Travelling Waves in Distributed Control

The thesis develops a novel approach, the so-called travelling-wave approach, for the analysis and control of a linear multi-agent system. The approach takes advantage of the wave-like behaviour of a multi-agent system by decomposing the outputs of the agents into two waves travelling through the system in opposite directions. The main advantage of the approach is that it splits the bidirectional interactions between the agents into two non-interacting waves. This allows us to study the interactions between two neighbouring agents without the necessity to consider the e ect of other agents in the system. Such a local analysis then allows us to infer system properties, such as the string stability of even a large scale system, which is di cult to carry out with the traditional approaches. Another bene t of the travelling-wave approach is that it allows us to design a feedback controller, which signi cantly shortens the transient of the system. The most challenging issue of the approach is that it employs irrational transfer functions, which are less mathematically studied than rational transfer functions. For instance, even the current state-of-the-art programs are not able to carry out the inverse Laplace transform of an irrational transfer function. Therefore, a part of the thesis focuses on the development of algorithms for the rational approximation of irrational transfer functions. The programs carrying out the approximation are published online on the webpage of Matlab Central and have already been downloaded by dozens of users.