Preface

This book is an introduction to machine learning control (MLC), a surprisingly simple model-free methodology to tame complex nonlinear systems. These systems are assumed to be manipulated by a finite number of actuators (inputs) and monitored by a finite number of sensors (outputs). The control logic is chosen to minimize a well-defined cost functional. MLC brings together three well-established disciplines: the theory of closed-loop feedback control, machine learning and regression, and the nonlinear dynamical systems that are characteristic of turbulent fluid flows. Over the past decades, control theory has developed into a mature discipline with a beautiful theoretical foundation and powerful associated numerical algorithms. Important advances have been made to enable robust control of systems with sensor noise, external disturbances, and model uncertainty. Modern methods from control theory now pervade the engineering sciences and have transformed the industrial landscape. However, challenges remain for the control of systems with strongly nonlinear dynamics leading to broadband frequency spectra, a high-dimensional state space, and large time delays. MLC begins to address these challenges using advanced methods from machine learning to discover effective control laws. Many turbulence control problems are not adequately described by linear models, have exceedingly large state spaces, and suffer from time delays from actuators to sensors via nonlinear convective fluid dynamic effects. Take for instance the aerodynamic drag minimization of a car with actuators at the back side, pressure sensors distributed over the car, and a smart feedback control logic. Numerical simulation of the underlying dynamics given by the Navier–Stokes equations requires days or weeks, while the control system requires actuation decisions on the order of milliseconds. Reduced-order models that incorporate nonlinearities, multiscale phenomena, and actuation effects have eluded many serious efforts and will likely remain elusive for years to come. In short, there may not even be a viable model for robust control design. Nevertheless, the literature contains many studies on turbulence control, with the majority either employing open-loop forcing such as periodic blowing, slowly adapting a working open-loop