On tuning leakage for performance-robust adaptive control

The behavior of a model reference adaptive control (MRAC) system is examined. The effect of the inclusion of leakage in the adaptive algorithm is studied, and the leakage mechanism of the σ-modification and the e₁-modification are discussed. A useful approximation is given for a particular MRAC problem for the small step-size average parameter estimate motion away from an arbitrary stabilizing adaptive controller parameterization. Arrow diagrams verify the conclusion that designer-selected leakage constants must be well chosen in relation to the unknown plant and environment to avoid bursting by an adaptive controller in the absence of adequate excitation by the external forcing function(s)