Karhunen-Loeve mode control of chaos in a reaction-diffusion process

We introduce a chaos control method that stabilizes unstable states of a spatiotemporal process based on analyzing the dynamics of the main coherent structure in the data represented by the highest energy Karhunen-Loeve mode. The problem is then reduced to the application of embedding techniques to the control of a time series given by the amplitude of a dominant spatial mode. The algorithm is applied to a reaction-diffusion process where we stabilize an unstable orbit inside a chaotic regime. One advantage of the control procedure is that it is independent of sensor placement. Furthermore, we find the desired control state is achieved exponentially, and the procedure can be applied directly to experimental data.