Nonlocal time-delayed feedback control of spatiotemporal patterns: controlling a network of digital phase-locked loops

Abstract

Control of spatially extended systems is an important and challenging topic of research. Previous control techniques rely on local or global feedback control. In this paper, for the first time, we propose the nonlocal time-delayed feedback control technique that can control spatiotemporal patterns of an important class of spatially extended systems, namely the coupled map lattice systems. We demonstrate the proposed technique in an engineering system, namely digital phase-locked loop, which is widely used in communication and signal processing systems, and at the same time its network mimics a physically realizable coupled map lattice system. We carry out stability analysis to derive the condition of controllability. Unlike other control techniques, apart from feedback strength, the proposed control scheme offers an additional control parameter, namely the feedback range that makes this technique more versatile. We show that depending upon these control parameters one can suppress spatiotemporal chaos and other complex patterns in order to establish a synchronized fixed point solution, which is the desired solution in most practical systems. We also derive the optimum value of the control parameter for which the control gives fastest convergence. We believe that the proposed technique will be useful in controlling spatially extended systems in other fields also.