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**Nonlinear control of engineering systems. A Lyapunov-based approach.**
*(English)*
Zbl 1060.93003

Control Engineering. Boston, MA: Birkhäuser (ISBN 0-8176-4265-X/hbk). xvii, 394 p. (2003).

The text is a reference book which provides both mathematically rigorous theoretical development and the application of various nonlinear, Lyapunov-based techniques to a broad class of practical engineering systems, including mechanical, electrical, robotic, aerospace, and underactuated systems.

The book consists of six chapters and two appendices with additional mathematical prerequisites. In Chapter 1, several examples are treated to show some of the pitfalls experienced by linear systems theory (limitations of linearization, loss of tracking performance, and peaking phenomena). In Chapter 2, control applications for certain mechanical systems (autobalancing systems, dynamically positioned ships, Euler-Langrange systems) are examined. In Chapter 3, controllers are developed for electrical machines, described by electrical and mechanical subsystem dynamics (induction motor, switched reluctance motor, active magnetic bearing system). In Chapter 4, several different robotic applications (learning control, position and force control, visual servo control) are examined. Chapter 5 presents various aerospace applications (attitude tracking, energy/power and attitude tracking, formation flying). The engineering systems treated in chapters 1-5 are fully actuated (i.e., the number of control inputs (actuators) is equal to the number of degrees of freedom). In Chapter 6, various design strategies are examined for some underactuated (overhead crane, vertical take-off and landing, satellite) systems.

Each chapter contains an exposition of the necessary mathematical background and is provided with detailed references for further reading. For each of the systems examined, simulation results are presented. The material in the text is intended for readers with a background in undergraduate systems theory and is beneficial for students and practicing research and development engineers in the area of control. Beautifully written, the book includes a wide range of applications making it suitable for an extensive audience.

The book consists of six chapters and two appendices with additional mathematical prerequisites. In Chapter 1, several examples are treated to show some of the pitfalls experienced by linear systems theory (limitations of linearization, loss of tracking performance, and peaking phenomena). In Chapter 2, control applications for certain mechanical systems (autobalancing systems, dynamically positioned ships, Euler-Langrange systems) are examined. In Chapter 3, controllers are developed for electrical machines, described by electrical and mechanical subsystem dynamics (induction motor, switched reluctance motor, active magnetic bearing system). In Chapter 4, several different robotic applications (learning control, position and force control, visual servo control) are examined. Chapter 5 presents various aerospace applications (attitude tracking, energy/power and attitude tracking, formation flying). The engineering systems treated in chapters 1-5 are fully actuated (i.e., the number of control inputs (actuators) is equal to the number of degrees of freedom). In Chapter 6, various design strategies are examined for some underactuated (overhead crane, vertical take-off and landing, satellite) systems.

Each chapter contains an exposition of the necessary mathematical background and is provided with detailed references for further reading. For each of the systems examined, simulation results are presented. The material in the text is intended for readers with a background in undergraduate systems theory and is beneficial for students and practicing research and development engineers in the area of control. Beautifully written, the book includes a wide range of applications making it suitable for an extensive audience.

Reviewer: Georgy Osipenko (St. Peterburg)

### MSC:

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

93C95 | Application models in control theory |

93D30 | Lyapunov and storage functions |

93C10 | Nonlinear systems in control theory |

93C85 | Automated systems (robots, etc.) in control theory |

70Q05 | Control of mechanical systems |

93B51 | Design techniques (robust design, computer-aided design, etc.) |