NP-completeness of sensor selection problems arising in partially observed discrete-event systems

doi:10.1109/TAC.2002.802762

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NP-completeness of sensor selection problems arising in partially observed discrete-event systems

Journal Article•DOI•

NP-completeness of sensor selection problems arising in partially observed discrete-event systems

Tae-Sic Yoo¹, Stéphane Lafortune¹•Institutions (1)

University of Michigan¹

07 Nov 2002-IEEE Transactions on Automatic Control (IEEE)-Vol. 47, Iss: 9, pp 1495-1499

TL;DR: The three properties of diagnosability, normality, and observability of discrete-event systems are considered and it is proved that these search problems are computationally hard by showing that the corresponding decision problems are NP-complete.

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Abstract: We consider the three properties of diagnosability, normality, and observability of discrete-event systems. In each case, we consider the problem of finding an observable event set with minimum cardinality such that the property under consideration holds. We prove that these search problems are computationally hard by showing that the corresponding decision problems are NP-complete.

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Journal Article•DOI•

Overview of fault diagnosis methods for Discrete Event Systems

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Janan Zaytoon¹, Stéphane Lafortune²•Institutions (2)

University of Reims Champagne-Ardenne¹, University of Michigan²

01 Dec 2013-Annual Reviews in Control

TL;DR: The aim of this paper is to review the state-of-the art of methods and techniques for fault diagnosis of Discrete Event Systems based on models that include faulty behaviour.

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295 citations

Cites methods from "NP-completeness of sensor selection..."

...…problem for off-line testing of diagnosability using diagnosers, the so-called ‘‘twin machine’’ technique (Jiang, Huang, Chandra, & Kumar, 2001; Yoo & Lafortune, 2002a) was introduced to provide a worst-case polynomial test in the number of states of the system for diagnosability, without…...
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...…different approaches have been proposed to select a minimal subset of sensors (Debouk, Lafortune, & Teneketzis, 2002; Jiang, Kumar, & Garcia, 2003; Yoo & Lafortune, 2002b), a least expensive set of sensors (Ribot, Pencolé, & Combacau, 2008), or an optimal sensor configuration to balance the…...
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Journal Article•DOI•

Sensor Placement for Fault Diagnosis

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Mattias Krysander¹, Erik Frisk¹•Institutions (1)

Linköping University¹

01 Nov 2008

TL;DR: An algorithm is developed for computing which sensors to add to meet a diagnosis requirement specification concerning fault detectability and fault isolability based only on the structural information in a model, which means that possibly large and nonlinear differential-algebraic models can be handled in an efficient manner.

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Abstract: An algorithm is developed for computing which sensors to add to meet a diagnosis requirement specification concerning fault detectability and fault isolability. The method is based only on the structural information in a model, which means that possibly large and nonlinear differential-algebraic models can be handled in an efficient manner. The approach is exemplified on a model of an industrial valve where the benefits and properties of the method are clearly shown.

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183 citations

Cites background from "NP-completeness of sensor selection..."

...and [18] and [19] where an optimization problem related to sensor selection is studied....
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Journal Article•DOI•

A modified monkey algorithm for optimal sensor placement in structural health monitoring

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Ting-Hua Yi¹, Hong-Nan Li¹, Xu-Dong Zhang¹•Institutions (1)

Dalian University of Technology¹

30 Aug 2012-Smart Materials and Structures

TL;DR: Results showed that the innovations in the MA proposed in this paper could improve the convergence of the algorithm and the method is effective in solving combinatorial optimization problems such as optimal sensor placement.

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Abstract: Proper placement of sensors plays a key role in construction and implementation of an effective structural health monitoring (SHM) system. This paper outlines a novel methodology called the modified monkey algorithm (MA) for the optimum design of SHM system sensor arrays, which is very different from the conventional method and is simple to implement. The integer coding method instead of the binary coding method is proposed to code the solution. The Euclidean distance operator and the stochastic perturbation mechanism of the harmony search algorithm are employed to improve the local and global search capability. A computational case of a high-rise building has been implemented to demonstrate the effectiveness of the modified method. The obtained sensor placements using the modified MA are compared with those gained by the existing MA using the integer coding method and the famous forward sequential sensor placement algorithm. Results showed that the innovations in the MA proposed in this paper could improve the convergence of the algorithm and the method is effective in solving combinatorial optimization problems such as optimal sensor placement.

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122 citations

Journal Article•

Fault Diagnosis with Static and Dynamic Observers

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Franck Cassez¹, Stavros Tripakis²•Institutions (2)

Centre national de la recherche scientifique¹, Cadence Design Systems²

01 Dec 2008-Fundamenta Informaticae

TL;DR: It is proved that amost permissive finite-state observer can be computed in doubly exponential time, using a game-theoretic approach, and further investigate optimization problems for dynamic observers and define a notion of cost of an observer.

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Abstract: We study sensor minimization problems in the context of fault diagnosis. Fault diagnosis consists in synthesizing a diagnoser that observes a given plant and identifies faults in the plant as soon as possible after their occurrence. Existing literature on this problem has considered the case of fixed static observers, where the set of observable events is fixed and does not change during execution of the system. In this paper, we consider static observers where the set of observable events is not fixed, but needs to be optimized (e.g., minimized in size). We also consider dynamic observers, where the observer can "switch" sensors on or off, thus dynamically changing the set of events it wishes to observe. It is known that checking diagnosability (i.e., whether a given observer is capable of identifying faults) can be solved in polynomial time for static observers, and we show that the same is true for dynamic ones. On the other hand, minimizing the number of (static) observable events required to achieve diagnosability is NP-complete. We show that this is true also in the case of mask-based observation, where some events are observable but not distinguishable. For dynamic observers' synthesis, we prove that amost permissive finite-state observer can be computed in doubly exponential time, using a game-theoretic approach. We further investigate optimization problems for dynamic observers and define a notion of cost of an observer. We show how to compute an optimal observer using results on mean-payoff games by Zwick and Paterson.

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101 citations

Journal Article•DOI•

Active Acquisition of Information for Diagnosis and Supervisory Control of Discrete Event Systems

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David Thorsley¹, Demosthenis Teneketzis²•Institutions (2)

University of Washington¹, University of Michigan²

01 Dec 2007-Discrete Event Dynamic Systems

TL;DR: The problems of fault diagnosis and supervisory control in discrete event systems through the context of a new observation paradigm is considered and a limited lookahead algorithm for computational savings is proposed.

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Abstract: This paper considers the problems of fault diagnosis and supervisory control in discrete event systems through the context of a new observation paradigm. For events that are considered observable, a cost is incurred each time a sensor is activated in an attempt to make an event observation. In such a situation the best strategy is to perform an "active acquisition" of information, i.e. to choose which sensors need to be activated based on the information state generated from the previous readings of the system. Depending on the sample path executed by the system, different sensors may be turned on or off at different stages of the process. We consider the active acquisition of information problem for both logical and stochastic discrete event systems. We consider three classes of increasing complexity: firstly, for acyclic systems where events are synchronized to clock ticks; secondly, for acyclic untimed systems; and lastly, for general cyclic automata. For each of these cases we define a notion of information state for the problem, determine conditions for the existence of an optimal policy, and construct a dynamic program to find an optimal policy where one exists. For large systems, a limited lookahead algorithm for computational savings is proposed.

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74 citations

Cites background from "NP-completeness of sensor selection..."

...A problem related to the verification of the diagnosability property is the sensor selection problem for DES (Debouk et al. 2002; Jiang et al. 2003; Yoo and Lafortune 2002a)....
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...Furthermore, we can test all remaining diagnoser states to see if the they are non-diagnosable (Yoo and Lafortune 2002b; Jiang et al. 2001) and assign infinite cost to any non-diagnosable state....
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...A problem related to the verification of the diagnosability property is the sensor selection problem for DES (Debouk et al. 2002; Jiang et al. 2003; Yoo and Lafortune 2002a )....
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...... (Debouk et al. 2002; Ding et al. 2002; Holloway and Chand 1994; Jiang et al. 2001, 2003; Khanna 1973; Kumar and Varaiya 1986; Kushner 1964, 1971; Lafortune et al. 2001; Lunze and Schroder 2001; Meier III et al. 1967 ;P encole2000; Pollard 2002; Rago et al. 1996; Roze and Cordier 1998; Sampath et al. 1995; Teneketzis 1996; Teneketzis and Andersland 2000; Thorsley and Teneketzis 2005; Witsenhausen 1971, 1975 ;Y oo and Garcia2003; ......
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...…Sampath et al. 1995; Teneketzis 1996; Teneketzis and Andersland 2000; Thorsley and Teneketzis 2005; Witsenhausen 1971, 1975; Yoo and Garcia 2003; Yoo and Lafortune 2002a), the objective is to select the fixed observation mask that minimizes the cost associated with purchasing sensors that are…...
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References

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Johnson: Computers and Intractability-A Guide to the Theory of NP-Completeness

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Michael Randolph Garey

01 Jan 1979

42,654 citations

Book•

Computers and Intractability: A Guide to the Theory of NP-Completeness

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Michael Randolph Garey, David S. Johnson

01 Jan 1979

TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.

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Abstract: This is the second edition of a quarterly column the purpose of which is to provide a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NP-Completeness,’’ W. H. Freeman & Co., San Francisco, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed. Readers having results they would like mentioned (NP-hardness, PSPACE-hardness, polynomial-time-solvability, etc.), or open problems they would like publicized, should send them to David S. Johnson, Room 2C355, Bell Laboratories, Murray Hill, NJ 07974, including details, or at least sketches, of any new proofs (full papers are preferred). In the case of unpublished results, please state explicitly that you would like the results mentioned in the column. Comments and corrections are also welcome. For more details on the nature of the column and the form of desired submissions, see the December 1981 issue of this journal.

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40,020 citations

Book•

Introduction to Algorithms

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Thomas H. Cormen¹, Charles E. Leiserson¹, Ronald L. Rivest¹•Institutions (1)

Massachusetts Institute of Technology¹

01 Jan 1990

TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.

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Abstract: From the Publisher: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures. Like the first edition,this text can also be used for self-study by technical professionals since it discusses engineering issues in algorithm design as well as the mathematical aspects. In its new edition,Introduction to Algorithms continues to provide a comprehensive introduction to the modern study of algorithms. The revision has been updated to reflect changes in the years since the book's original publication. New chapters on the role of algorithms in computing and on probabilistic analysis and randomized algorithms have been included. Sections throughout the book have been rewritten for increased clarity,and material has been added wherever a fuller explanation has seemed useful or new information warrants expanded coverage. As in the classic first edition,this new edition of Introduction to Algorithms presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers. Further,the algorithms are presented in pseudocode to make the book easily accessible to students from all programming language backgrounds. Each chapter presents an algorithm,a design technique,an application area,or a related topic. The chapters are not dependent on one another,so the instructor can organize his or her use of the book in the way that best suits the course's needs. Additionally,the new edition offers a 25% increase over the first edition in the number of problems,giving the book 155 problems and over 900 exercises thatreinforcethe concepts the students are learning.

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21,651 citations

"NP-completeness of sensor selection..." refers background or methods in this paper

...We briefly recall some necessary results and definitions from complexity theory (see [ 6 ] and [7] for further details)....
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...[ 6 ] C. G. Cassandras and S. Lafortune, Introduction to Discrete Event Sys-...
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Johnson: computers and intractability: a guide to the theory of np- completeness (freeman

[...]

Michael Randolph Garey

01 Jan 1979

12,336 citations

Book•

Introduction to Discrete Event Systems

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Christos G. Cassandras¹, Stéphane Lafortune²•Institutions (2)

Boston University¹, Carnegie Mellon University²

30 Sep 1999

TL;DR: This edition includes recent research results pertaining to the diagnosis of discrete event systems, decentralized supervisory control, and interval-based timed automata and hybrid automata models.

...read moreread less

Abstract: Introduction to Discrete Event Systems is a comprehensive introduction to the field of discrete event systems, offering a breadth of coverage that makes the material accessible to readers of varied backgrounds. The book emphasizes a unified modeling framework that transcends specific application areas, linking the following topics in a coherent manner: language and automata theory, supervisory control, Petri net theory, Markov chains and queuing theory, discrete-event simulation, and concurrent estimation techniques. This edition includes recent research results pertaining to the diagnosis of discrete event systems, decentralized supervisory control, and interval-based timed automata and hybrid automata models.

...read moreread less

4,330 citations

"NP-completeness of sensor selection..." refers background or methods in this paper

...More specifically, we consider the properties of diagnosability, observability, and normality that have been characterized in the discrete-event systems literature; see, e.g., [ 1 ] and [2]....
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...The language generated by is denoted by and defined in the usual manner [ 1 ]....
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...The readers are directed to [ 1 ] for more complete introductory materials....
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...[ 1 ] M. Sampath, R. Sengupta, K. Sinnamohideen, S. Lafortune, and D....
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...An immediate consequence of Theorem 3 is that the corresponding problem for the property of co-observability [10], [ 1 ], [11] is also NP-complete....
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