The paper investigates the Lipschitz/Hölder stability with respect to perturbations of optimal control problems with linear dynamic and cost functional which is quadratic in the state and linear in the control variable. The optimal control is assumed to be of bang-bang type and the problem to enjoy certain convexity properties. Conditions for bi-metric regularity and (Hölder) metric sub-regularity are established, involving only the order of the zeros of the associated switching function and smoothness of the data. These results provide a basis for the investigation of various approximation methods. They are utilized in this paper for the convergence analysis of a Newton-type method applied to optimal control problems which are affine with respect to the control.

Metric Regularity Properties in Bang-Bang Type Linear-Quadratic Optimal Control Problems

Scarinci T.;
2019

Abstract

The paper investigates the Lipschitz/Hölder stability with respect to perturbations of optimal control problems with linear dynamic and cost functional which is quadratic in the state and linear in the control variable. The optimal control is assumed to be of bang-bang type and the problem to enjoy certain convexity properties. Conditions for bi-metric regularity and (Hölder) metric sub-regularity are established, involving only the order of the zeros of the associated switching function and smoothness of the data. These results provide a basis for the investigation of various approximation methods. They are utilized in this paper for the convergence analysis of a Newton-type method applied to optimal control problems which are affine with respect to the control.
File in questo prodotto:
File Dimensione Formato  
11.pdf

accesso aperto

Tipologia: Documento in Versione Editoriale
Licenza: Dominio pubblico
Dimensione 793.98 kB
Formato Adobe PDF
793.98 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/151300
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? 8
social impact