Uniform global asymptotic stability of adaptively controlled nonlinear systems via strict lyapunov functions
We prove global uniform asymptotic stability of adoptively controlled dynamics by constructing explicit global strict Lya-punov functions. We assume a persistency of excitation condition that implies both asymptotic tracking and parameter identification. We also construct input-to-state stable Lyapunov functions under an added growth assumption on the regressor, assuming that the unknown parameter vector is subject to suitably bounded time-varying uncertainties. This quantifies the effects of uncertainties on the tracking and parameter estimation. We demonstrate our results using the Rössler system. Copyright © 2008 by ASME.
Publication Source (Journal or Book title)
2008 Proceedings of the ASME Dynamic Systems and Control Conference, DSCC 2008
Mazenc, F., De Queiroz, M., & Malisoff, M. (2009). Uniform global asymptotic stability of adaptively controlled nonlinear systems via strict lyapunov functions. 2008 Proceedings of the ASME Dynamic Systems and Control Conference, DSCC 2008 (PART A), 67-72. Retrieved from https://digitalcommons.lsu.edu/mathematics_pubs/988