Flocking for Multi-Agent Dynamical Systems
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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 asymptotic stability of the equilibrium of our models with impulsive control and discovery that by applying impulsive control to Olfati-Saber's continuous model, we can remove the damping term and improve the performance by avoiding the deficiency caused by time delay in velocity sensing. Additionally, we discuss both free-flocking and constrained-flocking algorithm for multi-agent dynamical system, we extend literature results by applying velocity feedbacks which are given by the dynamical obstacles in the environment to our impulsive control and successfully lead to flocking with obstacle avoidance capability in a more energy-efficient way. Simulations are given to support our results, some conclusions are made and future directions are given.