Extremals, SIAM Journal on Control (to appear). · Zbl 0354.49008
[12] Hestines, M.,Calculus of Variations and Optimal Control Theory, John Wiley and Sons, New York, New York, 1966.
[13] Krener, A. J.,A Generalization of Chow’s Theorem and the Bang-Bang Theorem to Nonlinear Control Problems, SIAM Journal on Control, Vol. 12, No. 1, 1974. · Zbl 0243.93008
[14] Whitaker, E. T., andWatson, G. N.,A Course of Modern Analysis, Cambridge University Press, Cambridge, England, 1902.
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