We extend an adaptive control algorithm recently suggested by Huberman and Lumer to
multi-parameter and higher-dimensional nonlinear systems. This control mechanism is
remarkably effective in returning a system to its original dynamics after a sudden
perturbation in the system parameters changes the dynamical behaviour. We find that in all
cases, the recovery time is linearly proportional to the inverse of control stiffness (for small
stiffness). In higher dimensions there is an additional optimization problem since increasing …