[Paper Review] Closed-Loop Turbulence Control Using Machine Learning

Thomas Duriez, Vladimir Parezanović+6 more|arXiv (Cornell University)|Apr 17, 2014

Model Reduction and Neural Networks24 references16 citations

TL;DR

This paper introduces Machine Learning Control (MLC), a model-free, feedback-based strategy using genetic programming to optimize nonlinear, multiple-input multiple-output (MIMO) control laws for turbulent flows. It successfully stabilizes nonlinearly coupled oscillators, maximizes chaos in a forced Lorenz system, and enhances mixing by 12% in an experimental mixing layer—outperforming periodic forcing without requiring a system model or prior knowledge of dynamics.

ABSTRACT

We propose a general model-free strategy for feedback control design of turbulent flows. This strategy called 'machine learning control' (MLC) is capable of exploiting nonlinear mechanisms in a systematic unsupervised manner. It relies on an evolutionary algorithm that is used to evolve an ensemble of feedback control laws until minimization of a targeted cost function. This methodology can be applied to any non-linear multiple-input multiple-output (MIMO) system to derive an optimal closed-loop control law. MLC is successfully applied to the stabilization of nonlinearly coupled oscillators exhibiting frequency cross-talk, to the maximization of the largest Lyapunov exponent of a forced Lorenz system, and to the mixing enhancement in an experimental mixing layer flow. We foresee numerous potential applications to most nonlinear MIMO control problems, particularly in experiments.

Motivation & Objective

• To develop a model-free, feedback control strategy for turbulent flows that does not rely on reduced-order models or linearized dynamics.
• To address the limitations of traditional control methods in handling nonlinear frequency cross-talk and complex interactions in turbulent systems.
• To enable real-time, in-time control of MIMO systems by evolving nonlinear control laws through unsupervised learning.
• To demonstrate the method’s effectiveness in stabilizing nonlinear oscillators, enhancing mixing in experimental flows, and maximizing chaos in a forced dynamical system.
• To provide a flexible, general-purpose control framework applicable to real-world experimental fluid dynamics where system models are unknown or intractable.

Proposed method

• MLC employs genetic programming (GP) to evolve an ensemble of nonlinear feedback control laws, treating each control law as an individual in a population.
• The control laws are represented as tree-structured functions of sensor measurements, enabling automatic discovery of both control structure and parameters.
• An objective function (cost function) is defined to guide evolution toward desired system behavior, such as stabilization, mixing enhancement, or chaos maximization.
• Each individual (control law) is evaluated through simulation or experiment, and the fittest individuals are selected for reproduction, mutation, and crossover over successive generations.
• The method is inherently parallelizable and can incorporate sensor history or time delays through extended input representations.
• The approach is applied to three test cases: a two-frequency mean-field model, a forced Lorenz system, and an experimental mixing layer wind tunnel.

Experimental results

Research questions

• RQ1 Can a model-free, feedback-based control strategy effectively stabilize nonlinearly coupled oscillators with frequency cross-talk without relying on linearized models?
• RQ2 Can genetic programming evolve control laws that maximize the largest Lyapunov exponent in a chaotic system like the forced Lorenz equations?
• RQ3 Can MLC outperform periodic open-loop forcing in enhancing mixing in a real experimental turbulent flow?
• RQ4 How does MLC handle real-world challenges such as broadband sensor dynamics, large convective time delays, and strong nonlinearity in experimental settings?
• RQ5 To what extent can MLC be generalized to other MIMO, nonlinear, and complex fluid dynamics problems where system models are unavailable?

Key findings

• MLC successfully stabilized a nonlinearly coupled two-frequency mean-field oscillator by exploiting frequency cross-talk, a phenomenon ignored by linear models.
• In the forced Lorenz system, MLC maximized the largest Lyapunov exponent by evolving control laws that enhanced chaotic behavior, demonstrating control over unpredictability.
• In the TUCOROM wind-tunnel experiment, MLC increased the mixing layer width by 12% compared to the best periodic forcing, achieving superior mixing efficiency.
• MLC reduced actuation cost in the mixing layer experiment, indicating improved energy efficiency compared to conventional open-loop forcing.
• The method overcame significant experimental challenges, including broadband sensor dynamics, large time delays, and strong nonlinearity, proving robustness in real-world conditions.
• The derived control laws were complex and nonlinear, indicating that MLC discovered mechanisms not accessible through linear or parameter-optimized control strategies.