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There has been a great deal of excitement in the last ten years over the emer gence of new mathematical techniques for the analysis and control of nonlinear systems: Witness the emergence of a set of simplified tools for the analysis of bifurcations, chaos, and other complicated dynamical behavior and the develop ment of a comprehensive theory of geometric nonlinear control. Coupled with this set of analytic advances has been the vast increase in computational power available for both the simulation and visualization of nonlinear systems as well as for the implementation in real time of sophisticated, real-time nonlinear control laws. Thus, technological advances havebolstered the impact of analytic advances and produced a tremendous variety of new problems and applications that are nonlinear in an essential way. Nonlinear controllaws have been implemented for sophisticated flight control systems on board helicopters, and vertical take offand landing aircraft; adaptive, nonlinearcontrollaws havebeen implementedfor robot manipulators operating either singly, or in cooperation on a multi-fingered robot hand; adaptive control laws have been implemented forjetengines andautomotive fuel injection systems, as well as for automated highway systems and air traffic management systems, to mention a few examples. Bifurcation theory has been used to explain and understand the onset of fiutterin the dynamics of aircraft wing structures, the onset of oscillations in nonlinear circuits, surge and stall in aircraft engines, voltage collapse in a power transmission network.
List of contents
1 Linear vs. Nonlinear.- 2 Planar Dynamical Systems.- 3 Mathematical Background.- 4 Input-Output Analysis.- 5 Lyapunov Stability Theory.- 6 Applications of Lyapunov Theory.- 7 Dynamical Systems and Bifurcations.- 8 Basics of Differential Geometry.- 9 Linearization by State Feedback.- 10 Design Examples Using Linearization.- 11 Geometric Nonlinear Control.- 12 Exterior Differential Systems in Control.- 13 New Vistas: Multi-Agent Hybrid Systems.- References.
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From the reviews:
A.J. van der Schaft in: Nieuw Archief voor Wiskunde, 2000
"(...) the book is very much recommended to every mathematician/engineer/physicist interested in nonlinear systems, especially because the book crosses one of the existing academic borderlines and illustrates the richness of problems and applications for nonlinear analysis and design in various areas of engineering."
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
"...stands alone in providing an integrated view of both the areas of non-linear analysis and control, and of non-linear dynamic systems theory. It also complements previous works in that it includes a range of new topics...Through the broad range of topics treated, the careful attention to detail in treating both topics familiar to the non-linear community and new research problems, and the historical anecdotes accompanying the development of different areas, the book does a superb job of conveying the 20 years of research experience of the author, and the excitement and enthusiasm that he has for the field...Sastry's book should be considered both as a research reference as well as a classroom textbook...Interesting worked examples are presented throughout, and a detailed set of exercises is included at the end of each chapter...Sastry's book is a comprehensive text on non-linear analysis and control. He has succeeded in bringing to life a wide range of mathematical techniques through a great many examples and applications to real non-linear systems, and his exposition relays his knowledge and enthusiasm about the field."
