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

Authors

  • Iguer L D Santos Sao Paulo State University

DOI:

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

Keywords:

time scales, control systems, optimal control

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.

Author Biography

Iguer L D Santos, Sao Paulo State University

Departament of Mathematics. Assistent Professor.

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.

Downloads

Additional Files

Published

2016-04-29

How to Cite

Santos, I. L. D. (2016). Existence of Solutions for Optimal Control Problems on Time Scales whose States are Absolutely Continuous. Trends in Computational and Applied Mathematics, 17(1), 81. https://doi.org/10.5540/tema.2016.017.01.0081

Issue

Section

Original Article