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.
- Dynamic Systems and Control Division
Stabilization of Nonlinear Systems by Switched Lyapunov Function
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Zelenak, A, & Pryor, M. "Stabilization of Nonlinear Systems by Switched Lyapunov Function." Proceedings of the 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. V001T03A002. ASME. https://doi.org/10.1115/DSCC2015-9650
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