# Leveraging Stochasticity for Open Loop and Model Predictive Control of Complex Fluid Systems

## TL;DR

This paper introduces a measure-theoretic framework for controlling stochastic spatio-temporal systems, enabling optimization of control policies based on thermodynamic principles, with promising simulation results across various processes.

## Contribution

It develops a novel variational control framework for stochastic fields using measure theory and thermodynamics, applicable to diverse spatio-temporal processes.

## Key findings

- Framework successfully applied to four stochastic processes
- Simulation results indicate effective control policy optimization
- Provides new insights into stochastic control of complex systems

## Abstract

Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by describing them as evolutionary processes on Hilbert spaces, and in doing so, derives a framework for spatio-temporal manipulation from fundamental thermodynamic principles. This approach yields a variational optimization framework for controlling stochastic fields. The resulting scheme is applicable to a wide class of spatio-temporal processes and can be used for optimizing parameterized control policies. Our simulated experiments explore the application of two forms of this approach on four stochastic spatio-temporal processes, with results that suggest new perspectives and directions for studying stochastic control problems for spatio-temporal systems.