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Minimum Information Variability in Linear Langevin Systems via Model Predictive Control.

Adrian-Josue Guel-Cortez1, Eun-Jin Kim1, Mohamed W Mehrez2

  • 1Centre for Fluid and Complex Systems, Coventry University, Priory St, Coventry CV1 5FB, UK.

Entropy (Basel, Switzerland)
|April 26, 2024
PubMed
Summary
This summary is machine-generated.

We developed a new control method for complex systems using model predictive control and information geometry. This approach minimizes "geometric information variability" in system dynamics, validated on Ornstein-Uhlenbeck and Kramers equations.

Keywords:
Langevin equationsentropyfluctuationsinformation theorymodel predictive control

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Area of Science:

  • Complex Systems Dynamics
  • Statistical Physics
  • Control Theory

Background:

  • Controlling the time evolution of probability distributions in complex systems is difficult.
  • Applications include controlling mesoscopic systems.
  • Existing methods may not sufficiently address geometric properties of system dynamics.

Purpose of the Study:

  • To propose a novel control approach for complex systems.
  • To minimize deviations from the geodesic of information length over time.
  • To ensure dynamics with minimum geometric information variability.

Main Methods:

  • Blending model predictive control (MPC) with information geometry theory.
  • Applying MPC's online optimization for system input determination.
  • Focusing on linear Langevin systems.

Main Results:

  • Validated the methodology on Ornstein-Uhlenbeck process and Kramers equation.
  • Demonstrated the feasibility of the proposed control approach.
  • Analyzed the impact on entropy production and entropy rate for the Ornstein-Uhlenbeck process.

Conclusions:

  • The proposed control strategy effectively minimizes geometric information variability.
  • Provides a physical understanding of control effects on entropy production.
  • Offers a promising direction for controlling complex system dynamics.