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About this book

This is the first textbook on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. In Chapter 3, methods of linear control theory are reviewed. In Chapter 4, MLC is shown to reproduce known optimal control laws for linear dynamics (LQR, LQG). In Chapter 5, MLC detects and exploits a strongly nonlinear actuation mechanism of a low-dimensional dynamical system when linear control methods are shown to fail. Experimental control demonstrations from a laminar shear-layer to turbulent boundary-layers are reviewed in Chapter 6, followed by general good practices for experiments in Chapter 7. The book concludes with an outlook on the vast future applications of MLC in Chapter 8. Matlab codes are provided for easy reproducibility of the presented results. The book includes interviews with leading researchers in turbulence control (S. Bagheri, B. Batten, M. Glauser, D. Williams) and machine learning (M. Schoenauer) for a broader perspective. All chapters have exercises and supplemental videos will be available through YouTube.

Table of Contents

Frontmatter

Chapter 1. Introduction

Abstract
This chapter provides an introduction to machine learning control (MLC), a surprisingly simple model-free technology to tame complex nonlinear systems. We identify the need for MLC in the context of the benefits and challenges of existing feedback control strategies, with motivation from the grand challenge problem of feedback turbulence control. MLC provides a powerful new framework to control complex dynamical systems that are currently beyond the capability of existing methods in control.
Thomas Duriez, Steven L. Brunton, Bernd R. Noack

Chapter 2. Machine Learning Control (MLC)

Abstract
This chapter discusses the central topic of this book: the use of powerful techniques from machine learning to discover effective control laws for complex, nonlinear dynamics. The machine learning control (MLC) framework is then developed using genetic programming as a search algorithm to find control laws that are not accessible through linear control theory. Implementation details and example codes are also provided.
Thomas Duriez, Steven L. Brunton, Bernd R. Noack

Chapter 3. Methods of Linear Control Theory

Abstract
This chapter provides a self-contained overview of modern linear feedback control theory. We focus on key methods for laminar and transitional flow stabilization, introducing concepts from optimal control theory and system identification to build intuition. Optimal regulators and filters are discussed, along with system identification.
Thomas Duriez, Steven L. Brunton, Bernd R. Noack

Chapter 4. Benchmarking MLC Against Linear Control

Abstract
In this chapter, we demonstrate the use of genetic programming for machine learning control (MLC) on linear systems where optimal control laws are known. In particular, we benchmark MLC against the linear quadratic regulator (LQR) for full-state feedback and the Kalman filter for full-state estimation, providing code for each example. MLC is able to identify the optimal linear control solutions and outperforms linear control even for small nonlinearity.
Thomas Duriez, Steven L. Brunton, Bernd R. Noack

Chapter 5. Taming Nonlinear Dynamics with MLC

Abstract
We investigate the application of machine learning control (MLC) to the stabilization of a nonlinear dynamical system. This plant features a frequently observed frequency crosstalk between actuation and unstable dynamics. MLC explores and exploits this frequency crosstalk as an enabling actuation mechanism. MLC-based feedback is benchmarked against open- and closed-loop forcing derived from Kryloff-Bogoliubov approximation.
Thomas Duriez, Steven L. Brunton, Bernd R. Noack

Chapter 6. Taming Real World Flow Control Experiments with MLC

Abstract
In this chapter, we present applications of machine learning control (MLC) to flow control experiments. Examples range from mixing enhancement of laminar flow to separation mitigation of a turbulent boundary layer. The discussion highlights the physical actuation mechanisms, challenges of alternative model-based control and enabling implementations of MLC in the data aquisition system.
Thomas Duriez, Steven L. Brunton, Bernd R. Noack

Chapter 7. MLC Tactics and Strategy

Abstract
In this chapter, we provide good practices for applying machine learning control (MLC) to a real-world flow control experiment. The recipes include common experimental challenges, like defining a cost function, implementing MLC on the computer, and dealing with imperfect plants, actuation and sensing. In addition, we show how MLC can learn faster by preconditioning the control problem and by planning, monitoring and post-processing the experimental campaign. Most of the advice is formulated for the non-ideal flow control experiment, but is easily applicable for any other real-world application.
Thomas Duriez, Steven L. Brunton, Bernd R. Noack

Chapter 8. Future Developments

Abstract
This chapter anticipates future developments in machine learning control (MLC), a rapidly evolving discipline with applications of epic proportions. First, methodological advantages are considered. Big data and machine learning offer a huge opportunities to learn the optimal control faster and to address more complex problems, e.g. time-varying plants and high-dimensional actuation and sensing. Second, we outline high-impact engineering applications of MLC in turbulence and nonlinear control. These applications may range from everyday life to transport and industrial production.
Thomas Duriez, Steven L. Brunton, Bernd R. Noack

Backmatter

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