CuckerSmale

CuckerSmale is a deterministic algorithm for consensus in a network of agents. It aims to achieve agreement on a common value among all agents, even in the presence of noisy information exchange. The algorithm operates in discrete time steps. At each step, every agent updates its estimate of the value by averaging its current estimate with the estimates of its neighbors.

The "Cucker-Smale" name is derived from the work of several researchers, including F. Cucker and S. Smale, who contributed significantly to the theoretical foundations of consensus algorithms. The core idea is that through repeated local averaging, global consensus can emerge. The network structure, or topology, plays a crucial role in the convergence properties of the algorithm. For instance, if the network is connected and remains connected over time, consensus is guaranteed.

The algorithm is typically described by a set of linear difference equations, where each agent's state at time t+1 is a function of the states of its neighbors at time t. Various extensions and modifications of the basic Cucker-Smale model exist, addressing aspects like dynamic network topologies, bounded communication, and asynchronous updates. It finds applications in distributed estimation, coordination of multi-agent systems, and sensor networks. The theoretical analysis often involves concepts from graph theory and linear algebra to prove convergence rates and conditions.