Algebraic and Geometric Methods in Nonlinear Control Theory

1. Front Matter

   Pages i-xii

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2. Controllability, Observability, Realization and other Structural Properties

   1. Front Matter

      Pages 1-1

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   2. Realization Theory for Nonlinear Systems; Three Approaches

      • Bronisław Jakubczyk

      Pages 3-31

   3. The Local Realization of Generating Series of Finite Lie Rank

      • Christophe Reutenauer

      Pages 33-43

   4. Realizations of Polynomial Systems

      • Zbigniew Bartosiewicz

      Pages 45-54

   5. Symmetries and Local Controllability

      • P. E. Crouch, C. I. Byrnes

      Pages 55-75

   6. The Intrinsic Geometry of Dynamic Observations

      • Arthur J. Krener

      Pages 77-87

   7. Design of Nonlinear Observers by a Two-Step-Transformation

      • H. Keller, H. Fritz

      Pages 89-98

3. Feedback Synthesis and Linearization Techniques

   1. Front Matter

      Pages 99-99

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   2. On the Input-Output Decoupling of Nonlinear Systems

      • Henk Nijmeijer

      Pages 101-119

   3. Control of Nonlinear Systems Via Dynamic State-Feedback

      • A. Isidori

      Pages 121-145

   4. A Classification of Nonlinear Systems Based on the Invariant Subdistribution Algorithm

      • Maria Domenia Di Benedetto

      Pages 147-157

   5. Asymptotic Expansions, Root-Loci and the Global Stability of Nonlinear Feedback Systems

      • Christopher I. Byrnes, Alberto Isidori

      Pages 159-179

   6. Everything You Always Wanted to Know about Linearization

      • Daniel Claude

      Pages 181-226

   7. Feedback Linearization and Simultaneous Output Block Decoupling of Nonlinear Systems

      • T. J. Tarn, Daizhan Cheng, Alberto Isidori

      Pages 227-241

   8. Global Feedback Linearizability of Locally Linearizable Systems

      • William M. Boothby

      Pages 243-256

   9. Global Aspects of Linearization, Equivalence to Polynomial Forms and Decomposition of Nonlinear Control Systems

      • Witold Respondek

      Pages 257-284

   10. The Extended-Linearization Approach for Nonlinear Systems Problems

       • Wilson J. Rugh

       Pages 285-309

   11. About the Local Linearization of Nonlinear Systems

       • C. Reboulet, P. Mouyon, C. Champetier

       Pages 311-322

4. Optimal Control

   1. Front Matter

      Pages 323-323

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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point"of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non­ trivially) in regional and theoretical economics; algebraic geometry interacts with physics; ihe Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras ·are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

• algebra
• algebraic geometry
• coding theory
• homotopy
• lie algebra
• transformation

`... this volume has already become one of the reference titles in nonlinear control theory. Moreover, the volume shows how modern sophisticated elements of mathematics can lead not only to new theoretical results but also to direct immediate industrial applications. This way, the volume has many samples of `The art of applying mathematics' as stated in the `manifest' written by Hazewinkel in the first number of Acta Applicandae Mathematicae.'
Acta Applicandae Mathematicae, Vol. 11, 1988.

• Laboratoire des Signaux et Systèmes, CNRS — École Supérieure d’Electricité, Gif-sur-Yvette, France

  M. Fliess

• Centre for Mathematics and Computer Science, Amsterdam, The Netherlands

  M. Hazewinkel

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