PART 3: Dynamics and Control

Data-driven discovery is currently revolutionizing how we model, predict, and control complex systems. The most pressing scientific and engineering problems of the modern era are not amenable to empirical models or derivations based on first-principles. Increasingly researchers are turning to data-driven approaches for a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. These systems are typically nonlinear, dynamic, multi-scale in space and time, high-dimensional, with dominant underlying patterns that should be characterized and modeled for the eventual goal of sensing, prediction, estimation, and control. With modern mathematical methods, enabled by unprecedented availability of data and computational resources, we are now able to tackle previously unattainable challenge problems.

The focus of this book has largely been on characterizing complex systems through dimensionality reduction, sparse sampling, and dynamical systems modeling. However, an overarching goal for many systems is the ability to actively manipulate their behavior for a given engineering objective. The study and practice of manipulating dynamical systems is broadly known as control theory, and it is one of the most successful fields at the interface of applied mathematics and practical engineering. Control theory is inseparable from data science, as it relies on sensor measurements (data) obtained from a system to achieve a given objective.

In fact, control theory deals with living data, as successful application modifies the dynamics of the system, thus changing the characteristics of the measurements. Control theory forces the reader to confront reality, as simplifying assumptions and model approximations are tested.

In this part, we will investigate several aspects of data-driven modeling and control. There are several Youtube playlists for this material:

[Chapter 7] Youtube playlist: Data-Driven Dynamical Systems

[Chapter 8] Youtube playlist: Control Bootcamp

[Chapters 9-10] Youtube playlist: Data-Driven Control

Data-driven discovery is currently revolutionizing how we model, predict, and control complex systems. The most pressing scientific and engineering problems of the modern era are not amenable to empirical models or derivations based on first-principles. Increasingly researchers are turning to data-driven approaches for a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. These systems are typically nonlinear, dynamic, multi-scale in space and time, high-dimensional, with dominant underlying patterns that should be characterized and modeled for the eventual goal of sensing, prediction, estimation, and control. With modern mathematical methods, enabled by unprecedented availability of data and computational resources, we are now able to tackle previously unattainable challenge problems.

The focus of this book has largely been on characterizing complex systems through dimensionality reduction, sparse sampling, and dynamical systems modeling. However, an overarching goal for many systems is the ability to actively manipulate their behavior for a given engineering objective. The study and practice of manipulating dynamical systems is broadly known as control theory, and it is one of the most successful fields at the interface of applied mathematics and practical engineering. Control theory is inseparable from data science, as it relies on sensor measurements (data) obtained from a system to achieve a given objective.

In fact, control theory deals with living data, as successful application modifies the dynamics of the system, thus changing the characteristics of the measurements. Control theory forces the reader to confront reality, as simplifying assumptions and model approximations are tested.

In this part, we will investigate several aspects of data-driven modeling and control. There are several Youtube playlists for this material:

[Chapter 7] Youtube playlist: Data-Driven Dynamical Systems

[Chapter 8] Youtube playlist: Control Bootcamp

[Chapters 9-10] Youtube playlist: Data-Driven Control