Research: Active-Adaptive Control

Parameter convergence in systems with nonlinear parametrization

When it comes to controlling systems with parametric uncertainty, one of the main benefits of an adaptive approach compared to a robuastness approach is the ability to estimate the uncertain parameter over time. Conditions for parameter convergence in systems with nonlinear parametrization are currently being studied. Even though the adaptive algorithms that have been developed for systems with nonlinear parametrization guarantee global stability, they also introduce other components into the system that make the parameter convergence problem nontrivial. Akin to the parameter convergence problem in linear adaptive control, conditions on the system signals, i.e. their persistent excitation, needs to be invoked. We have derived similar sufficient conditions, that corresponds to nonlinear persistent excitation (NLPE), under which parameter estimates converge to their true values for a specific class of nonlinear systems. Not surprisingly, these conditions are stronger than the linear persistent excitation conditions, and depend on the nature of the nonlinearity present in the parametrization. Current work is focused on the extension of this class, and a deeper examination of NLPE.

Publications:

C. Cao and A.M. Annaswamy, “Parameter convergence in nonlinearly parametrized systems,” IEEE Transactions on Automatic Control, vol. 48, No. 3, pp. 397-412, 2003.