Cooperative control of nonlinear networked systems. Infinite-time and finite-time design methods.

*(English)*Zbl 1422.93003
Communications and Control Engineering. Cham: Springer (ISBN 978-3-030-04971-3/hbk; 978-3-030-04972-0/ebook). xvi, 197 p. (2019).

During the past 20 years, cooperative control of large scale networked systems (LSNSs) have received a considerable attention from a wide range of areas such as systems and control, mathematics, physics, et. al., where the large scale networked systems include multi-agent systems and complex networks which consist of multiple agents that are interconnected through local interactions. As a consequence, cooperative control strategy is widely adopted to perform some specified tasks, such as frequency synchronization of microgrids, formation of unmanned aerial vehicles. Among the various cooperative behaviors, consensus of LSNSs, which can be defined mathematically as agents’ states synchronization, is the most fundamental one.

This book focus on studying the asymptotical (infinite time) and finite time consensus problems for LSNSs subject to nonvanishing uncertain dynamics and unknown non-parametric nonlinearities under certain communication topologies. It is a quite challenging problem to cancel the effects of uncertainties on consensus not only in theory but also in practice. Based on the adaptive control technology, various control strategies are proposed in this book such that the considered LSNSs can achieve asymptotic consensus and finite time consensus. In the first chapter of this book, a comprehensive overview of existing works on asymptotical consensus as well as finite time consensus of LSNSs is provided. Chapter 2 provides some preliminaries which include algebraic graph theory, matrix theory and stability theory. In Chapters 3–5, asymptotical leaderless consensus problems are studied for LSNSs with fixed topology. By using the finite time stability theory, finite time consensus problems for LSNSs are studied in Chapters 6–9.

This book contains some works of the authors that have been published in some top journals. It is not only a reference textbook for the researchers, but also can be used as an excellent graduate textbook. So the reviewer believe that this book will gain a significant number of readers in the near future.

This book focus on studying the asymptotical (infinite time) and finite time consensus problems for LSNSs subject to nonvanishing uncertain dynamics and unknown non-parametric nonlinearities under certain communication topologies. It is a quite challenging problem to cancel the effects of uncertainties on consensus not only in theory but also in practice. Based on the adaptive control technology, various control strategies are proposed in this book such that the considered LSNSs can achieve asymptotic consensus and finite time consensus. In the first chapter of this book, a comprehensive overview of existing works on asymptotical consensus as well as finite time consensus of LSNSs is provided. Chapter 2 provides some preliminaries which include algebraic graph theory, matrix theory and stability theory. In Chapters 3–5, asymptotical leaderless consensus problems are studied for LSNSs with fixed topology. By using the finite time stability theory, finite time consensus problems for LSNSs are studied in Chapters 6–9.

This book contains some works of the authors that have been published in some top journals. It is not only a reference textbook for the researchers, but also can be used as an excellent graduate textbook. So the reviewer believe that this book will gain a significant number of readers in the near future.

Reviewer: Peijun Wang (Wuhu)

##### MSC:

93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |

93D99 | Stability of control systems |

93C40 | Adaptive control/observation systems |

93C41 | Control/observation systems with incomplete information |

93A15 | Large-scale systems |

93A14 | Decentralized systems |

68T42 | Agent technology and artificial intelligence |

93C10 | Nonlinear systems in control theory |