Design of LQ controller for the logistic map using grey prediction

A novel control of chaos is proposed in this paper. The compensator for a specific chaotic system (the logistic map) is composed of an LQ regulator and a grey predictor. The LQ regulator is designed according to the linearized model of the logistic map. The state error of the linearized model is predicted by the grey system theory. The control signal is appropriately adjusted in advance and the performance of the control system would be improved at the same time. Simulation results demonstrate that the LQ-grey compensator can stabilize the logistic map to a desired fixed point of period 1 or period 2. Furthermore, the transient response using the compensator is faster than that using only the regulator. The total control energy of the compensator is less than that of the regulator.