Kavli Affiliate: L. Mahadevan
| First 5 Authors: Sumit Sinha, Vishaal Krishnan, L Mahadevan, ,
| Summary:
Active many-body systems composed of many interacting degrees of freedom
often operate out of equilibrium, giving rise to non-trivial emergent behaviors
which can be functional in both evolved and engineered contexts. This naturally
suggests the question of control to optimize function. Using navigation as a
paradigm for function, we deploy the language of stochastic optimal control
theory to formulate the inverse problem of shepherding a system of interacting
active particles across a complex landscape. We implement a solution to this
high-dimensional problem using an Adjoint-based Path Integral Control (APIC)
algorithm that combines the power of recently introduced continuous-time
back-propagation methods and automatic differentiation with the classical
Feynman-Kac path integral formulation in statistical mechanics. Numerical
experiments for controlling individual and interacting particles in complex
landscapes show different classes of successful navigation strategies as a
function of landscape complexity, as well as the intrinsic noise and drive of
the active particles. However, in all cases, we see the emergence of paths that
correspond to traversal along the edges of ridges and ravines, which we can
understand using a variational analysis. We also show that the work associated
with optimal strategies is inversely proportional to the length of the time
horizon of optimal control, a result that follows from scaling considerations.
All together, our approach serves as a foundational framework to control active
non-equilibrium systems optimally to achieve functionality, embodied as a path
on a high-dimensional manifold.
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