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April  1998, 4(2): 241-272. doi: 10.3934/dcds.1998.4.241

Sensitivity analysis for state constrained optimal control problems

1. 

Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland

2. 

Westfälische Wilhelms-Universität Münster, Institut für Numerische und instrumentelle Mathematik, Einsteinstrasse 62, 48149 Münster, Germany

Received  September 1996 Revised  January 1997 Published  February 1998

A family of parameter dependent optimal control poblems for nonlinear ODEs is considered. The problems are subject to pointwise control and state inequality type constraints. It is assumed that, at the reference value of the parameter the reference optimal solution exists and is regular. Regularity conditions are formulated under which the original problems are locally equivalent to some problems subject to equality type constraints only. The classical implicit function theorem is applied to these new problems to investigate Fréchet differentiability of the solutions with respect to the parameter. A numerical example is provided.
Citation: Kazimierz Malanowski, Helmut Maurer. Sensitivity analysis for state constrained optimal control problems. Discrete & Continuous Dynamical Systems - A, 1998, 4 (2) : 241-272. doi: 10.3934/dcds.1998.4.241
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