Dynamic Optimization of Transportation Networks with Delays
(2020) In Research Reports TFRT3275 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:
https://lup.lub.lu.se/record/5579ee123a324f8d8f350505e7438722
 author
 Heyden, Martin ^{LU}
 supervisor

 Anders Rantzer ^{LU}
 Richard Pates ^{LU}
 organization
 publishing date
 20200318
 type
 Thesis
 publication status
 epub
 subject
 in
 Research Reports TFRT3275
 pages
 102 pages
 publisher
 Department of Automatic Control, Lund Institute of Technology, Lund University
 ISSN
 02805316
 project
 Structured Controllers for Transportation
 language
 English
 LU publication?
 yes
 id
 5579ee123a324f8d8f350505e7438722
 date added to LUP
 20200318 16:19:03
 date last changed
 20200323 16:26:18
@misc{5579ee123a324f8d8f350505e7438722, 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 = {02805316}, language = {eng}, month = {03}, note = {Licentiate Thesis}, publisher = {Department of Automatic Control, Lund Institute of Technology, Lund University}, series = {Research Reports TFRT3275}, title = {Dynamic Optimization of Transportation Networks with Delays}, url = {https://lup.lub.lu.se/search/ws/files/77330961/lic_without_unpubl.pdf}, year = {2020}, }