Adaptive control of chaotic systems with uncertainties

In this paper, an adaptive control scheme, that employs a Gaussian radial basis function network with output weights updated on-line according to the Lyapunov stability theory, is suggested for regulation of a class of chaotic systems with uncertainties. Theoretical analysis guarantees that under the control of the proposed adaptation law, uncertain chaotic systems can asymptotically track target orbits within arbitrarily small tolerance bounds. As an example, control of the uncertain Duffing-Holmes system is presented with computer simulations, which verifies and visualizes the theory and design of the adaptive controller.