Split and merge algorithm for identification of Piecewise Affine systems

Baptista, Roberto de Souza; Ishihara, J.Y.; Borges, Geovany A.

doi:10.1109/acc.2011.5991041

Cited by 12 publications

(6 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such approaches have been well studied [22,32,43]. The majority of works can be divided into three categories: algebraic based [9, 34, 52ś54], clustering-based [10,13,19,23,27], and optimization based [8,28,30,37,42]. The algebraic methods regard the identiication of multi-models as one single model.…”

Section: Related Workmentioning

confidence: 99%

A Framework for Identification and Validation of Affine Hybrid Automata from Input-Output Traces

Yang

Beg

Kenigsberg

et al. 2022

ACM Trans. Cyber-Phys. Syst.

View full text Add to dashboard Cite

Automata-based modeling of hybrid and cyber-physical systems (CPS) is an important formal abstraction amenable to algorithmic analysis of its dynamic behaviors, such as in verification, fault identification, and anomaly detection. However, for realistic systems, especially industrial ones, identifying hybrid automata is challenging, due in part to inferring hybrid interactions, which involves inference of both continuous behaviors, such as through classical system identification, as well as discrete behaviors, such as through automata (e.g., L*) learning. In this paper, we propose and evaluate a framework for inferring and validating models of deterministic hybrid systems with linear ordinary differential equations (ODEs) from input/output execution traces. The framework contains algorithms for the approximation of continuous dynamics in discrete modes, estimation of transition conditions, and the inference of automata mode merging. The algorithms are capable of clustering trace segments and estimating their dynamic parameters, and meanwhile, deriving guard conditions that are represented by multiple linear inequalities. Finally, the inferred model is automatically converted to the format of the original system for the validation. We demonstrate the utility of this framework by evaluating its performance in several case studies as implemented through a publicly available prototype software framework called HAutLearn and compare it with a membership-based algorithm.

show abstract

Section: Related Workmentioning

confidence: 99%

A Framework for Identification and Validation of Affine Hybrid Automata from Input-Output Traces

Yang

Beg

Kenigsberg

et al. 2022

ACM Trans. Cyber-Phys. Syst.

View full text Add to dashboard Cite

show abstract

“…(2) Let t � 1; set the initial values of the parameter estimate vectors and the covariance matrix according to (20), and give the parameter estimation precision ε � 0.01. (3) Collect input data u 1 (t) and u 2 (t).…”

Section: The Clustered Input Signals Based Recursive Least Squares (Cib-rls) Algorithmmentioning

confidence: 99%

“…In particular, the proposed method exploits a process of fuzzy clustering to obtain a subset of representatives from the original data set. Reference [20] assumed the number of modes of the PWARX system to be unknown and proposed a split-and-merge clustering algorithm to estimate the correct number of modes. Reference [21] discusses the use of correlation clustering algorithms for robust identification of PWARX models with reduced complexity.…”

Section: Introductionmentioning

confidence: 99%

“…Given this recursive algorithm, we can produce more accurate parameter estimation compared to existing multivariable recursive estimation methods, for example, [14,15]. Compared with the clustering techniques used in a PieceWise affine ARX model [19][20][21], the modified recursive algorithm in this paper can produce highly accurate estimation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Clustering Input Signals Based Identification Algorithms for Two-Input Single-Output Models with Autoregressive Moving Average Noises

Elamin

2020

Complexity

View full text Add to dashboard Cite

This study focused on the identification problems of two-input single-output system with moving average noises based on unsupervised learning methods applied to the input signals. The input signal to the autoregressive moving average model is proposed to be arriving from a source with continuous technical and environmental changes as two separate featured input signals. These two input signals were grouped in a number of clusters using the K-means clustering algorithm. The clustered input signals were supplied to the model in an orderly fashion from cluster-1 up to cluster-K. To ensure that the output signal can be best predicted from the input signal which in turn leads to selecting good enough model for its intended use, the magnitude-squared coherence (MSC) measure is applied to the input/output signals in the cases of clustered and nonclustered inputs, which indicates best correlation coefficient when measured with clustered inputs. From collected input-output signals, we deduce a K-means clustering based recursive least squares method for estimating the parameter of autoregressive moving average system. The simulation results indicate that the suggested method is effective.

show abstract

“…A large majority of the contributions published in the literature deal with models in input-output forms such as piecewise auto-regressive exogenous (PWARX) or switched ARX (SARX) models [5], [6], [7], [8], [9]. However, state-space models are more suitable for dealing with multiple-input, multiple-output (MIMO) systems because they provide a convenient and compact R representation.…”

Section: Introductionmentioning

confidence: 99%

New algorithm for identification of discrete-time switched linear systems

Lopes

Borges

Ishihara

2013

2013 American Control Conference

View full text Add to dashboard Cite

This paper addresses the problem of the identification of discrete-time switched linear MIMO state space systems. The methodology proposed explores the use of subspace identification techniques, clustering and classification of data to estimate the quantity, a matrix representation of the sub-models and an estimate of the instants of switching of the system. An important feature of the algorithm is that the matrices of the different sub-models can be directly combined because they are obtained for the same base states. The efficiency of the developed method is illustrated using a numerical simulation.

show abstract

Split and merge algorithm for identification of Piecewise Affine systems

Cited by 12 publications

References 16 publications

A Framework for Identification and Validation of Affine Hybrid Automata from Input-Output Traces

A Framework for Identification and Validation of Affine Hybrid Automata from Input-Output Traces

Clustering Input Signals Based Identification Algorithms for Two-Input Single-Output Models with Autoregressive Moving Average Noises

New algorithm for identification of discrete-time switched linear systems

Contact Info

Product

Resources

About