Zhang Y.,Sun Yat Sen University |
Zhang Y.,The SYSU CMU Shunde International Joint Research Institute |
Zhang Y.,Key Laboratory of Autonomous Systems and Networked Control |
Chen D.,Sun Yat Sen University |
And 12 more authors.
Nonlinear Dynamics | Year: 2014
Gradient dynamics systems and their exponential convergence theories are investigated in this paper. Differing from widely considered linear gradient dynamics system (LGDS), a class of nonlinear gradient dynamics system (NGDS) is investigated with the exponential convergence analyzed. As an application to scalar square root finding, by defining six different square-based nonnegative error-monitoring functions (i.e., energy functions), six different NGDSs are theoretically designed and proposed in the form of first-order differential equations. Moreover, inspired by the exponential convergence theory of the LGDS, for each of the six proposed NGDSs, the corresponding exponential convergence theory is proved rigorously based on Lyapunov theory. Numerical verification and comparison further illustrate the efficacy of the proposed six NGDSs, in which the main differences and respective usages, as well as the application background and condition, are discussed in detail. © 2014, Springer Science+Business Media Dordrecht.