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Optimal control design under limited model information for discrete-time linear systems with stochastically-varying parameters
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9940-5929
2015 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 60, no 3, 684-699 p.Article in journal (Refereed) Published
Abstract [en]

The value of plant model information available in the control design process is discussed. We design optimal state-feedback controllers for interconnected discrete-time linear systems with stochastically-varying parameters. The parameters are assumed to be independently and identically distributed random variables in time. The design of each controller relies only on (i) exact local plant model information and (ii) statistical beliefs about the model of the rest of the system. We consider both finite-horizon and infinite-horizon quadratic cost functions. The optimal state-feedback controller is derived in both cases. The optimal controller is shown to be linear in the state and to depend on the model parameters and their statistics in a particular way. Furthermore, we study the value of model information in optimal control design using the performance degradation ratio which is defined as the supremum (over all possible initial conditions) of the ratio of the cost of the optimal controller with limited model information scaled by the cost of the optimal controller with full model information. An upper bound for the performance degradation ratio is presented for the case of fully-actuated subsystems. Comparisons are made between designs based on limited, statistical, and full model information. Throughout the paper, we use a power network example to illustrate concepts and results.

Place, publisher, year, edition, pages
2015. Vol. 60, no 3, 684-699 p.
Keyword [en]
Linear systems, Stochastically-Varying Parameters, Stochastic systems, Optimal control, Limited Model Information
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-141488DOI: 10.1109/TAC.2014.2343091ISI: 000350206000007Scopus ID: 2-s2.0-84923632690OAI: oai:DiVA.org:kth-141488DiVA: diva2:697240
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation
Note

QC 20150408. Updated from accepted to published.

Available from: 2014-02-17 Created: 2014-02-17 Last updated: 2017-12-06Bibliographically 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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