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Content available Sensitivity analysis for state constrained optimal control problems
Malanowski K.
Control and Cybernetics
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2011
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Vol. 40, no 4
1043-1058
EN
A sensitivity result for cone-constrained optimization problem in abstract Hilbert spaces is obtained, using a slight modification of Haraux's theorem on differentiability of the metric projection onto polyhedric sets. This result is applied to sensitivity analysis for nonlinear optimal control problems subject to first order state constraints.
2
Content available remote A characterization of stability and sensitivity properties for state-constrained optimal control
Malanowski K.
Control and Cybernetics
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2007
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Vol. 36, no 3
711-726
EN
In a series of the recent papers of the author, it was shown that the solutions and Lagrange multipliers of state-constrained optimal control problems are locally Lipschitz continuous and directionally differentiable functions of the parameter, under usual constraint qualifications and weakened second order conditions. In this paper, it is shown that those conditions are not only sufficient, but also necessary. Thus, they consitute a characterization of Lipschitz stability and sensitivity properties for state-constrained optimal control problems.
3
Content available Lipschitz stability of solutions to parametric optimal control for elliptic equations
Malanowski K., Troeltzsch F.
Control and Cybernetics
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2000
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Vol. 29, no 1
237-256
EN
: A family of parameter dependent elliptic optimal control problems with nonlinear boundary control is considered. The control function is subject to amplitude constraints. A characterization of conditions is given under which solutions to the problems exist, are locally unique and Lipschitz continuous in a neighborhood of the reference value of the parameter.
4
Content available Application of the classical implicit function theorem in sensitivity analysis of parametric optimal control
Malanowski K.
Control and Cybernetics
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1998
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Vol. 27, no 3
335-352
EN
A family {(O[sub h])} of parametric optimal control problems for nonlinear ODEs is considered. The problems are subject to pointwise inequality type state constraints. It is assumed that the reference solution is regular. The original problems (O[sub h]) are substituted by problems [...] subject to equality type constraints with the sets of activity depending on the parameter. Using the classical implicit function theorem, conditions are derived under which stationary points of [...] are Frechet differentiable functions of the parameter. It is shown that, under additional conditions, the stationary points of [...] correspond to the solutions and Lagrange multipliers of (O[sub h]9).
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