A New Leakage Term in the Adaptive Law

The hyperstability theory of adaptive control systems is extended to encompass plants with unmodelled dynamics and disturbances. The analysis not only shows that leakage in the adaptive law is a natural way to avoid robustness problems (which is a known result in adaptive control theory), but also provides a new adaptive law that is a sort of signal-dependent σ-modification. The proposed adaptive law is less conservative than the σ-modification, but still ensures the global stability of the system, which is formally proven in the paper. Since it is shown that the design parameter σ of the proposed adaptive law is directly related to the H∞ norm of the parasitic dynamics, the criteria for system stability are derived. Based on these, some guidelines for choosing the leakage parameter σ and the bandwidth of the reference model are presented.