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Differential continuation for regular optimal control problems. (English) Zbl 1248.49025

Summary: Regular control problems in the sense of the Legendre condition are defined, and second-order necessary and sufficient optimality conditions in this class are reviewed. Adding a scalar homotopy parameter, differential path-following is introduced. The previous sufficient conditions ensure the definiteness and regularity of the path. The role of automatic differentiation for the implementation of this approach is discussed, and two examples excerpted from quantum and space mechanics are detailed.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
49-04 Software, source code, etc. for problems pertaining to calculus of variations and optimal control

Software:

ADIFOR; HOMPACK90
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Full Text: DOI

References:

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