Extremum Seeking for Force and Torque Actuated Systems

摘要

Extremum seeking (ES) is a powerful tool for the optimization and stabilization of unknown, open-loop unstable, noisy dynamic systems. It is particularly useful for autonomous systems and source seeking of analytically unknown functions. In this work we develop ES controllers for directly force-actuated noisy n-dimensional systems. We develop analytic forms for the controllers and demonstrate their effectiveness with simulation studies. We also consider a more constrained, 2D control problem in which a force is applied to the system dynamics, but the direction of the force is controlled via torque. Such a model is sometimes used to study under actuated ships as well as wheeled robots. We derive analytic formulas for the controllers, prove convergence results, and demonstrate with simulation studies.