Stability analysis of variational inequalities for bang-singular-bang controls

  • The paper is related to parameter dependent optimal control problems for control-affine systems. The case of scalar reference control with bang-singular-bang structure is considered. The analysis starts from a variational inequality (VI) formulation of Pontryagin's Maximum Principle. In a first step, under appropriate higher-order sufficient optimality conditions, the existence of solutions for the linearized problem (LVI) is proven. In a second step, for a certain class of right-hand side perturbation, it is shown that the controls from LVI have bang-singular-bang structure and, in L_1 topology, depend Lipschitz continuously on the data. Applying finally a common fixed-point approach to VI, the results are brought together to obtain existence and structural stability results for extremals of the original control problem under parameter perturbation.

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Metadaten
Author: Ursula Felgenhauer
ISSN:0324-8569
Title of the source (English):Control and Cybernetics
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2013
Tag:parametric optimal control problems, bang-singular control structure, approximation of extremals
Volume/Year:42
Issue number:3
First Page:557
Last Page:592
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Optimale Steuerung
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