Input signal design for identification of max-plus-linear systems

Schullerus, Gernot; Krebs, Volker; Schutter, Bart De; Boom, T.J.J. van den

doi:10.1016/j.automatica.2006.01.025

Cited by 19 publications

(17 citation statements)

References 11 publications

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“…MPC determines the control inputs by solving an optimisation problem in which the performance of the system for a finite step is formulated. In addition to MPC, a theory of adaptive control is applied in Schullerus et al (2006) and Boom et al (2003). In particular, Boom et al (2003) realises on-line control by combining a method for system identification and MPC, which they call adaptive MPC.…”

Section: Methodologiesmentioning

confidence: 99%

Modeling Methods Based on Discrete Algebraic Systems

Goto¹

2010

Discrete Event Simulations

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Section: Methodologiesmentioning

confidence: 99%

Modeling Methods Based on Discrete Algebraic Systems

Goto¹

2010

Discrete Event Simulations

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“…The behavior of this class can be represented by a pair of simple equations in max-plus algebra, called the state-space representation. Since this is similar to the representation in modern control theory, a number of research developments in modern control theory have been applied to various kinds of scheduling problems [7]- [9]. The state-space representation consists of a pair of state and output equations.…”

Section: Introductionmentioning

confidence: 99%

“…D.1798 in modern control theory have been applied to various kinds of scheduling problems [7]- [9]. The state-space representation consists of a pair of state and output equations.…”

Section: Introductionmentioning

confidence: 99%

High-Speed Computation of the Kleene Star in Max-Plus Algebraic System Using a Cell Broadband Engine

Goto

2010

IEICE Trans. Inf. & Syst.

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SUMMARYThis research addresses a high-speed computation method for the Kleene star of the weighted adjacency matrix in a max-plus algebraic system. We focus on systems whose precedence constraints are represented by a directed acyclic graph and implement it on a Cell Broadband Engine TM (CBE) processor. Since the resulting matrix gives the longest travel times between two adjacent nodes, it is often utilized in scheduling problem solvers for a class of discrete event systems. This research, in particular, attempts to achieve a speedup by using two approaches: parallelization and SIMDization (Single Instruction, Multiple Data), both of which can be accomplished by a CBE processor. The former refers to a parallel computation using multiple cores, while the latter is a method whereby multiple elements are computed by a single instruction. Using the implementation on a Sony PlayStation 3 TM equipped with a CBE processor, we found that the SIMDization is effective regardless of the system's size and the number of processor cores used. We also found that the scalability of using multiple cores is remarkable especially for systems with a large number of nodes. In a numerical experiment where the number of nodes is 2000, we achieved a speedup of 20 times compared with the method without the above techniques. key words: directed acyclic graph, max-plus algebra, scheduling, parallel processing, vector processing, Cell Broadband Engine IntroductionThis research aims to develop a fast computation method for the representation matrix in a state-space representation in max-plus algebra [1], [2]. This approach is often used in solvers for a class of scheduling problems. Specifically, we focus on quickly calculating the transition matrix, which requires a high computation load using this approach. For the computation, we use a processor called the Cell Broadband Engine (CBE) [3]-[6], which has instructions for vector operations and parallel processing.The features of the class of focused systems are: (1) parallel execution of multiple tasks, (2) synchronization of multiple tasks, and (3) no-concurrency between the previous or succeeding job. Such systems can also be explained as repetitive discrete event systems in which a number of jobs are processed sequentially using the same facilities in FIFO order. We assume that the precedence relationships of the system are described by a Directed Acyclic Graph (DAG). The behavior of this class can be represented by a pair of simple equations in max-plus algebra, called the state-space representation. Since this is similar to the representation in modern control theory, a number of research developments Manuscript received October 30, 2009. Manuscript revised January 29, 2010. † The author is with Nagaoka University of Technology, Nagaoka-shi, 940-2188 Japan.a) E-mail: hgoto@kjs.nagaokaut.ac.jp DOI: 10.1587/transinf.E93. D.1798 in modern control theory have been applied to various kinds of scheduling problems [7]- [9]. The state-space representation consists of a pair of state ...

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“…A possible method of change detection can be based on the identification of the holding times of Timed Event Graphs [24]. The assumption that all transitions are observable is taken (all transition firing times are measurable).…”

Section: Introductionmentioning

confidence: 99%

State estimation and detection of changes in time interval models

Declerck

Guezzi

2012

Discrete Event Dyn Syst

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This paper presents an estimation approach for Time Event Graphs such as P-Time Event Graphs and Time Stream Event Graphs. It is assumed that the nominal behavior is known and that transitions are partitioned as observable and unobservable transitions. The technique is applied to the detection of changes which are (possibly small) finite variations of dynamic models compared to this nominal behavior. The detected changes provide indications that can be used in future maintenance operations.Using the algebra of dioids, the approach uses a receding-horizon estimation of the greatest state and analyzes the consistency of the data.

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Input signal design for identification of max-plus-linear systems

Cited by 19 publications

References 11 publications

Modeling Methods Based on Discrete Algebraic Systems

Modeling Methods Based on Discrete Algebraic Systems

High-Speed Computation of the Kleene Star in Max-Plus Algebraic System Using a Cell Broadband Engine

State estimation and detection of changes in time interval models

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