Advanced

Piecewise Linear Quadratic Optimal Control

Rantzer, Anders LU and Johansson, Mikael LU (2000) In IEEE Transactions on Automatic Control 45(4). p.629-637
Abstract
The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semidefinite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex optimization problem using the given control law. A compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
optimal control, semidefinite programming, Nonlinear systems
in
IEEE Transactions on Automatic Control
volume
45
issue
4
pages
629 - 637
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:0034171765
ISSN
0018-9286
DOI
10.1109/9.847100
language
English
LU publication?
yes
id
71b4eace-e92e-412c-ae02-d62f729fd179 (old id 162930)
date added to LUP
2007-07-11 08:36:54
date last changed
2017-11-05 04:26:21
@article{71b4eace-e92e-412c-ae02-d62f729fd179,
  abstract     = {The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semidefinite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex optimization problem using the given control law. A compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy},
  author       = {Rantzer, Anders and Johansson, Mikael},
  issn         = {0018-9286},
  keyword      = {optimal control,semidefinite
programming,Nonlinear systems},
  language     = {eng},
  number       = {4},
  pages        = {629--637},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Automatic Control},
  title        = {Piecewise Linear Quadratic Optimal Control},
  url          = {http://dx.doi.org/10.1109/9.847100},
  volume       = {45},
  year         = {2000},
}