Simulation Studies on Various Tuning Methods for Convergence Stabilization in a Novel Approach of Model Reference Adaptive Control Based on Robust Fixed Point Transformations

Abstract

The concept of “Artificial Intelligence (AI)” also contains the adaptive controllers that are able to observe the behavior of the a priori only insufficiently known physical systems under their control, and automatically can adjust themselves in order to achieve precise control. Regarding their implementations, certain approaches use the rather “conventional” means of AI as rule bases, fuzzy, neural or neurofuzzy systems, others can more strictly utilize the specialties of the available analytical models. In this paper the behavior of a novel version of the “Model Reference Adaptive Controllers” is investigated. In contrast to the traditional approaches the design of these controllers does not need the use of the difficult technique of Lyapunov’s “direct” method. Instead of the use of Lyapunov functions that can guarantee global asymptotic stability it applies “Robust Fixed Point Transformations” that work with a local, bounded basin of convergence of the iteration that converges to the solution of the control task. The method applies only three control parameters that in the most of the cases can be fixed. It is shown that by properly tuning only one of the three parameters the convergence of the controller can be stabilized. The theory does not uniquely define the details of this tuning in which we have a great freedom. The operation of various tuning strategies were investigated for the adaptive control for two interesting paradigms: an underactuated mechanical system and an other mechanical system that contains a dynamically coupled internal degree of freedom neither observed nor directly manipulated by the controller.