Identification of piecewise affine systems based on statistical clustering technique

Nakada, Hayato; Takaba, Kiyotsugu; Katayama, Tohru

doi:10.1016/j.automatica.2004.12.005

Cited by 167 publications

(74 citation statements)

References 23 publications

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“…These main types of approaches were classified as optimisationbased, algebraic and recursive methods for Switched ARX (SARX) models, optimisationbased and clustering-based methods for PieceWise ARX (PWARX) models, and batch and recursive methods for state-space systems. According to Garulli et al (2012), a common feature of the approaches, which is present in works such as Vidal et al (2003), Roll et al (2004), Ferrari-Trecate et al (2003), Nakada et al (2005), Juloski et al (2005) and Bemporad et al (2005), is that they lead to suboptimal solutions to the problem of inferring a PWARX model from data, while keeping an affordable computational burden.…”

Section: A Brief Review Of the Multi-model Systemsmentioning

confidence: 99%

A simple multi-model prediction method

Strutzel

Bogle

2018

Chemical Engineering Research and Design

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The present work introduces a new multi-model state-space formulation called simultaneous multi-linear prediction (SMLP), which is suitable for systems with significant gain variation due to nonlinearity. Standard multi-model formulations usually make use of a partitioned state-space, i.e., a state-space that is divided into regions to shift parameters of the state update equation according to the current location of the state, with a view to having a better approximation of a nonlinear plant on each region. This multi-model framework, also known as linear hybrid systems framework, makes use of different boundaries or partition rules concepts, which vary from systems of linear inequalities, propositional logic rules, or a combination of these. This standard approach inevitably introduces discontinuities in the output prediction as the state update equation parameters shift noticeably. Instead, the SMLP is built by defining and updating multiple states simultaneously, thus eliminating the need for partitioning the state-input space into regions and associating with each region a different state update equation. Each state's contribution to the overall output is obtained according to the relative distance between their identification (or linearisation) point and the current operating point, in addition to a set of parameters obtained through regression analysis. Unlike the methods belonging to the hybrid systems framework, no discontinuities are introduced in the output prediction

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Section: A Brief Review Of the Multi-model Systemsmentioning

confidence: 99%

A simple multi-model prediction method

Strutzel

Bogle

2018

Chemical Engineering Research and Design

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“…It uses K‐means algorithm for clustering, and requires the piecewise linear function to be convex. Researchers use K‐means clustering technique or variations derived from that. The downside of this approach is that there is no guarantee that the union of regions obtained by clustering is able to cover the whole area of the original domain without gaps where the model is actually defined.…”

Section: Integration Of Scheduling and Control Based On Pwa Modelmentioning

confidence: 99%

An integrated framework for scheduling and control using fast model predictive control

Zhuge

Ierapetritou

2015

AIChE Journal

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in Wiley Online Library (wileyonlinelibrary.com) Integration of scheduling and control involves extensive information exchange and simultaneous decision making in industrial practice (Engell and Harjunkoski, Comput Chem Eng. 2012;47:121-133; Baldea and Harjunkoski I, Comput Chem Eng. 2014;71:377-390). Modeling the integration of scheduling and dynamic optimization (DO) at control level using mathematical programming results in a Mixed Integer Dynamic Optimization which is computationally expensive (Flores-Tlacuahuac and Grossmann, Ind Eng Chem Res. 2006;45(20):6698-6712). In this study, we propose a framework for the integration of scheduling and control to reduce the model complexity and computation time. We identify a piece-wise affine model from the first principle model and integrate it with the scheduling level leading to a new integration. At the control level, we use fast Model Predictive Control (fast MPC) to track a dynamic reference. Fast MPC also overcomes the increasing dimensionality of multiparametric MPC in our previous study (Zhuge and Ierapetritou, AIChE J. 2014;60(9):3169-3183). Results of CSTR case studies prove that the proposed approach reduces the computing time by at least two orders of magnitude compared to the integrated solution using mp-MPC. V C 2015 American Institute of Chemical Engineers AIChE J, 61: 3304-3319, 2015 Keywords: integration of scheduling and control, piece-wise affine approximation, fast model predictive control, Multiparametric model predictive control, mixed integer nonlinear programming

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“…The statistical clustering technique in (Nakada H, 2005) first computes the parameters of the affine local models, then partition of the regressor space. The greedy algorithm of (Sim one Paoletti, 2008) to partition in feasible sets of linear inequalities can be computationally heavy in case of large training sets.…”

Section: Introductionmentioning

confidence: 99%

Zonotope Parameter Identification for Piecewise Affine System

Wang

2020

Wseas Transactions on Systems

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This paper studies the identification problem for piecewise affine system, which is a special nonlinear system. As the difficulty in identifying piecewise affine system is to determine each separated region and each unknown parameter vector simultaneously, we propose a multi class classification process to determine each separated region. This multi class classification process is similar to the classical data clustering process, and the merit of our strategy is that the first order algorithm of convex optimization can be applied to achieve this classification process. Furthermore to relax the strict probabilistic description on external noise in identifying each unknown parameter vector, zonotope parameter identification algorithm is proposed to computes a set that contains the parameter vector, consistent with the measured output and the given bound of the noise. To guarantee our derived zonotope not growing unbounded with iterations, a sufficient condition for this requirement to hold may be formulated as one linear matrix inequality. Finally a numerical example confirms our theoretical results

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Identification of piecewise affine systems based on statistical clustering technique

Cited by 167 publications

References 23 publications

A simple multi-model prediction method

A simple multi-model prediction method

An integrated framework for scheduling and control using fast model predictive control

Zonotope Parameter Identification for Piecewise Affine System

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