Consensus problem in nonlinear spaces

The thesis studies the problem of consensus, considering a set of N agents locally exchanging information about their state in order to asymptotically reach a common value of agreement: a global consensus. Chapter 2 is devoted to recalling some mathematical preliminaries, such as concepts of stability, Lyapunov theory, graph theory; this chapter also gives some (intuitive) notions of critical concepts concerning nonlinear spaces (e.g. the concept of manifold, geodesic and geodesic distance, Lie group). Chapter 3 deals with the goal of the thesis: the consensus; firstly we introduce the problem in linear space and then in nonlinear spaces, focusing our attention on the circle. A natural adaptation of linear consensus on the circle is, in fact, the celebrated Kuramoto model. In Chapter 4 we give some critical examples of application of consensus both in biological (e.g. flashing fireflies) and engineering problems (e.g. AOSN, vehicle formations