Stability and sensitivity analysis for optimal control problems with control-state constraints

Kazimierz Malanowski

  • 2001

Abstract

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A family of parameter dependent optimal control problems ( O ) h with smooth data for nonlinear ODEs is considered. The problems are subject to pointwise mixed control-state constraints. It is assumed that, for a reference value h₀ of the parameter, a solution of ( O ) h ₀ exists. It is shown that if (i) independence, controllability and coercivity conditions are satisfied at the reference solution, then (ii) for each h from a neighborhood of h₀, a locally unique solution to ( O ) h and the associated Lagrange multiplier exist, are Lipschitz continuous and Bouligand differentiable functions of the parameter. If, in addition, the dependence of the data on the parameter is strong, then (ii) implies (i).

How to cite

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Kazimierz Malanowski. Stability and sensitivity analysis for optimal control problems with control-state constraints. 2001. <http://eudml.org/doc/285933>.

@book{KazimierzMalanowski2001,
abstract = {A family of parameter dependent optimal control problems $(O)_\{h\}$ with smooth data for nonlinear ODEs is considered. The problems are subject to pointwise mixed control-state constraints. It is assumed that, for a reference value h₀ of the parameter, a solution of $(O)_\{h₀\}$ exists. It is shown that if (i) independence, controllability and coercivity conditions are satisfied at the reference solution, then (ii) for each h from a neighborhood of h₀, a locally unique solution to $(O)_\{h\}$ and the associated Lagrange multiplier exist, are Lipschitz continuous and Bouligand differentiable functions of the parameter. If, in addition, the dependence of the data on the parameter is strong, then (ii) implies (i).},
author = {Kazimierz Malanowski},
keywords = {optimal control; stability; control-state constraints; Bouligand differentiability},
language = {eng},
title = {Stability and sensitivity analysis for optimal control problems with control-state constraints},
url = {http://eudml.org/doc/285933},
year = {2001},
}

TY - BOOK
AU - Kazimierz Malanowski
TI - Stability and sensitivity analysis for optimal control problems with control-state constraints
PY - 2001
AB - A family of parameter dependent optimal control problems $(O)_{h}$ with smooth data for nonlinear ODEs is considered. The problems are subject to pointwise mixed control-state constraints. It is assumed that, for a reference value h₀ of the parameter, a solution of $(O)_{h₀}$ exists. It is shown that if (i) independence, controllability and coercivity conditions are satisfied at the reference solution, then (ii) for each h from a neighborhood of h₀, a locally unique solution to $(O)_{h}$ and the associated Lagrange multiplier exist, are Lipschitz continuous and Bouligand differentiable functions of the parameter. If, in addition, the dependence of the data on the parameter is strong, then (ii) implies (i).
LA - eng
KW - optimal control; stability; control-state constraints; Bouligand differentiability
UR - http://eudml.org/doc/285933
ER -

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