A purely data-driven framework for prediction, optimization, and control of networked processes.

Area of Science:

• Complex Systems Science
• Network Science
• Dynamical Systems Theory

Background:

• Networks exhibit emergent behaviors from local interactions, but identifying their underlying nonlinear dynamics is challenging.
• Existing methods often require prior knowledge of network structure, limiting applicability.
• Controlling large-scale nonlinear network dynamics, especially with model predictive control (MPC), is computationally demanding.

Purpose of the Study:

• To develop a data-driven framework for identifying and controlling stochastic nonlinear dynamics in large-scale networks.
• To overcome the limitations of requiring prior network structure information.
• To enable effective control of complex network systems using a simplified optimization approach.

Main Methods:

• Utilized operator-theoretic techniques, specifically the Koopman operator, for system identification.
• Employed a data-driven approach using two-step state snapshots without needing network topology.
• Transformed nonlinear dynamics into a linear representation for tractable analysis and control.
• Applied the derived linear Koopman model to model predictive control (MPC).

Main Results:

• Successfully identified stochastic nonlinear dynamics using only state data.
• Developed a low-dimensional linear representation of complex network dynamics.
• Converted a challenging nonlinear programming problem in MPC to a convex quadratic programming problem.
• Demonstrated a significant reduction in variables for optimization in large-scale network control.

Conclusions:

• The proposed framework effectively identifies and controls nonlinear network dynamics from data alone.
• The Koopman operator approach simplifies complex system analysis and control.
• This method offers a computationally efficient solution for controlling large-scale nonlinear systems, particularly within MPC frameworks.