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Dynamic Optimization of Transportation Networks with Delays

Heyden, Martin LU (2020) In Research Reports TFRT-3275
Abstract
The topic of this thesis is the optimal control of transportation networks. The problem studied is a dynamical extension of a classical problem in economics, in which the objective is to distribute goods to maximize welfare, whilst satisfying constraints on production and consumption. The main contribution is to show that for a class of welfare functions and dynamics, the optimal control is highly structured, and can be implemented in a way that scales gracefully with network size.
More specifically, it is shown that if the underlying transportation network is structured by a string graph with delays on the edges, an LQ optimal controller can be found by explicitly constructing the solution to a Riccati equation. Next the problem is... (More)
The topic of this thesis is the optimal control of transportation networks. The problem studied is a dynamical extension of a classical problem in economics, in which the objective is to distribute goods to maximize welfare, whilst satisfying constraints on production and consumption. The main contribution is to show that for a class of welfare functions and dynamics, the optimal control is highly structured, and can be implemented in a way that scales gracefully with network size.
More specifically, it is shown that if the underlying transportation network is structured by a string graph with delays on the edges, an LQ optimal controller can be found by explicitly constructing the solution to a Riccati equation. Next the problem is studied from a user perspective. A method to compensate the users in the network, so that that their choices of levels are also the social optimum is derived. Finally the results are extended to handle directed tree graphs, more general cost functions, and variable production in the network.
In all cases the optimal control can be found by sweeping through the graph once, calculating aggregate utilities and levels. This gives a serial implementation, that is suitable for systems were the is no need for high sample times, such as district heating systems and transportation networks. (Less)
Abstract (Swedish)
The topic of this thesis is the optimal control of transportation networks. The problem studied is a dynamical extension of a classical problem in economics, in which the objective is to distribute goods to maximize welfare, whilst satisfying constraints on production and consumption. The main contribution is to show that for a class of welfare functions and dynamics, the optimal control is highly structured, and can be implemented in a way that scales gracefully with network size.

More specifically, it is shown that if the underlying transportation network is structured by a string graph with delays on the edges, an LQ optimal controller can be found by explicitly constructing the solution to a Riccati equation. Next the problem... (More)
The topic of this thesis is the optimal control of transportation networks. The problem studied is a dynamical extension of a classical problem in economics, in which the objective is to distribute goods to maximize welfare, whilst satisfying constraints on production and consumption. The main contribution is to show that for a class of welfare functions and dynamics, the optimal control is highly structured, and can be implemented in a way that scales gracefully with network size.

More specifically, it is shown that if the underlying transportation network is structured by a string graph with delays on the edges, an LQ optimal controller can be found by explicitly constructing the solution to a Riccati equation. Next the problem is studied from a user perspective. A method to compensate the users in the network, so that that their choices of levels are also the social optimum is derived. Finally the results are extended to handle directed tree graphs, more general cost functions, and variable production in the network.

In all cases the optimal control can be found by sweeping through the graph once, calculating aggregate utilities and levels. This gives a serial implementation, that is suitable for systems were the is no need for high sample times, such as district heating systems and transportation networks. (Less)
Please use this url to cite or link to this publication:
author
supervisor
organization
publishing date
type
Thesis
publication status
epub
subject
in
Research Reports TFRT-3275
pages
102 pages
publisher
Department of Automatic Control, Lund Institute of Technology, Lund University
ISSN
0280-5316
project
Structured Controllers for Transportation
language
English
LU publication?
yes
id
5579ee12-3a32-4f8d-8f35-0505e7438722
date added to LUP
2020-03-18 16:19:03
date last changed
2020-03-23 16:26:18
@misc{5579ee12-3a32-4f8d-8f35-0505e7438722,
  abstract     = {The topic of this thesis is the optimal control of transportation networks. The problem studied is a dynamical extension of a classical problem in economics, in which the objective is to distribute goods to maximize welfare, whilst satisfying constraints on production and consumption. The main contribution is to show that for a class of welfare functions and dynamics, the optimal control is highly structured, and can be implemented in a way that scales gracefully with network size.<br/> More specifically, it is shown that if the underlying transportation network is structured by a string graph with delays on the edges, an LQ optimal controller can be found by explicitly constructing the solution to a Riccati equation. Next the problem is studied from a user perspective. A method to compensate the users in the network, so that that their choices of levels are also the social optimum is derived. Finally the results are extended to handle directed tree graphs, more general cost functions, and variable production in the network.<br/> In all cases the optimal control can be found by sweeping through the graph once, calculating aggregate utilities and levels. This gives a serial implementation, that is suitable for systems were the is no need for high sample times, such as district heating systems and transportation networks.},
  author       = {Heyden, Martin},
  issn         = {0280-5316},
  language     = {eng},
  month        = {03},
  note         = {Licentiate Thesis},
  publisher    = {Department of Automatic Control, Lund Institute of Technology, Lund University},
  series       = {Research Reports TFRT-3275},
  title        = {Dynamic Optimization of Transportation Networks with Delays},
  url          = {https://lup.lub.lu.se/search/ws/files/77330961/lic_without_unpubl.pdf},
  year         = {2020},
}