Nonlinear control of dynamical systems from time series

Improved control of delayed measured systems

In this paper, we address the question of how the control of delayed measured chaotic systems can be improved. Both unmodified Ott-Grebogi-Yorke control and difference control can be successfully applied only for a certain range of Lyapunov numbers depending on the delay time. We show that this limitation can be overcome by at least two classes of methods, namely, by rhythmic control and by the memory methods of linear predictive logging control and memory difference control.

Decoding information by following parameter modulation with parameter adaptive control

It has been proposed to realize secure communication using chaotic synchronization via transmission of a binary message encoded by parameter modulation in the chaotic system. This paper considers the use of parameter adaptive control techniques to extract the message, based on the assumptions that we know the equation form of the chaotic system in the transmitter but do not have access to the precise values of the parameters which are kept secret as a secure set. In the case in which a synchronizing system can be constructed using parameter adaptive control by the transmitted signal and the synchronization is robust to parameter mismatches, the parameter modulation can be revealed and the message decoded without resorting to exact parameter values in the secure set. A practical local Lyapunov function method for designing parameter adaptive control rules based on originally synchronized systems is presented.

Nonlinear prediction, filtering, and control of chemical systems from time series

Prediction, filtering and control of nonlinear systems is formulated in terms of corresponding nonlinear surfaces in the phase space of delayed system readings and control parameters. The construction of these surfaces from time series and their use is demonstrated with a simple chemical model in the chaotic regime. (c) 1997 American Institute of Physics.