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Ill-conditioning in optimal control computation. (English) Zbl 0914.49022

Bainov, D. (ed.), Proceedings of the 8th international colloquium on differential equations, Plovdiv, Bulgaria, August 18–23, 1997. Utrecht: VSP. 81-88 (1998).
Summary: Optimal control computations are well known to be ill-conditioned, but there is little quantifiable knowledge on the topic. The mathematical machinery for the quantification of ill-conditioning in optimal control computation is presented. Implementation in the optimal control software MISER3 and computation of test examples are discussed. Some idea of how the condition numbers vary with the number of discretization parameters for controls of typical problems is given. Various constraint types are considered and a comparison of two methods for computing smooth controls is presented.
For the entire collection see [Zbl 0896.00024].

MSC:

49M99 Numerical methods in optimal control
65K10 Numerical optimization and variational techniques
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization

Software:

MISER3
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