Improvement of the stability of RFPT-based adaptive controllers by observing “precursor oscillations”

In the design of adaptive controllers the “Robust Fixed Point Transformations (RFPT)“-based approach is a recently developed, very simple alternative of “Lyapunov's 2nd Method”. The main difference between them is that while the traditional approach concentrates on guaranteeing global stability at the cost of directly not considering the primary design intent (i.e. the dynamic details of the tracking error relaxation) the novel one tries to precisely realize a prescribed error relaxation but in general cannot guarantee global stability. The iterative learning sequence it generates by a well defined mapping of little number of independent control parameters may not converge to the solution of the control task if this mapping loses its contractivity. In the present paper a simple parameter setting strategy is proposed that - by the use of a model-independent observer developed for monitoring little “precursor oscillations” - is able to so tune a single parameter of the controller that the iterative sequence always converges to the proper value. The method is designed for Single Input - Single Output (SISO) systems and also is generalized for Multiple Input - Multiple Output (MIMO) ones. The operation of the method is illustrated by a Model Reference Adaptive Controller (MRAC) controlling an indirectly driven and underactuated system.