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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.14 no.2 Temuco  2012

http://dx.doi.org/10.4067/S0719-06462012000200005 

CUBO A Mathematical Journal Vol.14, No 02, (81-90). June 2012

Texto completo disponíble en formato PDF

An Immediate Derivation of Maximum Principle in Banach spaces, Assuming Reflexive Input and State Spaces.

 

Paolo d'Alessandro

Department of Mathematics, Third university of Rome.Italy email: dalex@mat.uniroma3.it


ABSTRACT

We consider a standard setting for the norm optimal problem in Banach spaces and show that with a simple argument which invokes some appropriately selected powerful general Theorems for Banach spaces a straightforward derivation of the Maximum Principle is obtained.

Keywords and Phrases: Linear Control Systems in Banach Spaces, Norm Optimal Control, Support of Closed Convex Sets


RESUMEN

Consideramos una formulación estandar para el problema de norma optimal en espacios de Banach y mostramos que con un argumento simple que invoca algunos fuertes teoremas generales de la teoría de espacios de Banach elegidos apropiadamente se deriva directamente el Principio del Maximo.

 

2010 AMS Mathematics Subject Classification: 49K20.


 

References

[1] H.O. Fattorini "Infinite Dimensional Linear Control Systems", Elsevier, Amsterdam 2005.         [ Links ]

[2] H.O. Fattorini, "Strong Regularity of Time and Norm Optimal Controls", Submitted        [ Links ]

[3] H.O. Fattorini, "Linear Control Systems In Sequence Spaces" Functional Analysis and evolution equations, The Gunter Lumer Volume 2007, pp 273-290.         [ Links ]

[4] H.O. Fattorini, " Regular and Strongly Regular Time and Norm Optimal Controls" Submitted.         [ Links ]

[5] H.O. Fattorini, Private Communication.         [ Links ]

[6] J.L. Kelley and I. Namioka, Linear Topological Spaces, Springer, New York, 1963         [ Links ]

[7] K. Yosida, "Functional Analysis", Springer-Verlag, New York, 1974.         [ Links ]

[8] P. d'Alessandro, " Closure of Pointed Cones and Maximum Principle in Hilbert Spaces", CUBO a Mathematical Journal, Vol.13, No.2 (73-84), June 2011.         [ Links ]

[9] R.R. Phelps, "Support Cones in Banach Spaces and Their Application", Adv. in Math. 13 (1974), 1-19.         [ Links ]

[10] W.B. Johnson, J. Lindenstrauss Eds, "Handbook of The Geometry of Banach Spaces", Vol. 1, Elsevier, Amsterdam, 2001.         [ Links ]


Received: October 2010. Revised: October 2011.