We give a new explicit, global, strict Lyapunov function construction for the error dynamics for adaptive tracking control problems, under an appropriate persistency of excitation condition. We then allow time-varying uncertainty in the unknown parameters. In this case, we construct input-to-state stable Lyapunov functions under suitable bounds on the uncertainty, provided the regressor also satisfies an affine growth condition. This lets us quantify the effects of uncertainties on both the tracking and the parameter estimation. We illustrate our results using Rössler systems. © 2009 IEEE.
Publication Source (Journal or Book title)
IEEE Transactions on Automatic Control
Mazenc, F., de Queiroz, M., & Malisoff, M. (2009). Uniform global asymptotic stability of a class of adaptively controlled nonlinear systems. IEEE Transactions on Automatic Control, 54 (5), 1152-1158. https://doi.org/10.1109/TAC.2009.2013053