## Hybrid System Identification: Theory and Algorithms for Learning Switching ModelsHybrid System Identification helps readers to build mathematical models of dynamical systems switching between different operating modes, from their experimental observations. It provides an overview of the interaction between system identification, machine learning and pattern recognition fields in explaining and analysing hybrid system identification. It emphasises the optimization and computational complexity issues that lie at the core of the problems considered and sets them aside from standard system identification problems. The book presents practical methods that leverage this complexity, as well as a broad view of state-of-the-art machine learning methods.The authors illustrate the key technical points using examples and figures to help the reader understand the material. The book includes an in-depth discussion and computational analysis of hybrid system identification problems, moving from the basic questions of the definition of hybrid systems and system identification to methods of hybrid system identification and the estimation of switched linear/affine and piecewise affine models. The authors also give an overview of the various applications of hybrid systems, discuss the connections to other fields, and describe more advanced material on recursive, state-space and nonlinear hybrid system identification. Hybrid System Identification includes a detailed exposition of major methods, which allows researchers and practitioners to acquaint themselves rapidly with state-of-the-art tools. The book is also a sound basis for graduate and undergraduate students studying this area of control, as the presentation and form of the book provides the background and coverage necessary for a full understanding of hybrid system identification, whether the reader is initially familiar with system identification related to hybrid systems or not. |

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### Contents

1 | |

2 System Identification | 15 |

3 Classification | 59 |

4 Hybrid System Identification | 77 |

5 Exact Methods for Hybrid System Identification | 103 |

6 Estimation of Switched Linear Models | 141 |

7 Estimation of Piecewise Affine Models | 168 |

### Other editions - View all

Hybrid System Identification: Theory and Algorithms for Learning Switching ... Fabien Lauer,Gérard Bloch No preview available - 2018 |

Hybrid System Identification: Theory and Algorithms for Learning Switching ... Fabien Lauer,Gérard Bloch No preview available - 2019 |

### Common terms and phrases

algebraic algorithm Automatica binary bound chapter classification complexity computed considered convex optimization data points data set defined dimension discrete dynamical error sparsification estimation f(xk formulation given global optimization hybrid models hybrid system identification hyperplane I/O models identification of switched IEEE Trans IFAC input input–output iteration k-means algorithm kernel functions l1-norm Lauer Lecture Notes linear classifiers linear model linear regression loss function machine learning minimization noise nonlinear regression nonparametric NP-hard number of data number of modes number of submodels obtained optimization problem output parameter vectors partition piecewise affine systems polynomial procedure Proceedings PWA models PWA regression random regression problem regularization RKHS Sect smooth solution solving sparse sparsification sparsity Springer state-space submodels support vector machines support vector regression switched system switching linear regression switching regression term Theorem values variables yields zero