A Novel, Abstract Rotation-Based Fixed Point Transformation in Adaptive Control

As an alternative of the Lyapunov function-based design of adaptive controllers the Fixed Point Transformation based Adaptive controller was introduced that in the first step transforms the control task into a Fixed Point Problem then so solves it via iteration that during one digital control step one step of iteration happens. In the actual step this scheme takes into consideration the controlled system's response obtained for the control action in the previous step, therefore it applies delayed feedback that makes it very flexible in the adaptive control of time-delayed systems. In transforming the control problem into a fixed point problem countless mathematical possibilities exist. Till now only a few versions were in use. On the basis of certain old antecedents in this paper a novel version is suggested that creates abstract rotations in the n dimensional space on the basis of the generalization of the Rodrigues formula. Its main advantage is its simplicity, easy geometric interpretation, lucidity, and better fitting to the features of the particular control task. Its applicability is exemplified by simulations for the adaptive control of two mass-points coupled by nonlinear springs.