American Institute of Mathematical Sciences

Advanced
January  2009, 5(1): 1-10. doi: 10.3934/jimo.2009.5.1

A class of optimal control problems of systems governed by the first order linear dynamic equations on time scales

Y. Gong 1, and  X. Xiang 1,

1. 

Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, China

Received  February 2008 Revised  August 2008 Published  December 2008

This paper is mainly concerned with a class of optimal control problems of systems governed by the first order linear dynamic equations on time scales with quadratic cost functionals. Introducing the weak solutions of the first order linear dynamic equations and presenting the Arzela-Ascoli theorem on time scales, we prove the existence of solution to a class of linear quadratic optimal control problems on time scales.
Keywords: Banach space, optimal control., Arzela-Ascoli theorem, time scales, $\Delta$-derivative, dynamic equations.
Mathematics Subject Classification: 39A1.
Citation: Y. Gong, X. Xiang. A class of optimal control problems of systems governed by the first order linear dynamic equations on time scales. Journal of Industrial & Management Optimization, 2009, 5 (1) : 1-10. doi: 10.3934/jimo.2009.5.1
[1]

Sung Kyu Choi, Namjip Koo. Stability of linear dynamic equations on time scales. Conference Publications, 2009, 2009 (Special) : 161-170. doi: 10.3934/proc.2009.2009.161
[2]

Ruichao Guo, Yong Li, Jiamin Xing, Xue Yang. Existence of periodic solutions of dynamic equations on time scales by averaging. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 959-971. doi: 10.3934/dcdss.2017050
[3]

Raegan Higgins. Asymptotic behavior of second-order nonlinear dynamic equations on time scales. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 609-622. doi: 10.3934/dcdsb.2010.13.609
[4]

Loïc Bourdin, Emmanuel Trélat. Optimal sampled-data control, and generalizations on time scales. Mathematical Control & Related Fields, 2016, 6 (1) : 53-94. doi: 10.3934/mcrf.2016.6.53
[5]

B. Kaymakcalan, R. Mert, A. Zafer. Asymptotic equivalence of dynamic systems on time scales. Conference Publications, 2007, 2007 (Special) : 558-567. doi: 10.3934/proc.2007.2007.558
[6]

Saroj Panigrahi. Liapunov-type integral inequalities for higher order dynamic equations on time scales. Conference Publications, 2013, 2013 (special) : 629-641. doi: 10.3934/proc.2013.2013.629
[7]

Yongkun Li, Pan Wang. Almost periodic solution for neutral functional dynamic equations with Stepanov-almost periodic terms on time scales. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 463-473. doi: 10.3934/dcdss.2017022
[8]

Gastão S. F. Frederico, Delfim F. M. Torres. Noether's symmetry Theorem for variational and optimal control problems with time delay. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 619-630. doi: 10.3934/naco.2012.2.619
[9]

Mateusz Krukowski. Arzelà-Ascoli's theorem in uniform spaces. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 283-294. doi: 10.3934/dcdsb.2018020
[10]

Giulia Cavagnari. Regularity results for a time-optimal control problem in the space of probability measures. Mathematical Control & Related Fields, 2017, 7 (2) : 213-233. doi: 10.3934/mcrf.2017007
[11]

Yunfei Peng, X. Xiang, W. Wei. Backward problems of nonlinear dynamical equations on time scales. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1553-1564. doi: 10.3934/dcdss.2011.4.1553
[12]

Min Niu, Bin Xie. Comparison theorem and correlation for stochastic heat equations driven by Lévy space-time white noises. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 2989-3009. doi: 10.3934/dcdsb.2018296
[13]

Zbigniew Bartosiewicz, Ülle Kotta, Maris Tőnso, Małgorzata Wyrwas. Accessibility conditions of MIMO nonlinear control systems on homogeneous time scales. Mathematical Control & Related Fields, 2016, 6 (2) : 217-250. doi: 10.3934/mcrf.2016002
[14]

Yunfei Peng, X. Xiang. A class of nonlinear impulsive differential equation and optimal controls on time scales. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1137-1155. doi: 10.3934/dcdsb.2011.16.1137
[15]

Francis Clarke. A general theorem on necessary conditions in optimal control. Discrete & Continuous Dynamical Systems - A, 2011, 29 (2) : 485-503. doi: 10.3934/dcds.2011.29.485
[16]

Giselle A. Monteiro, Milan Tvrdý. Generalized linear differential equations in a Banach space: Continuous dependence on a parameter. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 283-303. doi: 10.3934/dcds.2013.33.283
[17]

Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial & Management Optimization, 2008, 4 (1) : 1-15. doi: 10.3934/jimo.2008.4.1
[18]

Marina V. Plekhanova. Strong solutions of quasilinear equations in Banach spaces not solvable with respect to the highest-order derivative. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 833-846. doi: 10.3934/dcdss.2016031
[19]

Agnieszka B. Malinowska, Delfim F. M. Torres. Euler-Lagrange equations for composition functionals in calculus of variations on time scales. Discrete & Continuous Dynamical Systems - A, 2011, 29 (2) : 577-593. doi: 10.3934/dcds.2011.29.577
[20]

Emmanuel Trélat. Optimal control of a space shuttle, and numerical simulations. Conference Publications, 2003, 2003 (Special) : 842-851. doi: 10.3934/proc.2003.2003.842

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (16)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences