Johan Thunberg: Consensus and Pursuit-Evasion in Nonlinear Multi-Agent Systems

This presentation covers Chapter 1-2 in the thesis, where the consensus
problem in nonlinear multi-agent systems is studied. we first provide

some theoretical results and then consider the problem of consensus

on SO(3) or attitude synchronization.

In Chapter 1, for agents with states in R^m, we present two theorems

along the lines of Lyapunov's second method that, under different

conditions, guarantee asymptotic state consensus in multi-agent

systems where the interconnection topologies are switching.

The first theorem is formulated by using the states of the agents in the

multi-agent system, whereas the second theorem is formulated by using

the pairwise states for pairs of agents in the multi-agent system.

In Chapter 2, the problem of consensus on SO(3) for

a multi-agent system with directed and switching interconnection

topologies is addressed. We provide two different types of kinematic

control laws for a broad class of local representations of SO(3).

The first control law consists of a weighted sum of pairwise differences

between positions of neighboring agents, expressed as coordinates in

a local representation. The structure of the control law is well known

in the consensus community for being used in systems of agents in

the Euclidean space, and here we show that the same type of control

law can be used in the context of consensus on SO(3). In a later part

of this chapter, based on the kinematic control laws, we introduce

torque control laws for a system of rigid bodies in space and show that the

system reaches consensus when these control laws are used.

Keywords: Multi-agent systems, consensus, attitude synchronization,

nonlinear control.