未知システムに対するDFCとPFCとのハイブリッド型カオス制御

抄録

Chaos control is stabilizing the state of a chaotic system into the peculiar unstable periodic orbit (UPO). In chaos control proposed until today, the target system is known in many cases. However, when the generating mechanism of chaos is unknown, the control only based on time series data observed from the system is also required. Delayed feedback control (DFC) applies control input based on the difference between the τ-time delayed state and the current state. Where τ denotes the periods of UPO. Although this method needs correctly no chaos orbit if the periods of UPO is known, there exists the limitation of the odd number property. As the method to compensate this fault, there is prediction-based feedback control (PFC) using the prediction value of τ-time future state. However, PFC needs to calculate this prediction value analytically by using the known mathematical model of the target system.
Then, in this paper, chaos control for unknown chaotic systems is proposed. This technique has the hybrid type control input to improve faults of DFC and PFC. The prediction value to be used in the control input is determined by using neural network or fuzzy neural network. The control inputs are impressed only near periodic points of the target UPO using the concept of the unstable periodic region.