Nonsmooth Analysis in Control Theory: A Survey

In the classical calculus of variations, the question of regularity (smoothness or otherwise of certain functions) plays a dominant role. This same issue, although it emerges in different guises, has turned out to be crucial in nonlinear control theory, in contexts as various as necessary conditions...

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Bibliographic Details
Published inEuropean journal of control Vol. 7; no. 2-3; pp. 145 - 159
Main Author Clarke, Francis
Format Journal Article Conference Proceeding
LanguageEnglish
Published Cachan Elsevier Ltd 2001
Lavoisier
Subjects
Applied sciences
Computer science; control theory; systems
Control system synthesis
Control theory. Systems
Exact sciences and technology
Feedback
Generalised gradients
Lyapunov function
Nonsmooth analysis
Optimal control
Proximal analysis
Stabilization
Nonsmooth analysis
Proximal analysis
Feedback
Stabilization
Optimal control
Generalised gradients
Lyapunov function
Proximal
Generalized gradient
Non linear control
Lyapunov method
Review
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Summary:In the classical calculus of variations, the question of regularity (smoothness or otherwise of certain functions) plays a dominant role. This same issue, although it emerges in different guises, has turned out to be crucial in nonlinear control theory, in contexts as various as necessary conditions for optimal control, the existence of Lyapunov functions, and the construction of stabilizing feedbacks. In this report we give an overview of the subject, and of some recent developments.
ISSN:0947-3580
1435-5671
DOI:10.3166/ejc.7.145-159