Scalable control of interconnected systems
Modern society is critically dependent on large-scale networks for services such as energy supply, transportation and communications. The design and control of such networks is becoming increasingly complex, due to their growing size, heterogeneity and autonomy. A systematic theory and methodology for control of large-scale interconnected systems is therefore needed. In an ambitious effort towards this goal, this project will develop rigorous tools for control synthesis, adaptation and verification. 

Many large-scale systems exhibit properties that have not yet been systematically exploited by the control community. One such property is positive (or monotone) system dynamics. This correspond to the property that all states of a network respond in the same direction when the demand or supply is perturbed in some node. Scalable methods for control of positive systems are starting to be developed, but several fundamental questions remain: How can existing results be extended to scalable synthesis of dynamic controllers? Can results for linear positive systems be extended to nonlinear monotone ones? How about systems with resonances? 

The second focus area, adaptation, takes advantage of recent progress in machine learning, such as statistical concentration bounds and approximate dynamic programming. Adaptation is of fundamental importance for scalability, since high-fidelity models are very expensive to generate manually and hard to maintain. Thirdly, since systematic procedures for control synthesis generally rely on simplified models and idealized assumptions, we will also develop scalable methods to bound the effect of imperfections, such as nonlinearities, time-variations and parameter uncertainty that are not taken into account in the original design. 

The research will be carried out in interaction with industry studying a new concept for district heating networks. This collaboration will give access to experimental data from a full scale demonstration plant.