Infinite dimensional uncertain dynamic systems on Banach spaces and their optimal output feedback control

N.U. Ahmed

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2015)

  • Volume: 35, Issue: 1, page 65-87
  • ISSN: 1509-9407

Abstract

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In this paper we consider a class of partially observed semilinear dynamic systems on infinite dimensional Banach spaces subject to dynamic and measurement uncertainty. The problem is to find an output feedback control law, an operator valued function, that minimizes the maximum risk. We present a result on the existence of an optimal (output feedback) operator valued function in the presence of uncertainty in the system as well as measurement. We also consider uncertain stochastic systems and present similar results on the question of existence of optimal feedback laws.

How to cite

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N.U. Ahmed. "Infinite dimensional uncertain dynamic systems on Banach spaces and their optimal output feedback control." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 35.1 (2015): 65-87. <http://eudml.org/doc/276490>.

@article{N2015,
abstract = {In this paper we consider a class of partially observed semilinear dynamic systems on infinite dimensional Banach spaces subject to dynamic and measurement uncertainty. The problem is to find an output feedback control law, an operator valued function, that minimizes the maximum risk. We present a result on the existence of an optimal (output feedback) operator valued function in the presence of uncertainty in the system as well as measurement. We also consider uncertain stochastic systems and present similar results on the question of existence of optimal feedback laws.},
author = {N.U. Ahmed},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {partially observed; uncertain systems; stochastic systems; operator valued functions; feedback operators; existence of optimal operators in the presence of uncertainty},
language = {eng},
number = {1},
pages = {65-87},
title = {Infinite dimensional uncertain dynamic systems on Banach spaces and their optimal output feedback control},
url = {http://eudml.org/doc/276490},
volume = {35},
year = {2015},
}

TY - JOUR
AU - N.U. Ahmed
TI - Infinite dimensional uncertain dynamic systems on Banach spaces and their optimal output feedback control
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2015
VL - 35
IS - 1
SP - 65
EP - 87
AB - In this paper we consider a class of partially observed semilinear dynamic systems on infinite dimensional Banach spaces subject to dynamic and measurement uncertainty. The problem is to find an output feedback control law, an operator valued function, that minimizes the maximum risk. We present a result on the existence of an optimal (output feedback) operator valued function in the presence of uncertainty in the system as well as measurement. We also consider uncertain stochastic systems and present similar results on the question of existence of optimal feedback laws.
LA - eng
KW - partially observed; uncertain systems; stochastic systems; operator valued functions; feedback operators; existence of optimal operators in the presence of uncertainty
UR - http://eudml.org/doc/276490
ER -

References

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  1. [1] N.U. Ahmed, Optimal control of infinite dimensional stochastic systems via generalized solutions of HJB equations, Discuss. Math. DICO 21 (2001), 97-126. doi: 10.7151/dmdico.1019 Zbl1013.93054
  2. [2] N.U. Ahmed, Optimization and Identification Systems Governed by Evolution Equations on Banach Space, Pitman research Notes in Mathematics series, 184, Longman Scientific and Technical, U.K; and Co-published with John-Wiely and Sons, Inc. New York, 1988. 
  3. [3] N.U. Ahmed and X. Xiang, Differential inclusions on Banach spaces and their optimal control, Nonlinear Funct. Anal. & Appl. 8 (3) (2003), 461-488. 
  4. [4] N.U. Ahmed, Optimal relaxed controls for systems governed by impulsive differential inclusions, Nonlinear Funct. Anal. & Appl. 10 (3) (2005), 427-460. Zbl1092.49002
  5. [5] N.U. Ahmed and C.D. Charalambous, Minimax games for stochastic systems subject to relative entropy uncertainty: Applications to SDE's on Hilbert spaces, J. Math. Control, Signals and Systems 19 (2007), 65-91. doi: 10.1007/s00498-006-0009-x Zbl1149.49006
  6. [6] N.U. Ahmed and Suruz Miah, Optimal feedback control law for a class of partially observed dynamic systems: A min-max problem, Dynamic Syst. Appl. 20 (2011), 149-168. 
  7. [7] N.U. Ahmed, Optimal Output Feedback Control Law for a Class of Uncertain Infinite Dimensional Dynamic Systems, (2015), submitted. 
  8. [8] L. Cesari, Optimization Theory and Applications (Springer-Verlag, 1983). doi: 10.1007/978-1-4613-8165-5 
  9. [9] H.O. Fattorini, Infinite Dimensional Optimization and Control Theory, Encyclopedia of Mathematics and its Applications, 62 (Cambridge University Press, 1999). doi: 10.1017/CBO9780511574795 
  10. [10] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, (Theory), Kluwer Academic Publishers (Dordrecht, Boston, London, 1, 1997). doi: 10.1007/978-1-4615-6359-4_1 Zbl0887.47001
  11. [11] F. Mayoral, Compact sets of compact operators in absence of l₁, Proc. AMS 129 (1) (2001), 79-82. doi: 10.1090/S0002-9939-00-06007-X Zbl0961.47010
  12. [12] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Encyclopedia of Mathematics and Its Applications, Vol. 44 (Cambridge University Press, 1992). doi: 10.1017/CBO9780511666223 

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