Input Signal Design for Discrete Event Model Based Batch Process Diagnosis

IFAC Proceedings Volumes

2011

Max-plus linear systems belong to a special class of discrete-event systems that consists of systems with synchronization but no choice. Our focus in this paper is on stochastic max-plus linear systems, i.e., perturbed systems that are linear in the max-plus algebra. One interesting topic is the identification of such systems. Previous works report on a method for identifying the parameters of a state space model for a stochastic max-plus linear system from measured data. However, due to the structure of such systems, this method results in a complex identification problem. Therefore, the aim of this paper is to decrease the computational complexity and the computation time of this problem. To this end, we use an approximation approach that is based on the higher-order raw moments of a random variable. This method results in a less complex problem that can be solved efficiently using gradient search techniques.

Section: Identification Of Stochastic Max-plus Linear Systemsmentioning

confidence: 99%

An Approximation Approach for Identification of Stochastic Max-Plus Linear Systems

Farahani

IFAC Proceedings Volumes

2011

“…Suppose that for a given MPL DES of the form (6) we have an input-state sequence {(u(k), x(k)} N k=1 , and that we want to identify the system parametersθ andλ from this sequence. We make the standard assumption that the inputstate sequence is sufficiently rich to capture all the relevant information about the system (see also [17]). We consider the following identification problem:…”

Section: Identification Of Stochastic Mpl Systemsmentioning

confidence: 99%

“…In [7,16,17,18] state space identification methods have been derived in which the internal structure of the system is assumed to be completely known and the state is assumed to be measurable. In [7] we assumed that only input-output sequences were available.…”

Section: Introductionmentioning

confidence: 99%

Identification of stochastic max-plus-linear systems

2003 European Control Conference (ECC)

Verdult

2003

We present a method to identify the parameters of a state space model for a max-plus-linear discrete event system from measured data. Previous papers report on results with noise-free measured data. In this paper we extend this to identification for perturbed max-plus-linear systems in a stochastic setting. The approach is based on recasting the identification problem as an optimization problem. We show that under quite general conditions the resulting optimization problems can be solved very efficiently using gradient search techniques.

“…We make the standard assumption of system identification that all modes of the system are observable and that the input-output sequence is sufficiently rich to capture all the relevant information about the system (see also [14]). For the sake of simplicity of notation we assume that the given system is SISO.…”

Section: Problem Statementmentioning

confidence: 99%

“…In [13,14] a state space identification method has been derived in which the internal structure of the system is assumed to be completely known and the state is assumed to be measurable. In this paper, we assume that only inputoutput sequences are available (i.e., we do not require measurements of the (full) state of the system 2 ).…”

Section: Introduction 1overviewmentioning

confidence: 99%

State space identification of max-plus-linear discrete event systems from input-output data

Proceedings of the 41st IEEE Conference on Decision and Control, 2002.

Verdult

We present a method to identify the parameters of a state space model for a max-plus-linear discrete event system from input-output sequences. The approach is based on recasting the identification problem as an optimization problem over the solution set of an extended linear complementarity problem. Recently, we have shown that such a problem can be solved much more efficiently than previously by using a mixed integer programming approach. The resulting algorithm allows us to identify a state space model of a max-plus-linear discrete event system from input-output data. This method works for both structured and fully parameterized state space identification. In addition, we also obtain an estimate of the state sequence. Introduction 1.OverviewA discrete event system (DES) is a dynamic, asynchronous system, where the state transitions are initiated by events that occur at discrete time instants. Typical examples of DES are flexible manufacturing systems, telecommunication networks, parallel processing systems, traffic control systems, and logistic systems. There exist many different modeling and analysis frameworks for DES such as Petri nets, finite state machines, automata, languages, process algebra, computer models, etc. In this paper we consider the class of DES with synchronization but no concurrency. Such DES can be described by models that are "linear" in the max-plus algebra [1], and therefore, they are called maxplus-linear (MPL) DES.