A clustering technique for the identification of piecewise affine systems

By Giancarlo Ferrari-Trecate, M. Muselli, Diego Liberati, Manfred Morari. at - Automatisierungstechnik, 2001

660 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/88b301efef7f1bf534e2ab2660622d07d819da59

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Citations in the corpus

From experiment design to closed-loop control (2005, methodology): “This type of problem has been coined “least-costly identification experiments” inBombois, Scorletti, Van den Hof, and Gevers (2004) .”
Models and Algorithms for Optimal Piecewise-Linear Function Approximation (2015, methodology): “Some techniques are based on point clustering, such as 𝐾 -means, which has found applications in nonlinear dynamic systems and control [5].”
Predictive Control for Linear and Hybrid Systems (2017, background): “Identification techniques for piecewise affine systems were recently developed [104, 255, 163, 39, 165, 282, 227], that allow one to derive models (or parts of models) from input/output data.”
An algebraic geometric approach to the identification of a class of linear hybrid systems (2003, methodology): “When the model parameters and the switching mechanism are unknown, the identication problem becomes even more challenging: [ 11 ] assumes that the number of models is known, and proposes an identication algorithm that combines clustering, regression and classication techniques; [5] uses mixed-intege”
Optimization Models for Machine Learning: A Survey (2019, background): “Alternatively, clustering techniques can be adopted for domain partitioning [92].”
HYSDEL-a tool for generating computational hybrid models for analysis and synthesis problems (2004, methodology): “Finally, we mention that identification techniques for piecewise affine systems were recently developed [17]–[20], that allow one to derive models (or parts of models) from input– output data.”
A Bayesian approach to identification of hybrid systems (2004, methodology): “In the clustering-based procedure [6], the data classification and the parameter estimation steps are performed simultaneously by solving an optimal clustering problem in the parameter space.”
Identification of Hybrid Systems: A Tutorial (2007, methodology): “In this section, four procedures for the identification of SARX/PWARX models are briefly discussed, namely the algebraic procedure [51, 74, 78], the clustering-based procedure [27], the Bayesian procedure [47], and the bounded-error procedure [5].”
Identification of piecewise affine systems via mixed-integer programming (2004, background): “Most of these approaches [15–22,27] assume that the system dynamics is continuous , while, e.g., [12] allows for discontinuities.”
Data-based hybrid modelling of the component placement process in pick-and-place machines (2004, methodology): “In this work, the algorithm developed by Ferrari-Trecate et al. (2003) is adopted.”
Constrained Optimal Control of Linear and Hybrid Systems (2003, methodology): “Such a model is based on a simplified model and a set of parameters provided by Ford Research Laboratories, and involves piecewise linearization techniques of the nonlinear torque function that are based on hybrid system identification tools [63].”
A bounded-error approach to piecewise affine system identification (2005, background): “In [9], piecewise affine ARX (PWARX) models are considered and the combined use of clustering, linear identification, and pattern recognition techniques is exploited in order to identify both the affine submodels and the polyhedral partition of the regressor set.”
Local and Piecewise Affine Approaches to System Identification (2003, methodology): “The methods in [48, 65, 119, 143, 144] belong to this category.”