Control in the presence of limited information - systematic design methods with performance guarantees for distributed systems.

From satellite constellations and aeroplanes to power grids, computer networks and manufacturing processes, our modern society heavily depends on the operation of complex systems, many of which can be modelled as networks of dynamical systems. Control action is indispensable to ensure proper and safe operation of such systems, and to meet specified performance objectives. However, restricted communication and limited processing resources in such distributed systems present a major challenge for control design: designing controllers with stability and performance guarantees despite a lack of "perfect information".

In this project, we will explore the role of information in the control of linear and nonlinear networked systems, with the aim of developing systematic control design methods. In this context, any control design should be based solely on limited local information, yet it should provide guarantees for the global system. This calls for distributed control methods. Towards this end, we will study how measured data can be used to account for missing system information in the context of distributed systems.

Many modern processes generate and store large amounts of data. Consequently, developing methods to utilise measured data for controller design is an exciting, actively researched topic. The merger of machine learning and control is a popular approach addressing this challenge. Fascinating demonstrations, such as Boston Dynamics' Atlas robot performing backflips, highlight its potential. However, a major open question remains: how to guarantee safe operation under noisy real-world conditions? Complex algorithms are susceptible to bugs and performance is sensitive to initial conditions. These are uncertainties which have no place in the control of safety critical systems, such as aerospace systems.

In the initial phase of this project, we will build upon a low-complexity learning framework allowing to compute control policies with stability, performance and robustness guarantees for unknown linear systems directly from data. We will explore how this framework can be introduced to the areas of dynamic games and time-varying systems. The former represents a powerful tool to model the interactions between strategic agents in a distributed system, whereas the latter is encountered both in the context of certain classes of games and in the context of networked systems, where interactions between agents may evolve and change over time.

We will then turn our focus to nonlinear systems, considering data-driven control as well as alternative methods to overcome lack of information in the context of distributed control. We will, for instance, explore how system properties, such as passivity, can be utilised to derive controller guarantees, despite limited available information, and how available partial information can be used efficiently, without substituting all system dependencies with data.

The ultimate goal of the project is to develop systematic methods to design stable, robust and efficient controllers for linear and nonlinear distributed systems. The development of such methods can be a game-changer for a range of current and future technologies across various engineering disciplines including, but not limited to, power systems, industrial processes, air traffic control, agriculture, robotics, and space exploration.