Multi-Agent Systems

Consensus and Cooperation in Networked Multi-Agent Systems

Ideas to Think About

• What can be done to resolve node/link failures?
• Proximity graphs sound super interesting. Useful in flocking and swarms.

Note: Adversarial agents exist in non-cooperative games but this paper isn’t focused on that.

Outline

Section II

Basic concepts and theoretical results in information consensus.

Section III

Convergence and performance analysis of consensus on networks with switching topology.

Section IV

Theoretical framework for cooperative control f formations of networked multi-agent vehicle systems.

Section V

Some simulation results related to complex networks including small-worlds.

Information Consensus

Achieving agreement between all agents within a system on a single value. Requires cooperation i.e. giving consent to providing one’s state and following a common protocol that serves the group objective.

Reaching a consensus means to asymptotically converge to a one-dimensional agreement space characterized by:

$$x_1=x_2=...=x_n$$

The collective decision of a network of agents can be found in the agreement space expressed as: $x=\alpha 1$

• $\alpha \in \mathbb{R}$
• $1=(1,...,1{)}^T$

Distributed Consensus Algorithm

Guarantees convergence to a collective decision via local inter-agent interactions and is represented by the linear system:

$${\dot{x}}_i(t)=\sum _{j\in N_i}{a}_{ij}\left(x_j(t)-x_i(t)\right)$$

Note: $\dot{x}$ represents the state.

Related

• Graph Laplacians
• Spectral Graph Theory
• Algebraic Graph Theory
• Matrix Theory
• Dynamical Systems
• Perron-Frobenius Theorem