Nonlinear control with two complementary Lyapunov function




Zelenak, Andrew J.

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If a Lyapunov function is known, a dynamic system can be stabilized. However, computing or selecting a Lyapunov function is often challenging. This dissertation presents a new approach which eliminates this challenge: a simple control Lyapunov function [CLF] is assumed then the algorithm seeks to reduce the value of the Lyapunov function. If the control effort would have no effect at any iteration, the CLF is switched in an attempt to regain control. There is some flexibility in choosing these two complementary CLF’s but they must satisfy a few characteristics. The method is proven to asymptotically stabilize a wide range of nonlinear systems and was tested on an even broader variety in simulation. It was also tested on an industrial robot to provide compliant behavior. The simulated and hardware demonstrations provide a broad perspective on the algorithm’s usefulness and limitations. In comparison to the ubiquitous PID controller, the algorithm’s advantages include enhanced performance, ease of tuning, and extensions to higher-order and/or coupled systems. Those claimed advantages are validated by a test with four engineering students, which validates the controller as a viable option for nonlinear control (even at the undergraduate level). The algorithm’s drawbacks include the necessity of a dynamic model and, when linearization is required, the reliance on a small simulation time step; however, for the motivating application –interactive industrial robotic systems – both requirements were already met. Finally, the developed software was released to the public as part of the Robot Operating System (ROS) and the details of that release are included in this report.


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