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Hybrid Control Laws From Convex Dynamic Programming

Hedlund, Sven LU and Rantzer, Anders LU (2000) In Proceedings of the 39th IEEE Conference on Decision and Control, 2000. 1. p.472-477
Abstract
In a previous paper, we showed how classical ideas for dynamicprogramming in discrete networks can be adapted to hybrid systems. The approach is based on discretization of the continuous Bellman inequality which gives a lower bound on the optimal cost. The lower bound is maximized by linear programming to get an approximation of the optimal solution.In this paper, we apply ideas from infinite-dimensional convex analysis to get an inequality which is dual to the well known Bellman inequality. The result is a linear programming problem that gives an estimate of the approximation error in the previous numerical approaches.
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
duality (mathematics), discrete time systems, convex programming, dynamic programming, optimal control, linear programming
in
Proceedings of the 39th IEEE Conference on Decision and Control, 2000.
volume
1
pages
472 - 477
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • Scopus:0034439605
ISBN
0-7803-6638-7
DOI
10.1109/CDC.2000.912810
language
English
LU publication?
yes
id
ab5cc584-b089-4bce-8933-01e662b15479 (old id 538016)
date added to LUP
2007-09-19 15:49:27
date last changed
2016-10-13 04:45:56
@misc{ab5cc584-b089-4bce-8933-01e662b15479,
  abstract     = {In a previous paper, we showed how classical ideas for dynamicprogramming in discrete networks can be adapted to hybrid systems. The approach is based on discretization of the continuous Bellman inequality which gives a lower bound on the optimal cost. The lower bound is maximized by linear programming to get an approximation of the optimal solution.In this paper, we apply ideas from infinite-dimensional convex analysis to get an inequality which is dual to the well known Bellman inequality. The result is a linear programming problem that gives an estimate of the approximation error in the previous numerical approaches.},
  author       = {Hedlund, Sven and Rantzer, Anders},
  isbn         = {0-7803-6638-7},
  keyword      = {duality (mathematics),discrete time systems,convex programming,dynamic programming,optimal control,linear programming},
  language     = {eng},
  pages        = {472--477},
  publisher    = {ARRAY(0xc56a050)},
  series       = {Proceedings of the 39th IEEE Conference on Decision and Control, 2000.},
  title        = {Hybrid Control Laws From Convex Dynamic Programming},
  url          = {http://dx.doi.org/10.1109/CDC.2000.912810},
  volume       = {1},
  year         = {2000},
}