Optimization Approach to the Estimation and Control of Lyapunov Exponents

In this paper, we describe an algorithm for estimating the Lyapunov exponents from the chaotic dynamics of control systems. Attention is focused on optimization methods for estimating tangent maps from experimental time series data. Our numerical tests show that the algorithm is robust and quite effective, and that its performance is comparable with that of other algorithms. The properties of the algorithm are demonstrated by application to a range of data sets. We consider numerical and experimental data and discuss the computational aspects of the proposed algorithm. New feedback rules for use with optimization techniques in the stimulation of the epileptic brain are proposed. This work was supported by NIH, NSF, and CRDF grants.