Identification Of Piecewise Affine Models Research Articles

Clustering based identification of piece-wise affine models for systems with friction

This paper proposes an identification method of piece-wise affine(PWA) models for systems with friction. The friction compensation is generally based on a friction model. The identification method of conventional friction models requires many experiments for each parameters. The proposed method is able to identify PWA models from single experimental data using clustering methods. It’s known that PWA models have high approximation performance of not only hybrid systems but non-linear systems. The effectiveness of the proposed method and its comparison with the conventional method is illustrated by experiments using the linear drive unit equipped the ball screw.

Compression Based Identification of PWA Systems

Piecewise affine (PWA) models serve as an important class of models for nonlinear systems. The identification of PWA models is known to be a difficult task and often implies solving a non-convex combinatorial optimization problems. In this paper, we revisit a recently proposed PWA identification method. We do this to give a novel derivation of the identification method and to show that under certain conditions, the method is optimal in the sense that it finds the PWA function that passes through the measurements and has the least number of hinges. We also show how the alternating direction method of multipliers (ADMM) can be used to solve the underlying convex optimization problem.

Identification of PWA models via optimal data compression

In this paper, a new identification method for non-parametric piecewise affine (PWA) models is introduced. The method is based on the non-parametric data-based representation of PWA maps and the data compression with l1 optimization technique, which enable the method to deal with large data sets. In the proposed scheme, the prior knowledge about partitioning of the PWA map is not required, and the trade-off between complexity and accuracy of the model is easily adjusted by one parameter, which can be determined by holdout validation technique in practical situations. These features of the proposed method provide the high usability in practical problems, which is demonstrated through numerical and experimental examples.

A recursive identification algorithm for switched linear/affine models

In this work, a recursive procedure is derived for the identification of switched linear models from input–output data. Starting from some initial values of the parameter vectors that represent the different submodels, the proposed algorithm alternates between data assignment to submodels and parameter update. At each time instant, the discrete state is determined as the index of the submodel that, in terms of the prediction error (or the posterior error), appears to have most likely generated the regressor vector observed at that instant. Given the estimated discrete state, the associated parameter vector is updated based on recursive least squares or any fast adaptive linear identifier. Convergence of the whole procedure although not theoretically proved, seems to be easily achieved when enough rich data are available. It has been also observed that by appropriately choosing the data assignment criterion, the proposed on-line method can be extended to deal also with the identification of piecewise affine models. Finally, performance is tested through some computer simulations and the modeling of an open channel system.

Identification of PieceWise Affine Models of Genetic Regulatory Networks: the Data Classification Problem

In this paper we consider the identification of PieceWise Affine (PWA) models of Genetic Regulatory Networks (GRNs) and focus on data classification that is a task of the whole identification process. By assuming that gene expression profiles have been split into segments generated by a single affine mode, data classification amounts to group together segments that have been produced by the same mode. In particular, this operation must be performed in a noisy setting and without using any knowledge on the number of modes excited in the experiment. At a mathematical level, classification amounts to find all partitions of the set of segments that verify a statistical criterion and as such it has a combinatorial nature. In order to minimize the computational complexity we propose a pruning strategy for reducing the dimension of the search space. In particular, our approach hinges on a new algorithm for generating in an efficient way all partitions of a finite set that verify a bound on a monotone cost function.

Set Membership Identification of Piecewise Affine Models

This paper addresses the problem of identification of piecewise affine (PWA) models, which involves the joint estimation of both the parameters of the affine submodels and the partition of the PWA map from data. According to ideas from set-membership identification, the key approach is to characterize the model by its maximum allowed prediction error, which is used as a tuning knob for trading off between prediction accuracy and model complexity. At initialization, the proposed procedure for PWA identification exploits a technique for partitioning an infeasible system of linear inequalities into a (possibly minimum) number of feasible subsystems. This provides both an initial clustering of the datapoints and a guess of the number of required submodels, which therefore is not fixed a priori. A refinement procedure is then applied in order to improve both data classification and parameter estimation. The partition of the PWA map is finally estimated by considering multicategory classification techniques.

Identification of piecewise affine models in noisy environment

This paper addresses the identification of non-linear systems. A wide class of these systems can be described using non-linear time-invariant regression models, that can be approximated by means of piecewise affine prototypes with an arbitrary degree of accuracy. This work concerns the identification of piecewise affine model parameters through input-output data affected by additive noise. In order to show the effectiveness of the developed technique, the results obtained in the identification of both a simple simulated system and a real dynamic process are reported.