Local Controls for Large Assemblies of Nonlinear Elements

We introduce a set of local procedures that are capable of controlling distributed systems that exhibit complex dynamical behavior. These local controllers need only perturb local parameters and use local information about the state of the system. Besides eliminating the wiring and overhead needed for implementing a central controller, our procedure leads to desired states in short times. By resoring to a probabalistic dynamical argument, we also show that there are critical values for the couplings among the nonlinear elements beyond which the local controllers do not achieve the desired final state.

[1]  A. Fleischmann.  Distributed Systems , 1994, Springer Berlin Heidelberg.

[2]  A. Winfree.  The geometry of biological time , 1991 .

[3]  B. Huberman,et al.  Dynamics of adaptive systems , 1990 .

[4]  Qu,et al.  Controlling spatiotemporal chaos in coupled map lattice systems. , 1994, Physical review letters.

[5]  Tad Hogg,et al.  The Emergence of Computational Ecologies , 1993 .

[6]  Grégoire Nicolis,et al.  Synchronous versus asynchronous dynamics in spatially distributed systems , 1994 .

[7]  K. Kaneko.  Pattern dynamics in spatiotemporal chaos: Pattern selection, diffusion of defect and pattern competition intermettency , 1989 .

[8]  Sepulchre,et al.  Controlling chaos in a network of oscillators. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Kurt Wiesenfeld,et al.  Stability results for in-phase and splay-phase states of solid-state laser arrays , 1993 .

[10]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[11]  Joel E. Cohen,et al.  Review: Arthur T. Winfree, The geometry of biological time , 1982 .

[12]  M. Mehregany,et al.  Microelectromechanical systems , 1993, IEEE Circuits and Devices Magazine.

[13]  IMENTATION PAGE,et al.  The Use of Adaptive Structures in Reducing Drag of Underwater Vehicles , 1991 .

[14]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

[15]  Gang,et al.  Controlling chaos in systems described by partial differential equations. , 1993, Physical review letters.

[16]  E. Ott,et al.  Controlling Chaotic Dynamical Systems , 1991, 1991 American Control Conference.

[17]  S. Leibler.  Recent Developments in the Physics of Fluctuating Membranes , 1991 .

[18]  S. Strogatz,et al.  Integrability of a globally coupled oscillator array. , 1993, Physical Review Letters.

[19]  Roy,et al.  Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system. , 1992, Physical review letters.