Path Following and Output Synchronization of Homogeneous Linear Time-Invariant Systems

Abstract

This thesis examines two aspects of the path following control design problem for Linear Time-Invariant (L.T.I.) systems assigned closed curves in their output space. In the first part of the thesis we define a path following normal form for L.T.I. systems and study structural properties related to this normal form. We isolate how unstable zero dynamics alter the feasibility of using the path following normal form for control design. In the second half of the thesis we consider a synchronized path following problem for a homogenous multi-agent system and cast the problem as an instance of an output synchronization problem to leverage recent results from the literature. It is desired that each individual agent follow a specified path. The agents communicate with one another over an idealized communication network to synchronize their positions along the path. The main result is the construction of a dynamic feedback coupling that drives all the agents in the network to their respective reference paths while simultaneously synchronizing their positions along the path. Laboratory results are presented to illustrate the effectiveness of the proposed approach.