An Experimental Suppression of Spatial Instability in One-Way Open Coupled Chua's Circuits

Controlling chaos has attracted a growing interest in the field of nonlinear science [Fradkov & Pogromsky, 1998; Chen & Dong, 1998]. Pyragas proposed a delayed feedback control (DFC) method [Pyragas, 1992], which does not require a reference signal corresponding to the desired unstable periodic orbits. The DFC method has been widely applied to real systems, since it is a practical scheme for experimental situations [Chen & Dong, 1998]. In recent years, an increasing interest has been devoted to the study of spatiotemporal chaos and its control [Astakhov et al., 1995; Hu et al., 1997; Konishi et al., 1998, 2000a]. There has been some interest in a wide variety of complex spatiotemporal behavior of coupled map lattices (CMLs) [Kaneko, 1993]. The one-way open CML [Kaneko, 1985] is well known as a typical open flow model. In this CML the spatial instability was discovered by Kaneko [1985], and it was examined in detail theoretically [Yamaguchi, 1997] and numerically [Willeboordse & Kaneko, 1995]. Recently, the mechanism of the instability in this CML was clarified by the H∞-norm concept, which plays important roles in the robust control theory [Konishi et al., 1999]. Konishi, Kokame and Hirata reported that the decentralized delayed feedback control (DDFC) method can stabilize chaotic behavior in a one-way open CML [Konishi et al., 1998, 2000a]. Imai et al. observed the instability in the electronic CML circuits, and demonstrated the suppression of the instability by the DDFC method [Imai et al., 2002]. Konishi et al. [2000b] verified that the mechanism of the spatial instability in the CML can be extended to continuoustime systems. The instability was observed in coupled diode resonator circuits [Johnson et al., 1995] and coupled Chua’s circuits [Konishi et al., 2001]. Furthermore, it was reported that the LMI-based H∞ control can suppress the instability in the oneway coupled Lorenz systems [Konishi et al., 2002].