Data-driven control of complex systems
Automatic control keeps modern engineering systems---power grids, robots, industrial processes---stable and safe. Traditionally, engineers design controllers from a mathematical model of the system, but for complex nonlinear systems such models are difficult or impossible to obtain. This thesis takes a different route: it designs controllers directly from measurement data collected on the real system, while still providing the mathematical guarantees that conventional methods are valued for.
The thesis makes three contributions. First, it develops techniques that keep a system stable even when the data are corrupted by noise and the system is exposed to external disturbances. A computer-aided design procedure returns both the controller and a mathematical certificate proving that stability is guaranteed for every system compatible with the recorded data. Second, it shows how to reduce communication between sensor and controller: instead of updating the control signal continuously, updates occur only when the system's state truly requires it, saving computation and network resources while preserving stability. Third, it estimates the safe operating region---the set of initial states from which the system is guaranteed to return to its desired equilibrium---for systems whose dynamics involve trigonometric terms, such as generators in a power grid. Knowing this region helps assess whether the grid survives large disturbances such as short circuits.
Together, the results show that rigorous, safety-critical control tasks can be carried out directly from data, a step towards reliably controlling future complex systems such as power grids dominated by renewable sources.