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Stabilization of Nonlinear Systems by Switched Lyapunov Function

[+] Author Affiliations
Andy Zelenak, Mitch Pryor

The University of Texas at Austin, Austin, TX

Paper No. DSCC2015-9650, pp. V001T03A002; 9 pages
doi:10.1115/DSCC2015-9650
From:
  • ASME 2015 Dynamic Systems and Control Conference
  • Volume 1: Adaptive and Intelligent Systems Control; Advances in Control Design Methods; Advances in Non-Linear and Optimal Control; Advances in Robotics; Advances in Wind Energy Systems; Aerospace Applications; Aerospace Power Optimization; Assistive Robotics; Automotive 2: Hybrid Electric Vehicles; Automotive 3: Internal Combustion Engines; Automotive Engine Control; Battery Management; Bio Engineering Applications; Biomed and Neural Systems; Connected Vehicles; Control of Robotic Systems
  • Columbus, Ohio, USA, October 28–30, 2015
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5724-3
  • Copyright © 2015 by ASME

abstract

If a Lyapunov function is known, a dynamic system can be stabilized. However, computing a Lyapunov function is often challenging. This paper takes a new approach; it assumes a basic Lyapunov-like function then seeks to numerically diminish the Lyapunov value. If the control effort would have no effect at any iteration, the Lyapunov-like function is switched in an attempt to regain control. The method is tested on four simulated systems to give some perspective on its usefulness and limitations. A highly coupled 3rd order system demonstrates the approach’s general applicability and finally the coordinated control of 7 motors for a robotic application is considered. Details on the publicly available software packages for application agnostic software and hardware environments are also presented.

Copyright © 2015 by ASME

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