Decentralized delayed-feedback control of a coupled map model for open flow

Abstract

A decentralized delayed-feedback control of a coupled map model for open flow is studied theoretically. The decentralized controllers can suppress turbulent behavior in the open flow model. The stability of the control system is analyzed, and then we provide a procedure to design the decentralized controllers from uncertain information of the local map and the coupling strength. The theoretical results are verified by some numerical simulations. ͓S1063-651X͑98͒06209-6͔ PACS number͑s͒: 05.45.ϩb PHYSICAL REVIEW E SEPTEMBER 1998 VOLUME 58, NUMBER 3 PRE 58 1063-651X/98/58͑3͒/3055͑5͒/$15.00 3055

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

“…The spatiotemporal stability of homogeneous solution (2) of system (1) [Konishi et al, 1998[Konishi et al, , 2000b[Konishi et al, , 2001]. …”

“…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, 1998Konishi et al, , 2000a.…”

“…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[Konishi et al, , 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].…”

Spatiotemporal stability of one-way open coupled nonlinear systems

“…It is confirmed that ʈG(s)ʈ ϱ is greater than 1 and G(s) is stable. The trajectories in the phase plane for sites 5,8,11,13,30, and 50 are shown in Fig. 6.…”

Experimental evidence for spatiotemporal stability in one-way open coupled double-scroll circuits

“…They are classified into several types according to the connection and the boundary conditions. Among them, the one-way open CML is well known as a typical open flow model [1]- [5]. Kaneko discovered a spatial perio-doubling bifurcation in the one-way open CML [2], and it was examined in detail by numerical simulations [3], [4].…”