Leveraging Stochasticity for Open Loop and Model Predictive Control of Spatio-Temporal Systems.

Area of Science:

• Physics
• Applied Mathematics
• Quantum Mechanics

Background:

• Stochastic spatio-temporal processes are fundamental in diverse scientific fields, including plasma physics, fluid dynamics, and quantum systems.
• Existing methods for analyzing and controlling these processes often lack a unified theoretical foundation.

Purpose of the Study:

• To develop a measure-theoretic framework for describing and manipulating stochastic spatio-temporal systems.
• To derive a variational optimization approach for controlling stochastic fields based on fundamental thermodynamic principles.

Main Methods:

• Describing stochastic spatio-temporal systems as evolutionary processes on Hilbert spaces.
• Applying measure-theoretic concepts to derive a control framework.
• Developing a variational optimization scheme for parameterized control policies.

Main Results:

• A novel framework for spatio-temporal manipulation derived from thermodynamic principles.
• A versatile variational optimization scheme applicable to a broad range of stochastic fields.
• Simulated experiments demonstrating the effectiveness of the proposed control methods on four distinct stochastic spatio-temporal processes.

Conclusions:

• The developed framework provides new perspectives for studying and controlling complex spatio-temporal systems.
• The variational optimization approach offers a powerful tool for optimizing control policies in stochastic environments.
• This work opens new research directions in stochastic control for spatio-temporal dynamics.