ASPR-based Adaptive Feedback Control with Adaptive PFC and FF Input based on RBF NN for Unstable Systems

Abstract

It is well recognized that Almost Strictly Positive Real (ASPR)-based output feedback control has robustness with respect to disturbances and system’s uncertainty. However, most practical systems do not have ASPR property. To solve this problem, the introduction of a parallel feedforward compensator (PFC) bas been proposed in order to render the resulting augmented system ASPR and adaptive type PFC design methods have been also provided already. The adaptive method can design an appropriate PFC by only utilizing input and output online data of the system without the strict information of the system, and thus it is effective for the uncertain systems. However, most of the schemes were only for stable systems. In this paper, we proposed the adaptive PFC design method for unstable systems. Moreover, the adaptive feedforward (FF) input based on Radial Basis Function (RBF) Neural Network (NN) is introduced in order to achieve the adequate output tracking. The stability of the obtained adaptive control system is also analyzed and the boundedness of all the signals in the control system will be shown.