Nonlinear dynamic systems and optimal control problems on time scales

Yunfei Peng; Xiaoling Xiang; Yang Jiang

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 3, page 654-681
  • ISSN: 1292-8119

Abstract

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This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear dynamic systems on time scales. Introducing the reasonable weak solution of nonlinear dynamic systems, the existence of the weak solution for the nonlinear dynamic systems on time scales and its properties are presented. Discussing L1-strong-weak lower semicontinuity of integral functional, we give sufficient conditions for the existence of optimal controls. Using integration by parts formula and Hamiltonian function on time scales, the necessary conditions of optimality are derived respectively. Some examples on continuous optimal control problems, discrete optimal control problems, mathematical programming and variational problems are also presented for demonstration.

How to cite

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Peng, Yunfei, Xiang, Xiaoling, and Jiang, Yang. "Nonlinear dynamic systems and optimal control problems on time scales." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 654-681. <http://eudml.org/doc/272772>.

@article{Peng2011,
abstract = {This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear dynamic systems on time scales. Introducing the reasonable weak solution of nonlinear dynamic systems, the existence of the weak solution for the nonlinear dynamic systems on time scales and its properties are presented. Discussing L1-strong-weak lower semicontinuity of integral functional, we give sufficient conditions for the existence of optimal controls. Using integration by parts formula and Hamiltonian function on time scales, the necessary conditions of optimality are derived respectively. Some examples on continuous optimal control problems, discrete optimal control problems, mathematical programming and variational problems are also presented for demonstration.},
author = {Peng, Yunfei, Xiang, Xiaoling, Jiang, Yang},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {time scale; weak solution; optimal control; subdifferentials; existence; necessary conditions of optimality},
language = {eng},
number = {3},
pages = {654-681},
publisher = {EDP-Sciences},
title = {Nonlinear dynamic systems and optimal control problems on time scales},
url = {http://eudml.org/doc/272772},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Peng, Yunfei
AU - Xiang, Xiaoling
AU - Jiang, Yang
TI - Nonlinear dynamic systems and optimal control problems on time scales
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2011
PB - EDP-Sciences
VL - 17
IS - 3
SP - 654
EP - 681
AB - This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear dynamic systems on time scales. Introducing the reasonable weak solution of nonlinear dynamic systems, the existence of the weak solution for the nonlinear dynamic systems on time scales and its properties are presented. Discussing L1-strong-weak lower semicontinuity of integral functional, we give sufficient conditions for the existence of optimal controls. Using integration by parts formula and Hamiltonian function on time scales, the necessary conditions of optimality are derived respectively. Some examples on continuous optimal control problems, discrete optimal control problems, mathematical programming and variational problems are also presented for demonstration.
LA - eng
KW - time scale; weak solution; optimal control; subdifferentials; existence; necessary conditions of optimality
UR - http://eudml.org/doc/272772
ER -

References

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