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When Do Potential Functions Exist in Heterogeneous Routing Games?
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
University of California at Berkeley.
University of California at Berkeley.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9940-5929
2014 (English)Report (Other academic)
Abstract [en]

We study a heterogeneous routing game in which vehicles might belong to more than one type. The type determines the cost of traveling along an edge as a function of the flow of various types of vehicles over that edge. We relax the assumptions needed for the existence of a Nash equilibrium in this heterogeneous routing game. We extend the available results to present necessary and sufficient conditions for the existence of a potential function. We characterize a set of tolls that guarantee the existence of a potential function when only two types of users are participating in the game. We present an upper bound for the price of anarchy (i.e., the worst-case ratio of the social cost calculated for a Nash equilibrium over the social cost for a socially optimal flow) for the case in which only two types of players are participating in a game with affine edge cost functions. A heterogeneous routing game with vehicle platooning incentives is used as an example throughout the article to clarify the concepts and to validate the results.

Place, publisher, year, edition, pages
2014.
Series
TRITA-EE, ISSN 1653-5146 ; 2014:009
Keyword [en]
Heterogeneous Routing Game, Nash Equilibrium, Potential Functions, Optimization
National Category
Control Engineering Transport Systems and Logistics
Identifiers
URN: urn:nbn:se:kth:diva-141199OAI: oai:DiVA.org:kth-141199DiVA: diva2:695605
Note

QC 20140213

Available from: 2014-02-11 Created: 2014-02-11 Last updated: 2014-02-21Bibliographically approved
In thesis
1. Decentralized Control of Networked Systems: Information Asymmetries and Limitations
Open this publication in new window or tab >>Decentralized Control of Networked Systems: Information Asymmetries and Limitations
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Designing local controllers for networked systems is challenging, because in these systems each local controller can often access only part of the overall information on system parameters and sensor measurements. Traditional control design cannot be easily applied due to the unconventional information patterns, communication network imperfections, and design procedure complexities. How to control large-scale systems is of immediate societal importance as they appear in many emerging applications, such as intelligent transportation systems, smart grids, and energy-efficient buildings. In this thesis, we make three contributions to the problem of designing networked controller under information asymmetries and limitations.

In the first contribution, we investigate how to design local controllers to optimize a cost function using only partial knowledge of the model governing the system. Specifically, we derive some fundamental limitations in the closed-loop performance when the design of each controller only relies on local plant model information. Results are characterized in the structure of the networked system as well as in the available model information. Both deterministic and stochastic formulations are considered for the closed-loop performance and the available information. In the second contribution of the thesis, we study decision making in transportation systems using heterogeneous routing and congestion games. It is shown that a desirable global behavior can emerge from simple local strategies used by the drivers to choose departure times and routes. Finally, the third contribution is a novel stochastic sensor scheduling policy for ad-hoc networked systems, where a varying number of control loops are active at any given time. It is shown that the policy provides stochastic guarantees for the network resources dynamically allocated to each loop.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. xii, 84 p.
Series
TRITA-EE, ISSN 1653-5146 ; 2014:003
Keyword
Networked Control Systems, Decentralized Control, Limited Model Information, Transportation Systems, Sensor Scheduling
National Category
Control Engineering Transport Systems and Logistics Communication Systems
Identifiers
urn:nbn:se:kth:diva-141492 (URN)978-91-7595-021-1 (ISBN)
Public defence
2014-03-21, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20140221

Available from: 2014-02-21 Created: 2014-02-17 Last updated: 2014-02-21Bibliographically approved

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Johansson, Karl Henrik

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