Existence of Solutions for Optimal Control Problems on Time Scales whose States are Absolutely Continuous

Iguer L D Santos

Abstract


This paper considers a class of optimal control problems on time scales described by dynamic equations on time scales. We have established sufficient conditions for the
existence of optimal controls.


Keywords


time scales; control systems; optimal control

Full Text:

PDF

References


M. Bohner & A. Peterson. “Dynamic Equations on Time Scales”, Birkha ̈user Boston Inc., Boston, (2001).

A. Cabada & D.R. Vivero. Criterions for absolute continuity on time scales, J. Difference Equ. Appl., 11(11) (2005), 1013–1028.

A. Cabada & D.R. Vivero. Expression of the Lebesgue -integral on time scales as a usual Lebesgue integral: application to the calculus of -antiderivatives, Math. Comput. Modelling, 43(1-2) (2006), 194–207.

A.F. Filippov. On certain questions in the theory of optimal control, J. SIAM Control Ser. A 1 (1962), 76–84.

G.S. Guseinov. Integration on time scales, J. Math. Anal. Appl., 285(1) (2003), 107–127.

R. Hilscher & V. Zeidan. Weak maximum principle and accessory problem for control problems on

time scales, Nonlinear Anal. 70(9) (2009), 3209–3226.

Y. Peng, X. Xiang & Y. Jiang. Nonlinear dynamic systems and optimal control problems on time

scales, ESAIM Control Optim. Calc. Var., 17(3) (2011), 654–681.

E. Roxin. The existence of optimal controls, Michigan Math. J., 9 (1962), 109–119.

W. Rudin. “Real and Complex Analysis”, third edition, McGraw-Hill Book Company, New York (1987).

I.L.D. Santos & G.N. Silva. Absolute continuity and existence of solutions to dynamic inclusions in time scales, Math. Ann., 356(1) (2013), 373–399.

I.L.D. Santos & G.N. Silva. Filippov’s selection theorem and the existence of solutions for optimal control problems in time scales, Comput. Appl. Math., 33(1) (2014), 223–241.

R.B. Vinter. “Optimal Control”, Systems and Control: Foundations and Applications, Birkha ̈user, Boston (2000).

Z. Zhan, W. Wei, Y. Li & H. Xu. Existence for calculus of variations and optimal control problems on time scales, Int. J. Innov. Comput. Inf. Control, 8 (2012), 3793–3808.




DOI: https://doi.org/10.5540/tema.2016.017.01.0081

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.



Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia