Measures of controllability and observability for large-scale systems

Since the start of the 20th century, many techniques for state estimation and control have been developed. These techniques are in practice applied to small-scale systems with up to ~ 10 states. Examples include PID, LQR, Hinf, robust
control and Kalman filtering.

From industry there is an increasing interest in working with large-scale models that contain over 1;000 states. These models typically show up for systems that are described by partial differential equations and are discretized using finite
elements or finite volume methods. Model based control techniques are in practice rarely considered in these applications, due to model complexity. Instead, SISO PID controllers are widely applied, while large-scale models are
mainly used for simulation and validation purposes.

There is an increasing need for applying advanced control approaches in these applications to increase system performance. The main goal of the project is therefore to use these large-scale models directly for model based control
purposes. In this presentation, extensions of classical systems and control notions are considered as a first step to enable efficient numerical calculations for large-scale systems.