A common approach to control design involves first obtaining a mathematical model of the to-be-controlled system. This model can take various forms, including ordinary or partial differential equations, difference equations, or transfer matrices. One way to derive a model is through first-principles modeling, which relies on fundamental physical laws governing the system, such as Newton’s laws for mechanical systems or Kirchhoff’s laws for electrical circuits. An alternative approach is system identification, where experimental data is used to derive a mathematical representation of the system based on observed input-output relationships. However, in many practical scenarios, obtaining an accurate model of a system can be challenging or even infeasible due to system complexity, unknown dynamics, or measurement noise. In such cases, data-driven control offers an alternative paradigm. Rather than relying on explicit mathematical models, data-driven methods synthesize control laws directly from measured data. Ensuring that data-driven methods provide the same stability and performance guarantees as traditional model-based control remains a significant challenge. This course provides a comprehensive introduction to the principles and methods of data-driven control. Students will delve into various methods, such as data-driven stabilization, regulation and predictive control, as well as their theoretical underpinnings like persistency of excitation, the fundamental lemma, and matrix versions of Yakubovich’s S-lemma.

1. Historical perspective 

Subspace identification, fundamental lemma and its applications in data-driven tracking, data-enabled predictive control, and data-based closed-loop parametrization.

2. Foundations of the data informativity approach 

The data informativity framework, stability and controllability analysis from data, stabilization and linear quadratic regulation by using only data.

3. Designing stabilizing controllers using noisy data 

Noise models based on quadratic matrix inequalities (QMIs), Schur complement and its consequences for QMIs, from S-lemma to matrix S-lemma, stabilizing controllers from noisy data. 

4. Advanced data-driven analysis and control 

H-infinity control design by using noisy data, dissipativity analysis from data, stabilization by using only input-output data.

5. Analysis and design for continuous-time systems from measurements 

Generalized sampling, orthogonal polynomial bases, data informativity framework for continuous-time systems. 

6. Data informativity for system identification and experiment design 

Necessary and sufficient conditions for system identification, the problem of experiment design, the shortest experiment for linear system identification.