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Invariance, monotonicity, and applications

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Nonlinear Analysis, Differential Equations and Control

Part of the book series: NATO Science Series ((ASIC,volume 528))

Abstract

An overview of recent results in nonsmooth analysis and control theory, with particular emphasis on proximal methods, is presented. The topics covered include proximal aiming and weak invariance (this being the core concept for many of the subsequent results presented), monotonicity along trajectories and Lyapunov stabilization, feedback synthesis in optimal control, existence of equilibria under invariance hypotheses, set smoothings and approximations, differential inequalities, and invariance theory in Hilbert space.

Research supported by the Natural Sciences and Engineering Research Council of Canada and Le Fonds pour la Formation de Chercheurs et l'Aide à la Recherche du Québec.

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Author information

Authors and Affiliations

  1. Institut Desargues, Université Lyon I (bât. 101), 69622, Villeurbanne, France

    F. H. Clarke

  2. Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI, 49008, USA

    Yu. S. Ledyaev

  3. Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, H4B 1R6, Canada

    R. J. Stern

Authors
  1. F. H. Clarke
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  2. Yu. S. Ledyaev
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  3. R. J. Stern
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Editor information

Editors and Affiliations

  1. Institut Gérard Desargues, Université Claude Bernard (Lyon 1), Villeurbanne, France

    F. H. Clarke

  2. Department of Mathematics and Statistics, Concordia University, Montréal, Québec, Canada

    R. J. Stern

  3. Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, Canada

    G. Sabidussi

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Clarke, F.H., Ledyaev, Y.S., Stern, R.J. (1999). Invariance, monotonicity, and applications. In: Clarke, F.H., Stern, R.J., Sabidussi, G. (eds) Nonlinear Analysis, Differential Equations and Control. NATO Science Series, vol 528. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4560-2_4

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  • DOI: https://doi.org/10.1007/978-94-011-4560-2_4

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