Targeting spatiotemporal patterns in extended systems with multiple coexisting attractors

Abstract

We set up adaptive control algorithms which can be used to achieve control to desired attractors in spatially extended systems. Traditional adaptive control methods often fail in such systems due to the presence of multiple coexisting attractors that lead to a high probability of the system getting trapped in an undesired attractor despite the application of control. We use quenching techniques to achieve control in such difficult scenarios. When the control parameter evolves through parameter regions that lead to undesired attractors, the control parameter is changed sufficiently fast so that the system does not get time to get trapped in these attractors, but gets quenched instead to the desirable attractor. The rate of change of the parameter is guided by using variable stiffness of control. We demonstrate the efficacy of our technique in a system of coupled sine-circle maps. Further, such variable stiffness schemes can also be used to step up the efficiency of adaptive control algorithms by making frequent suitable changes in the stiffness of control during the control dynamics. This strategy is very successful in reducing the time required to achieve control, while maintaining the stability of the control dynamics.