Abstract

A nonsmooth extension of the speed-gradient algorithms in finite form is proposed. The conditions ensuring control goal (convergence of the goal function to zero) are established. A new algorithm is applied to almost global stabilization of the Brockett integrator that has become a popular benchmark for nonsmooth and discontinuous algorithms. It is proved that the designed control law stabilizes the Brockett integrator for any initial point that does not lie on the x3-axis. Besides, it is shown that the speed-gradient algorithm ensures stabilization with an arbitrarily small control level. An important feature of the proposed control is the fact that it is continuous along trajectories of the closed-loop system.

Keywords

  1. nonsmooth systems
  2. nonholonomic integrator
  3. speed-gradient
  4. nonlinear control

MSC codes

  1. 93D15

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Information & Authors

Information

Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 2116 - 2131
ISSN (online): 1095-7138

History

Submitted: 23 March 2015
Accepted: 6 June 2016
Published online: 24 August 2016

Keywords

  1. nonsmooth systems
  2. nonholonomic integrator
  3. speed-gradient
  4. nonlinear control

MSC codes

  1. 93D15

Authors

Affiliations

Funding Information

Russian Science Foundation http://dx.doi.org/10.13039/501100006769 : 14-29-00142

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