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A self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students. "Algebraic Methods for Nonlinear Control Systems" develops a linear-algebraic alternative to the usual differential-geometric approach to nonlinear control, using vector spaces over suitable fields of nonlinear functions. It describes a range of results, some of which can be derived using differential geometry but many of which cannot. They include: classical and generalized realization in the nonlinear context; accessibility and observability recast for the linear-algebraic setting; discussion and solution of basic feedback problems; results for dynamic and static state and output feedback. Dynamic feedback and realization are shown to be dealt with and solved much more easily in the algebraic framework. The second edition has been completely revised with new text, examples and exercises; it is divided into two parts: necessary methodology and applications to control problems.
List of contents
Methodology.- Preliminaries.- Modeling.- Accessibility.- Observability.- Systems Structure and Inversion.- System Transformations.- Applications to Control Problems.- Input-output Linearization.- Noninteracting Control.- Input-state Linearization.- Disturbance Decoupling.- Model Matching.- Measured Output Feedback Control Problems.
Summary
A self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students. "Algebraic Methods for Nonlinear Control Systems" develops a linear-algebraic alternative to the usual differential-geometric approach to nonlinear control, using vector spaces over suitable fields of nonlinear functions. It describes a range of results, some of which can be derived using differential geometry but many of which cannot. They include: classical and generalized realization in the nonlinear context; accessibility and observability recast for the linear-algebraic setting; discussion and solution of basic feedback problems; results for dynamic and static state and output feedback. Dynamic feedback and realization are shown to be dealt with and solved much more easily in the algebraic framework. The second edition has been completely revised with new text, examples and exercises; it is divided into two parts: necessary methodology and applications to control problems.
Additional text
From the reviews of the second edition:
“Algebraic Methods for Nonlinear Control Systems is a book published under the Springer Communication and Control Engineering publication program, which presents major technological advances within these fields. The book aims at presenting one of the two approaches to nonlinear control systems, namely the differential algebraic method. … is an excellent textbook for graduate courses on nonlinear control systems. … The differential algebraic method presented in this book appears to be an excellent tool for solving the problems associated with nonlinear systems.” (Dariusz Bismor, International Journal of Acoustics and Vibration, Vol. 14 (4), 2009)
Report
From the reviews of the second edition: "Algebraic Methods for Nonlinear Control Systems is a book published under the Springer Communication and Control Engineering publication program, which presents major technological advances within these fields. The book aims at presenting one of the two approaches to nonlinear control systems, namely the differential algebraic method. ... is an excellent textbook for graduate courses on nonlinear control systems. ... The differential algebraic method presented in this book appears to be an excellent tool for solving the problems associated with nonlinear systems." (Dariusz Bismor, International Journal of Acoustics and Vibration, Vol. 14 (4), 2009)
