Harnessing chaotic dynamics with optimized reservoir computer

Due to their unique properties, chaotic signals have been proposed for use in radar, communications, structural monitoring, and other fields. One complication of using chaotic signals is that there are no general rules for designing a chaotic system with specific properties. There are libraries of chaotic signals in the literature [J. C. Sprott, Phys. Rev. E 50, R647 (1994)], but there is no way to predict the particular properties of their signals in advance. Additionally, many chaotic signals lack desirable features for certain sensor applications, such as radar imaging. For instance, these signals introduce large, undesirable ambiguities with a broad mainlobe width and high sidelobe levels, which limit radar sensing capabilities. In this work, we show that a reservoir computer, combined with a nonlinear optimization procedure, can be used to design signals with targeted features. As an example, we consider a high-dimensional Rössler chaotic system and optimize it to reduce the mainlobe width and minimize sidelobes, thereby improving radar detection.