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Feedback control is essential to the performance of dynamical systems, helping to drive nonequilibrium systems from one state to another. In this review, we discuss feedback control applied to living and synthetic active matter—systems that are constantly dynamical and out of equilibrium. We review the experimental and theoretical work in controlling the trajectory and distribution of active matter, from single particles to collective populations. Modern advances in microscopy and numerical computation have enabled data-rich studies of active systems, aided by data-driven approaches to model, forecast, and control the complex and chaotic behaviors of active matter. We describe the basic mathematical structure of active Brownian particles, with a focus on observability and time delay embedding to control particle motion using density data alone. Finally, we comment on the future outlook of controlling complex systems with multibody interparticle and hydrodynamic interactions.
Takatori et al. (Mon,) studied this question.