Non-Lipschitz continuous adaptive regulation of nonlinear systems with uncontrollable unstable linearization

• Published in: Proceedings of the 41st IEEE Conference on Decision and Control, 2002 Vol. 4; pp. 3825 - 3830 vol.4
• Main Authors: Back, J., Jo, N.H., Seo, J.H.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2002
• Subjects: Adaptive control; Computer science; Control systems; Ear; Eigenvalues and eigenfunctions; Jacobian matrices; Nonlinear control systems; Nonlinear systems; Power engineering and energy; Programmable control
• ISBN: 0780375165; 9780780375161
• ISSN: 0191-2216
• DOI: 10.1109/CDC.2002.1184961

Adaptive regulation problem is solved for a class of nonlinear systems whose Jacobian linearization may have uncontrollable modes with eigenvalues lying on the right half-plane. By proposing a continuous version of the LaSalle-Yoshizawa theorem and using the technique of adding a power integrator, we developed a constructive design tool that solves the adaptive regulation problem under continuous framework. We designed a C/sup 0/ adaptive control input, an update law for unknown parameters, and a C/sup 1/ control Lyapunov function which is positive definite and proper. A physical example is provided to illustrate the proposed adaptive control schemes.