NDLI: Solution Differentiability for Nonlinear Parametric Control Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Pesch, Hans Josef Maurer, Helmut
Copyright Year	1994
Abstract	Perturbed nonlinear control problems with data depending on a vector parameter are considered. Using second-order sufficient optimality conditions, it is shown that the optimal solution and the adjoint multipliers are differentiable functions of the parameter. The proof exploits the close connections between solutions of a Riccati differential equation and shooting methods for solving the associated boundary value problem. Solution differentiability provides a firm theoretical basis for numerical feedback schemes that have been developed for computing neighbouring extremals. The results are illustrated by an example that admits two extremal solutions. Second-order sufficient conditions single out one optimal solution for which a sensitivity analysis is carried out.
Starting Page	1542
Ending Page	1554
Page Count	13
File Format	PDF
ISSN	03630129
DOI	10.1137/S0363012992232269
e-ISSN	10957138
Issue Number	6
Volume Number	32
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-14
Access Restriction	Subscribed
Subject Keyword	second-order sufficient conditions parametric control problems solution differentiability shooting methods Sensitivity, stability, well-posedness feedback controls Problems involving ordinary differential equations
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics

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