Optimal tracking strategies in a turbulent flow

Abstract

Pursuing a drifting target in a turbulent flow is an extremely difficult task whenever the searcher has limited propulsion and maneuvering capabilities. Even in the case when the relative distance between pursuer and target stays below the turbulent dissipative scale, the chaotic nature of the trajectory of the target represents a formidable challenge. Here, we show how to successfully apply optimal control theory to find navigation strategies that overcome chaotic dispersion and allow the searcher to reach the target in a minimal time. We contrast the results of optimal control -- which requires perfect observability and full knowledge of the dynamics of the environment -- with heuristic algorithms that are reactive -- relying on local, instantaneous information about the flow. While the latter display significantly worse performances, optimally controlled pursuers can track the target for times much longer than the typical inverse Lyapunov exponent and are considerably more robust.

References in corpus (7)

• Pulling and Pushing a Cargo With a Catalytically Active Carrier
• Lagrangian Statistics for Navier-Stokes Turbulence under Fourier-mode reduction: Fractal and Homogeneous Decimations
• Optimal active particle navigation meets machine learning
• Optimising low-Reynolds-number predation via optimal control and reinforcement learning
• Optimal navigation of microswimmers in complex and noisy environments
• Long-distance migration with minimal energy consumption in a thermal turbulent environment
• Taming Lagrangian Chaos with Multi-Objective Reinforcement Learning

Cited by in corpus (7)

• Synthetic Lagrangian Turbulence by Generative Diffusion Models
• Energetic cost of microswimmer navigation: the role of body shape
• Theory for Optimal Estimation and Control under Resource Limitations and Its Applications to Biological Information Processing and Decision-Making
• A critical assessment of reinforcement learning methods for microswimmer navigation in complex flows
• Super-resolution reconstruction of turbulent flows from a single Lagrangian trajectory
• Data-driven Mori-Zwanzig modeling of Lagrangian particle dynamics in turbulent flows
• Optimal navigation in two-dimensional flows: Control theory and reinforcement learning