Note on local quadratic growth estimates in bang-bang optimal control problems

  • Strong second-order conditions in mathematical programming play an important role not only as optimality tests but also as an intrinsic feature in stability and convergence theory of related numerical methods. Besides of appropriate firstorder regularity conditions, the crucial point consists in local growth estimation for the objective which yields inverse stability information on the solution. In optimal control, similar results are known in case of continuous control functions, and for bang–bang optimal controls when the state system is linear. The paper provides a generalization of the latter result to bang–bang optimal control problems for systems which are affine-linear w.r.t. the control but depend nonlinearly on the state. Local quadratic growth in terms of L1 norms of the control variation are obtained under appropriate structural and second-order sufficient optimality conditions.

Export metadata

Additional Services

Search Google Scholar
Metadaten
Author: Ursula Felgenhauer
URL:http://www.tandfonline.com/doi/abs/10.1080/02331934.2013.773000
DOI:https://doi.org/10.1080/02331934.2013.773000
ISSN:1029-4945
Title of the source (English):Optimization : a Journal of Mathematical Programming and Operations Research
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2015
Tag:bang–bang control structure; solution stability; strong local optimality; sufficient optimality conditions
Volume/Year:64
Issue number:3
First Page:521
Last Page:537
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Optimale Steuerung
Einverstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.