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Differential Geometric Methods in Nonlinear Control

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Encyclopedia of Systems and Control

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Abstract

In the early 1970s, concepts from differential geometry were introduced to study nonlinear control systems. The leading researchers in this effort were Roger Brockett, Robert Hermann, Henry Hermes, Alberto Isidori, Velimir Jurdjevic, Arthur Krener, Claude Lobry, and Hector Sussmann. These concepts revolutionized our knowledge of the analytic properties of control systems, e.g., controllability, observability, minimality, and decoupling. With these concepts, a theory of nonlinear control systems emerged that generalized the linear theory. This theory of nonlinear systems is largely parallel to the linear theory, but of course it is considerably more complicated.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, USA

    Arthur J. Krener

Authors
  1. Arthur J. Krener
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Correspondence to Arthur J. Krener .

Editor information

Editors and Affiliations

  1. College of Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Technological Leadership Institute, University of Minnesota, Minneapolis, MA, USA

    Tariq Samad

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J. Krener, A. (2021). Differential Geometric Methods in Nonlinear Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-44184-5_80

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