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
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topPeng, 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/221900>.
@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; time scale; optimal control; necessary conditions of optimality},
language = {eng},
month = {8},
number = {3},
pages = {654-681},
publisher = {EDP Sciences},
title = {Nonlinear dynamic systems and optimal control problems on time scales*},
url = {http://eudml.org/doc/221900},
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
DA - 2011/8//
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; time scale; optimal control; necessary conditions of optimality
UR - http://eudml.org/doc/221900
ER -
References
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