Abstract
In the existing results on chaos control and synchronization based on the adaptive controlling technique (ACT), a uniform Lipschitz condition on a given dynamical system is always assumed in advance. However, without this uniform Lipschitz condition, the ACT might be failed in both theoretical analysis and in numerical experiment. This Letter shows how to utilize the ACT to get a rigorous control for the system which is not uniformly Lipschitz but only locally Lipschitz, and even for the system which has unbounded trajectories. In fact, the ACT is proved to possess some limitation, which is actually induced by the nonlinear degree of the original system. Consequently, a piecewise ACT is proposed so as to improve the performance of the existing techniques.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
