Identification Of Hybrid Systems Research Articles

Inferring Moore Machine for adaptive online Hybrid Automaton Identification

In the context of CPS modeling, this paper proposes a new method for online adaptive identification of hybrid systems. The method relies on a Moore machine identification process; A mapping between a hybrid automaton and a discrete event Moore machine is proposed, and a new online adaptive Moore machine identification method is proposed. A case study illustrates the proposed method.

Hierarchical identification of nonlinear hybrid systems in a Bayesian framework

This paper presents a hierarchical framework for the identification of nonlinear hybrid systems in the form of Switched Nonlinear AutoRegressive models with eXogenous variables (SNARX). The identification is done via three levels of inference, using Bayes' rule. In the first level, model parameters are computed via a Maximum a Posteriori (MAP) estimator. The posterior distribution therein involved depends on hyper-parameters that are tuned in the second level of inference. Such terms determine model complexity, and the Bayesian framework is key in returning values that trade off complexity with accuracy by automatically embodying the Occam's razor principle. Lastly, the third level compares different model structures by means of a quality measure that encompasses data fitness, model complexity, and data classification. The proposed framework is compared with existing relevant methods and is tested on different numerical models, showing promising performance.

Development of A Comprehensive Quality Measure for Identification of Nonlinear Hybrid Systems

Development of A Comprehensive Quality Measure for Identification of Nonlinear Hybrid Systems

Modelling framework for artificial hybrid dynamical systems

Many current industry branches use hybrid approaches to solve complex application problems. Over the last decades, different tools for the simulation of such hybrid systems (e.g. Hysdel and YAMLIP) as well as the identification of hybrid systems (e.g. HIT, MLP and OAF NN) have been developed. The framework presented in this work facilitates the integration of artificial feed-forward neural networks in the modelling process of hybrid dynamical systems (HDS). Additionally, the framework provides a structured language for characterising these feed-forward networks itself. Therefore, an interdisciplinary exchange in the field of neural networks and its integration into hybrid dynamical systems is enabled. Focusing on hybrid systems with autonomous events, two different approaches, namely the artificial hybrid model and the artificial hybrid dynamics, are introduced. Challenges of the modelling process of HDS are reflected and advantages as well as disadvantages are discussed. The case study includes two common examples of HDS and analyses the simulation results and examines limitations of the modelling framework.

A Bayesian Framework for Large-Scale Identification of Nonlinear Hybrid Systems

Abstract In this paper, a two-level Bayesian framework is proposed for the identification of nonlinear hybrid systems from large data sets by embedding it in a four-stage procedure. At the first stage, feature vector selection techniques are used to generate a reduced-size set from the given training data set. The resulting data set then is used to identify the hybrid system using a Bayesian method, where the objective is to assign each data point to a corresponding sub-mode of the hybrid model. At the third stage, this data assignment is used to train a Bayesian classifier to separate the original data set and determine the corresponding sub-mode for all the original data points. Finally, once every data point is assigned to a sub-mode, a Bayesian estimator is used to estimate a regressor for each sub-system independently. The proposed method tested on three case studies.

New trends in modeling and control of hybrid systems

New trends in modeling and control of hybrid systems

Piecewise affine identification of a hydraulic pumping system using evolutionary computation

Identification of piecewise affine hybrid systems is not an easy task since both the parameters determining the discrete modes and the submodels parameters have to be obtained, leading to a non-convex combinatorial optimisation problem. One way around this problem is to solve it in two steps. This work presents an approach for simultaneously estimating the parameters for PieceWise Autoregressive eXogeneous and PieceWise Output Error models. This is accomplished by using evolutionary algorithms for finding the parameters of the discrete modes (Gaussian mixture models) and employing the proposed weighted and extended least squares algorithm to estimate the ARX or ARMAX submodels. The main advantages of the proposed algorithm are: (i) it can be applied to output error models - which correspond to system with measurement noise, (ii) it is less likely to get trapped in local minima and (iii) it is applicable to problems with large datasets. The proposed approach, which is offline, was validated using simulated and experimental data and was compared with another method from the literature. In the case of an experimental plant, parsimonious models with good performance in both dynamic and static regimes were obtained.

Model selection for hybrid dynamical systems via sparse regression.

Hybrid systems are traditionally difficult to identify and analyse using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations solely from measurement data. In this article, we develop a new methodology, Hybrid-Sparse Identification of Nonlinear Dynamics, which identifies separate nonlinear dynamical regimes, employs information theory to manage uncertainty and characterizes switching behaviour. Specifically, we use the nonlinear geometry of data collected from a complex system to construct a set of coordinates based on measurement data and augmented variables. Clustering the data in these measurement-based coordinates enables the identification of nonlinear hybrid systems. This methodology broadly empowers nonlinear system identification without constraining the data locally in time and has direct connections to hybrid systems theory. We demonstrate the success of this method on numerical examples including a mass–spring hopping model and an infectious disease model. Characterizing complex systems that switch between dynamic behaviours is integral to overcoming modern challenges such as eradication of infectious diseases, the design of efficient legged robots and the protection of cyber infrastructures.

Sensitivity analysis and parameter identification of nonlinear hybrid systems for glycerol transport mechanisms in continuous culture

In this paper, we establish a modified fourteen-dimensional nonlinear hybrid dynamic system with genetic regulation to describe the microbial continuous culture, in which we consider that there are three possible ways for glycerol to pass the cell's membrane and one way for 1,3-PD (passive diffusion and active transport). Then we discuss the existence, uniqueness, continuous dependence of solutions and the compactness of the solution set. We construct a global sensitivity analysis approach to reduce the number of kinetic parameters. In order to infer the most reasonable transport mechanism of glycerol, we propose a parameter identification model aiming at identifying the parameter with higher sensitivity and transport of glycerol, which takes the robustness index of the intracellular substance together with the relative error between the experimental data and the computational values of the extracellular substance as a performance index. Finally, a parallel algorithm is applied to find the optimal transport of glycerol and parameters.

New Approaches to Identification of PWARX Systems

We consider the clustering-based procedures for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. These methods exploit three main techniques which are clustering, linear identification, and pattern recognition. The clustering method based on thek-means algorithm is treated in this paper. It consists in estimating both the parameter vector of each submodel and the coefficients of each partition while knowing the model ordersnaandnband the number of submodelss. The performance of this approach can be threatened by the presence of outliers and poor initializations. To overcome these problems, we propose new techniques for data classification. The proposed techniques exploit Chiu’s clustering technique and the self-artificial Kohonen neural network approach in order to improve the performance of both the clustering and the final linear regression procedure. Simulation results are presented to illustrate the performance of the proposed method.

A game-theoretic approach to fault diagnosis and identification of hybrid systems

Physical systems can fail. For this reason the problem of identifying and reacting to faults has received a lot of attention in the control and computer science communities. In this paper we study the fault diagnosis problem for hybrid systems from a game-theoretical point of view. A hybrid system is a system mixing continuous and discrete behaviours that cannot be faithfully modelled neither by using a formalism with continuous dynamics only nor by a formalism including only discrete dynamics. We model hybrid systems as Hybrid Automata and add distinguished actions to describe faults. We define a Fault Identification Game on them, using two players: the environment and the identifier. The environment controls the evolution of the system and chooses whether and when a fault occurs. The identifier observes the external behaviour of the system and announces whether a fault has occurred or not. Existence of a winning strategy for the identifier implies that faults can be detected correctly, while computing such a winning strategy corresponds to implementing an identifier for the system. We will show how to determine the existence of a winning strategy, and how to compute it, for all decidable classes of hybrid automata that admit a finite bisimulation quotient.

Mode Identification of Hybrid Systems in the Presence of Fault

A mode identification method for hybrid system diagnosis is proposed. The method is presented as a module of a quantitative health monitoring framework for hybrid systems. After fault occurrence, the fault is detected and isolated. The next step is fault parameters estimation, where the size of the fault is identified. Fault parameter estimation is based on data collected from the hybrid system while the system is faulty, and its dynamical model is partially unknown. A hybrid system's dynamics consists of continuous behavior and discrete states represented by modes. Fault parameter estimation requires knowledge of the monitored system's operating mode. The new method utilizes the partially known dynamical model to identify hybrid system modes in the presence of a single parametric fault.

A product-of-errors framework for linear hybrid system identification

We propose a general framework for identification of linear discrete-time hybrid systems in which arbitrary loss functions can be easily included. Our framework includes the algebraic (Vidal et al., 2003) and support vector regression (Lauer and Bloch, 2008a,b) methods as particular cases. Inspired by these approaches, we then propose an optimization framework that relies on the minimization of a product of loss functions. Here, the identification problem is recast as a nonlinear and non-convex, though continuous, optimization program that involves only the model parameters as variables. As a result, its complexity scales linearly with the number of data and it can easily be solved using standard global optimization methods. Moreover, we show that by choosing a saturated loss function, such as Hampel's loss function, the algorithm can efficiently deal with noise and outliers in the data. The final result is a general framework for linear hybrid system identification that can deal efficiently with noise, outliers, and large data sets. Numerical experiments demonstrate the efficiency and robustness of the proposed approach.

Identification of Hybrid Systems A Tutorial

This tutorial paper is concerned with the identification of hybrid models, i.e. dynamical models whose behavior is determined by interacting continuous and discrete dynamics. Methods specifically aimed at the identification of models with a hybrid structure are of very recent date. After discussing the main issues and difficulties connected with hybrid system identification, and giving an overview of the related literature, this paper focuses on four different approaches for the identification of switched affine and piecewise affine models, namely an algebraic procedure, a Bayesian procedure, a clustering-based procedure, and a bounded-error procedure. The main features of the selected procedures are presented, and possible interactions to still enhance their effectiveness are suggested.

A Bayesian approach to identification of hybrid systems

In this paper, we present a novel procedure for the identification of hybrid systems in the class of piecewise ARX systems. The presented method facilitates the use of available a priori knowledge on the system to be identified, but can also be used as a black-box method. We treat the unknown parameters as random variables, described by their probability density functions. The identification problem is posed as the problem of computing the a posteriori probability density function of the model parameters, and subsequently relaxed until a practically implementable method is obtained. A particle filtering method is used for a numerical implementation of the proposed procedure. A modified version of the multicategory robust linear programming classification procedure, which uses the information derived in the previous steps of the identification algorithm, is used for estimating the partition of the piecewise ARX map. The proposed procedure is applied for the identification of a component placement process in pick-and-place machines.

ONE-STEP AHEAD PREDICTION FOR PARAMETER ESTIMATION IN PHYSIOLOGICAL HYBRID MODELS

Identification of hybrid systems is complex because it is not a priori known which data is generated by which discrete mode of the system. A novel procedure is presented for the simultaneous determination of the model parameters and classification of the data. Initial parameter estimates are obtained based on a priori knowledge of the modes of the system. Next, the data points are subsequently classified and with each new classified data point the parameter estimates are refined. The proposed procedure is applied in the estimation of parameters in a hybrid description of calcium cycling in the intact heart.

On the use of hybrid system identification methods for max-plus-linear system identification

In recent years, different approaches for identification of hybrid systems and max-plus linear systems that are a special class of discrete event systems, have been developed. This paper introduces a new identification method for piecewise affine hybrid systems and shows that this approach is also easily applicable for identification of max-plus-linear systems.

A clustering technique for the identification of piecewise affine systems

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.

Using Wavelets for the Detection of Discrete Events in Time Series of Hybrid Systems

This contribution deals with the use of wavelets for the analysis of time series of systems which are hybrid in the sense that they contain discrete and continuous dynamics. We focus on the detection of discrete events which is an important step in the identification of hybrid systems. A brief overview of the characteristics of the wavelet transform is given, which shows that the wavelet transform is an appropriate method for the analysis of time series of hybrid systems. By the combination of two wavelet-based analysis techniques, a two-step procedure is obtained which allows the detection of switching points in the presence of weak noise. In this context, emphasis is given to the problems which arise when the theoretical results are used to detect discrete events in real time series. The procedure is demonstrated for a time series obtained from the simulation of a nonlinear laboratory plant.

A numerical scheme for the identification of hybrid systems describing the vibration of flexible beams with tip bodies

A cubic spline-based Galerkin-like method is developed for the identification of a class of hybrid systems which describe the transverse vibration of flexible beams with attached tip bodies. The identification problem is formulated as a least-squares fit to data subject to the system dynamics given by a coupled system of ordinary and partial differential equations recast as an abstract evolution equation (AEE) in an appropriate infinite-dimensional Hilbert space. Projecting the AEE into splinebased subspaces leads naturally to a sequence of approximating finite-dimensional identification problems. The solutions to these problems are shown to exist, are relatively easily computed, and are shown to, in some sense, converge to solutions to the original identification problem. Numerical results for a variety of examples are discussed.