Flocking for Multi-Agent Dynamical Systems

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii In this thesis, we discuss models for multi-agent dynamical systems. We study the tracking/migration problem for flocks and a theoretical framework for design and analysis of flocking algorithm is presented. The interactions between agents in the systems are denoted by potential functions that act as distance functions, hence, the design of proper potential functions are crucial in modelling and analyzing the flocking problem for multi-agent dynamical systems. Constructions for both non-smooth potential functions and smooth potential functions with finite cut-off are investigated in detail. The main contributions of this thesis are to extend the literature of continuous flocking models with impulsive control and delay. Lyapunov function techniques and techniques for stability of continuous and impulsive switching system are used, we study the asymptoti