Effects of Saturating Nonlinearities on the Stability of Reduced order Adaptive Systems in the Presence of Parasitics: Regulation and Tracking

The problem of robust stability of adaptive systems is considered. The introduction of saturating nonlinearities in the adaptation law improves the stability of the adaptive system significantly in the presence of parasitics. Improved stability is achieved in both regulation and tracking. The proposed adaptation laws lead to analytical and quantitative conditions for robust stability which can be tested a priori and can be used as design criteria. Furthermore, the analysis provides us with a more precise characterization of the behavior of the adaptive system and a systematic approach for robust adaptive control design. In the tracking case, the only requirement on the system inputs is boundedness, with the common requirement of sufficiently exciting inputs, necessary for other adaptation schemes being eliminated. Stability is achieved even in the presence of fast parasitics or high frequency inputs. Systems that in the literature are considered highly unstable without the use of saturating nonlinearities, are easily stabilized with adaptation laws incorporating saturating nonlinearities as shown by numerical simulation of several characteristic cases.