Optimal navigation of interacting active particles on complex landscapes

Active many-body systems composed of many interacting degrees of freedom and operating out of equilibrium give rise to non-trivial emergent behaviors across several scales. While non-equilibrium statistical physics provides an effective theoretical framework for developing bottom-up forward models, a corresponding inverse, top-down framework to ascribe function to active many-body systems is lacking. Here we use stochastic optimal control theory to achieve the emergence of functional active matter, in the context of navigation on complex landscapes. We develop the Adjoint-based Path Integral Control (Adjoint-PI Control) algorithm which implements optimal control based on the Feynman-Kac path integral formulation using continuous-time back-propagation. We use numerical experiments of stochastic optimal control of single and many interacting particles in complex external landscapes, and use theory to show that optimal work done is inversely proportional to the length of the time horizon of optimal control. We also study the competition between extrinsic noise strength and the intrinsic energy-scale encoded in the interaction potential. Taken together, our Adjoint-PI Control algorithm provides a foundational framework to control non-equilibrium systems optimally to achieve navigational functionality.