Nonsmooth Analysis in Control Theory: A Survey

@article{Clarke2001NonsmoothAI,
  title={Nonsmooth Analysis in Control Theory: A Survey},
  author={Frank H. Clarke},
  journal={Eur. J. Control},
  year={2001},
  volume={7},
  pages={145-159}
}
  • F. Clarke
  • Published 2001
  • Mathematics
  • Eur. J. Control
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. 

Nonsmooth Analysis in Systems and Control Theory

  • F. Clarke
  • Mathematics
    Encyclopedia of Complexity and Systems Science
  • 2009
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This article synthesizes in this article a number of recent developments bearing upon the regularity properties of Lyapunov functions, and discusses the equivalence between open-loop controllability, feedback stabilizability, and the existence of Lyapsinov functions with appropriateregularity properties.

Optimal control: Nonlocal conditions, computational methods, and the variational principle of maximum

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Necessary conditions in optimal control: a new approach

TLDR
The principal focus here is the development of structural criteria on the problem which guarantee a priori that the necessary conditions apply to any local minimizer.

Sliding mode control for a class of second-order systems via linear Lipschitz surfaces

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Regularization and bang-bang conjugate times in optimal control

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On a small gain theorem for ISS networks in dissipative Lyapunov form

TLDR
This paper considers several interconnected ISS systems supplied with ISS Lyapunov functions defined in the dissipative form and provides a condition of a small gain type under which this construction is possible and describes a method of an explicit construction of such an ISS LyAPunov function.

Discontinuous feedbacks, discontinuous optimal controls, and continuous-time model predictive control

It is known that there is a class of nonlinear systems that cannot be stabilized by a continuous time-invariant feedback. This class includes systems with interest in practice, such as nonholonomic

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