Optimization of local control of chaos by an evolutionary algorithm

An evolutionary algorithm for optimizing local control of chaos is presented. Based on a Lyapunov approach, a linear control law and the state-space region in which this control law is activated are determined. In addition, we study a relation between certain adjustable design parameters and a particular measure of the uncontrolled chaotic attractor in the state-space region of control (SSRC). From this relation the objective function to be optimized is derived. In that context, we assume a linear control law to be given and optimize size and shape of the SSRC using an evolutionary algorithm. It is shown by examples how the algorithm can also be applied to higher-dimensional systems with possibly more than one positive Lyapunov exponent.