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Stabilizing unstable periodic orbits in a chaotic invariant set not onlyreveals information about its structure but also leads to various interestingapplications. For the successful application of a chaos control scheme,convergence speed is of crucial importance. Here we present a predictivefeedback chaos control method that adapts a control parameter online to yieldoptimal asymptotic convergence speed. We study the adaptive control map bothanalytically and numerically and prove that it converges at least linearly to avalue determined by the spectral radius of the control map at the periodicorbit to be stabilized. The method is easy to implement algorithmically and mayfind applications for adaptive online control of biological and engineeringsystems.

Adapting Predictive Feedback Chaos Control for Optimal Convergence Speed