A clustering technique for the identification of piecewise affine systems

Authors:
Giancarlo Ferrari-Trecate;Marco Muselli;Diego Liberati;Manfred Morari
Affiliations:
Institut für Automatik, ETH, Swiss Federal Institute of Technology, ETHZ - ETL, CH 8092 Zurich, Switzerland and INRIA, Domaine de Voluceau, 78153 Le Chesnay Cedex, France;Istituto per i Circuiti Elettronici, Consiglio Nazionale delle Ricerche, Via De Marini, 6 16149 Genova, Italy;Centro di studio sulle Tecnologie dell'Informatica e dell'Automazione, Consiglio Nazionale delle Ricerche, Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vin ...;Institut für Automatik, ETH, Swiss Federal Institute of Technology, ETHZ - ETL, CH 8092 Zurich, Switzerland
Venue:
Automatica (Journal of IFAC)
Year:
2003

Citing 15
Cited 37

Identification of non-linear system structure and parameters using regime decomposition

Automatica (Journal of IFAC)
Support-Vector Networks

Machine Learning
Interconnected automata and linear systems: a theoretical framework in discrete-time

Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Multicategory Classification by Support Vector Machines

Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Verification of Hybrid Systems via Mathematical Programming

HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
A Clustering Technique for the Identification of Piecewise Affine Systems

HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
K-Means-Type Algorithms: A Generalized Convergence Theorem and Characterization of Local Optimality

IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear filters based on combinations of piecewise polynomialswith compact support

IEEE Transactions on Signal Processing
Brief Analysis of discrete-time piecewise affine and hybrid systems

Automatica (Journal of IFAC)
Control of systems integrating logic, dynamics, and constraints

Automatica (Journal of IFAC)
Multisurface method of pattern separation

IEEE Transactions on Information Theory
Hinging hyperplanes for regression, classification, and function approximation

IEEE Transactions on Information Theory
A tree-structured piecewise linear adaptive filter

IEEE Transactions on Information Theory
Nonlinear adaptive control using networks of piecewise linear approximators

IEEE Transactions on Neural Networks
Constructive neural networks with piecewise interpolation capabilities for function approximations

IEEE Transactions on Neural Networks

Switching systems: active mode recognition, identification of the switching law

Journal of Control Science and Engineering
Recursive identification of switched ARX systems

Automatica (Journal of IFAC)
Algebraic Identification of MIMO SARX Models

HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Switched and PieceWise Nonlinear Hybrid System Identification

HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Identification of piecewise affine systems by means of fuzzy clustering and competitive learning

Engineering Applications of Artificial Intelligence
2009 Special Issue: Time series modeling by a regression approach based on a latent process

Neural Networks
Modeling driver operation behavior by linear prediction analysis and auto associative neural network

SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
Symbolic modeling of driving behavior based on hierarchical segmentation and formal grammar

IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Identifiability of discrete-time linear switched systems

Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
A stochastic framework for hybrid system identification with application to neurophysiological systems

HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
A greedy approach to identification of piecewise affine models

HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Conditions of optimal classification for piecewise affine regression

HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
A class of fuzzy clusterwise regression models

Information Sciences: an International Journal
Brief paper: A continuous optimization framework for hybrid system identification

Automatica (Journal of IFAC)
Reconfigurable control of piecewise affine systems with actuator and sensor faults: Stability and tracking

Automatica (Journal of IFAC)
Identification of switched linear systems via sparse optimization

Automatica (Journal of IFAC)
A k-plane clustering algorithm for identification of hybrid systems

ACMOS'06 Proceedings of the 8th WSEAS international conference on Automatic control, modeling & simulation
Employing correlation clustering for the identification of piecewise affine models

Proceedings of the 2011 workshop on Knowledge discovery, modeling and simulation
A clustering-based approach for the identification of a class of temporally switched linear systems

Pattern Recognition Letters
A general framework for motion segmentation: independent, articulated, rigid, non-rigid, degenerate and non-degenerate

ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Reconstruction of switching thresholds in piecewise-affine models of genetic regulatory networks

HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Comparison of four procedures for the identification of hybrid systems

HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Identification of deterministic switched ARX systems via identification of algebraic varieties

HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Applying enterprise models to design cooperative scientific environments

BPM'05 Proceedings of the Third international conference on Business Process Management
Brief paper: Weighted least squares based recursive parametric identification for the submodels of a PWARX system

Automatica (Journal of IFAC)
Identification of piecewise affine systems based on statistical clustering technique

Automatica (Journal of IFAC)
From experiment design to closed-loop control

Automatica (Journal of IFAC)
Identification of piecewise affine systems via mixed-integer programming

Automatica (Journal of IFAC)
Hinging hyperplane models for multiple predicted variables

SSDBM'12 Proceedings of the 24th international conference on Scientific and Statistical Database Management
Research Infrastructure for Interactive Human- and Autonomous Guidance

Journal of Intelligent and Robotic Systems
Identification of switched linear regression models using sum-of-norms regularization

Automatica (Journal of IFAC)
Learning nonlinear hybrid systems: from sparse optimization to support vector regression

Proceedings of the 16th international conference on Hybrid systems: computation and control
A novel adaptive fuzzy predictive control for hybrid systems with mixed inputs

Engineering Applications of Artificial Intelligence
Learning symbolic representations of hybrid dynamical systems

The Journal of Machine Learning Research
Column Generation for the Minimum Hyperplanes Clustering Problem

INFORMS Journal on Computing
An experimental validation of a novel clustering approach to PWARX identification

Engineering Applications of Artificial Intelligence
Hybrid-fuzzy modeling and identification

Applied Soft Computing

Quantified Score

Hi-index	22.16

Visualization

Abstract

We propose a new technique for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional domain. In order to achieve our goal, we provide an algorithm that exploits the combined use of clustering, linear identification, and pattern recognition techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures. Moreover, the clustering step (used for classifying the datapoints) is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure.