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Decentralized Control of Networked Systems: Information Asymmetries and Limitations
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
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 [en]
Networked Control Systems, Decentralized Control, Limited Model Information, Transportation Systems, Sensor Scheduling
National Category
Control Engineering Transport Systems and Logistics Communication Systems
Identifiers
URN: urn:nbn:se:kth:diva-141492ISBN: 978-91-7595-021-1 (print)OAI: oai:DiVA.org:kth-141492DiVA: diva2:697250
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
List of papers
1. Optimal Structured Static State-Feedback Control Design with Limited Model Information for Fully-Actuated Systems
Open this publication in new window or tab >>Optimal Structured Static State-Feedback Control Design with Limited Model Information for Fully-Actuated Systems
2013 (English)In: Automatica, ISSN 0005-1098, Vol. 49, no 2, 326-337 p.Article in journal (Refereed) Published
Abstract [en]

We introduce the family of limited model information control design methods, which construct controllers by accessing the plant's model in a constrained way, according to a given design graph. We investigate the closed-loop performance achievable by such control design methods for fully-actuated discrete-time linear time-invariant systems, under a separable quadratic cost. We restrict our study to control design methods which produce structured static state feedback controllers, where each subcontroller can at least access the state measurements of those subsystems that affect its corresponding subsystem. We compute the optimal control design strategy (in terms of the competitive ratio and domination metrics) when the control designer has access to the local model information and the global interconnection structure of the plant-to-be-controlled. Finally, we study the trade-off between the amount of model information exploited by a control design method and the best closed-loop performance (in terms of the competitive ratio) of controllers it can produce.

Keyword
Linear control systems, Optimal control, Interconnected systems, Decentralized control, Large-scale systems, Structural constraints
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-108264 (URN)10.1016/j.automatica.2012.10.004 (DOI)000315003100002 ()2-s2.0-84872026002 (Scopus ID)
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation
Note

QC 20130208

Available from: 2012-12-20 Created: 2012-12-20 Last updated: 2014-02-21Bibliographically approved
2. Dynamic Control Design Based on Limited Model Information
Open this publication in new window or tab >>Dynamic Control Design Based on Limited Model Information
2011 (English)In: Proceedings of the 49th Annual Allerton Conference on Communication, Control, and Computing, 2011, 1576-1583 p.Conference paper, Published paper (Refereed)
Abstract [en]

The design of optimal H_2 dynamic controllers for interconnected linear systems using limited plant model information is considered. Control design strategies based on various degrees of model information are compared using the competitive ratio as a performance metric, that is, the worst case control performance for a given design strategy normalized with the optimal control performance based on full model information. An explicit minimizer of the competitive ratio is found. It is shown that this control design strategy is not dominated by any other strategy with the same amount of model information. The result applies to a class of system interconnections and design information characterized through given plant, control, and design graphs.

National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-52475 (URN)10.1109/Allerton.2011.6120356 (DOI)2-s2.0-84856102500 (Scopus ID)978-1-4577-1817-5 (ISBN)
Conference
Annual Allerton Conference on Communication, Control, and Computing (Allerton 2011)
Note
© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20120111Available from: 2012-01-11 Created: 2011-12-18 Last updated: 2014-02-21Bibliographically approved
3. Decentralized Disturbance Accommodation with Limited Plant Model Information
Open this publication in new window or tab >>Decentralized Disturbance Accommodation with Limited Plant Model Information
2013 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 51, no 2, 1543-1573 p.Article in journal (Refereed) Published
Abstract [en]

The design of optimal disturbance accommodation and servomechanism controllers with limited plant model information is studied in this paper. We consider discrete-time linear time-invariant systems that are fully actuated and composed of scalar subsystems, each of which is controlled separately and influenced by a scalar disturbance. Each disturbance is assumed to be generated by a system with known dynamics and unknown initial conditions. We restrict ourselves to control design methods that produce structured dynamic state feedback controllers where each subcontroller, at least, has access to the state measurements of those subsystems that can affect its corresponding subsystem. The performance of such control design methods is compared using a metric called the competitive ratio, which is the worst-case ratio of the cost of a given control design strategy to the cost of the optimal control design with full model information. We find an explicit minimizer of the competitive ratio and show that it is undominated, that is, there is no other control design strategy that performs better for all possible plants while having the same worst-case ratio. This optimal controller can be separated into a static feedback law and a dynamic disturbance observer. For step disturbances, it is shown that this structure corresponds to proportional-integral control.

Keyword
Linear optimal control problem, Linear-quadratic problems, Problems with incomplete information, Large scale system
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-116716 (URN)10.1137/110860112 (DOI)000318406900029 ()2-s2.0-84879644319 (Scopus ID)
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation
Note

QC 20130618

Available from: 2013-01-24 Created: 2013-01-24 Last updated: 2014-02-21Bibliographically approved
4. Optimal Control Design under Structured Model Information Limitation Using Adaptive Algorithms
Open this publication in new window or tab >>Optimal Control Design under Structured Model Information Limitation Using Adaptive Algorithms
2012 (English)Article in journal (Refereed) Submitted
Abstract [en]

Networked control strategies based on limited information about the plant model usually results in worse closed-loop performance than optimal centralized control with full plant model information. Recently, this fact has been established by utilizing the concept of competitive ratio, which is defined as the worst case ratio of the cost of a control design with limited model information to the cost of the optimal control design with full model information. In this paper, we show that with an adaptive networked controller with limited plant model information, it is indeed possible to achieve a competitive ratio equal to one. We show that an adaptive controller introduced by Campi and Kumar asymptotically achieves closed-loop performance equal to the optimal centralized controller with full model information. The plant model considered in the paper belongs to a compact set of stochastic linear time-invariant systems and the closed loop performance measure is the ergodic mean of a quadratic function of the state and control input. We illustrate the applicability of the results numerically on a vehicle platooning problem.

Keyword
Interconnected systems, Adaptive Control, Optimal Control, Structural Constraints
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-141486 (URN)
Note

QS 2015

Available from: 2014-02-17 Created: 2014-02-17 Last updated: 2015-03-27Bibliographically approved
5. Optimal H-Infinity Control Design under Model Information Limitations and State Measurement Constraints
Open this publication in new window or tab >>Optimal H-Infinity Control Design under Model Information Limitations and State Measurement Constraints
2013 (English)In: 2013 IEEE 52nd Annual Conference on Decision and Control (CDC), IEEE conference proceedings, 2013, 6218-6225 p.Conference paper, Published paper (Refereed)
Abstract [en]

We present a suboptimal control design algorithm for a family of continuous-time parameter-dependent linear systems that are composed of interconnected subsystems. We are interested in designing the controller for each subsystem such that it only utilizes partial state measurements (characterized by a directed graph called the control graph) and limited model parameter information (characterized by the design graph). The algorithm is based on successive local minimizations and maximizations (using the subgradients) of the H∞-norm of the closed-loop transfer function with respect to the controller gains and the system parameters. We use a vehicle platooning example to illustrate the applicability of the results.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2013
Series
IEEE Conference on Decision and Control. Proceedings, ISSN 0743-1546
Keyword
H-Infinity Control, Limited Model Information, Decentralized Control, Subgradients
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-138594 (URN)10.1109/CDC.2013.6760872 (DOI)000352223507009 ()2-s2.0-84902330264 (Scopus ID)978-1-4673-5716-6 (ISBN)
Conference
52nd IEEE Conference on Decision and Control, CDC 2013; Florence; Italy; 10 December 2013 through 13 December 2013
Note

QC 20140207

Available from: 2013-12-20 Created: 2013-12-20 Last updated: 2015-12-08Bibliographically approved
6. Optimal control design under limited model information for discrete-time linear systems with stochastically-varying parameters
Open this publication in new window or tab >>Optimal control design under limited model information for discrete-time linear systems with stochastically-varying parameters
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.

Keyword
Linear systems, Stochastically-Varying Parameters, Stochastic systems, Optimal control, Limited Model Information
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-141488 (URN)10.1109/TAC.2014.2343091 (DOI)000350206000007 ()2-s2.0-84923632690 (Scopus ID)
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: 2015-04-08Bibliographically approved
7. When Do Potential Functions Exist in Heterogeneous Routing Games?
Open this publication in new window or tab >>When Do Potential Functions Exist in Heterogeneous Routing Games?
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.

Series
TRITA-EE, ISSN 1653-5146 ; 2014:009
Keyword
Heterogeneous Routing Game, Nash Equilibrium, Potential Functions, Optimization
National Category
Control Engineering Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-141199 (URN)
Note

QC 20140213

Available from: 2014-02-11 Created: 2014-02-11 Last updated: 2014-02-21Bibliographically approved
8. A Study of Truck Platooning Incentives Using a Congestion Game
Open this publication in new window or tab >>A Study of Truck Platooning Incentives Using a Congestion Game
2015 (English)In: IEEE transactions on intelligent transportation systems (Print), ISSN 1524-9050, E-ISSN 1558-0016, Vol. 16, no 2, 581-595 p., 6847185Article in journal (Refereed) Published
Abstract [en]

We introduce an atomic congestion game with two types of agents, namely, cars and trucks, to model the traffic flow on a road over various time intervals of the day. Cars maximize their utility by finding a tradeoff between the time they choose to use the road, the average velocity of the flow at that time, and the dynamic congestion tax that they pay for using the road. In addition to these terms, the trucks have an incentive for using the road at the same time as their peers because they have platooning capabilities, which allow them to save fuel. The dynamics and equilibria of this game-theoretic model for the interaction between car traffic and truck platooning incentives are investigated. We use traffic data from Stockholm, Sweden, to validate parts of the modeling assumptions and extract reasonable parameters for the simulations. We use joint strategy fictitious play and average strategy fictitious play to learn a pure strategy Nash equilibrium of this game. We perform a comprehensive simulation study to understand the influence of various factors, such as the drivers' value of time and the percentage of the trucks that are equipped with platooning devices, on the properties of the Nash equilibrium.

Keyword
Heavy-Duty Vehicle Platooning, Atomic Congestion Game, Pure Strategy Nash Equilibrium, Learning Algorithm
National Category
Control Engineering Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-141490 (URN)10.1109/TITS.2014.2329317 (DOI)000352282500005 ()2-s2.0-84926671782 (Scopus ID)
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationVINNOVA
Note

QC 20150504. Updated from accepted to published.

Available from: 2014-02-17 Created: 2014-02-17 Last updated: 2015-05-18Bibliographically approved
9. Stochastic Sensor Scheduling for Networked Control Systems
Open this publication in new window or tab >>Stochastic Sensor Scheduling for Networked Control Systems
2014 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 5, 1147-1162 p.Article in journal (Refereed) Published
Abstract [en]

Optimal sensor scheduling with applications to networked estimation and control systems is considered. We model sensor measurement and transmission instances using jumps between states of a continuous-time Markov chain. We introduce a cost function for this Markov chain as the summation of terms depending on the average sampling frequencies of the subsystems and the effort needed for changing the parameters of the underlying Markov chain. By minimizing this cost function through extending Brockett's recent approach to optimal control of Markov chains, we extract an optimal scheduling policy to fairly allocate the network resources among the control loops. We study the statistical properties of this scheduling policy in order to compute upper bounds for the closed-loop performance of the networked system, where several decoupled scalar subsystems are connected to their corresponding estimator or controller through a shared communication medium. We generalize the estimation results to observable subsystems of arbitrary order. Finally, we illustrate the developed results numerically on a networked system composed of several decoupled water tanks.

Keyword
Sensor scheduling, Markov processes, Sensor networks, Networked control and estimation, Stochastic optimal control
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-141491 (URN)10.1109/TAC.2014.2298733 (DOI)000335218900003 ()2-s2.0-84899652016 (Scopus ID)
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation
Note

QC 20140602

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

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