Global asymptotic stability of a general biased min‐consensus protocol

Abstract

Abstract In this paper, a general biased min‐consensus protocol for continuous‐time multi‐agent systems is presented. In this protocol, agents considered as sources maintain static states, while the state of each non‐source agent evolves using a general min‐consensus‐like function, which takes the states of its neighbours and a biased term as inputs. The properties of the general function have been identified so that the proposed protocol can achieve global asymptotic stability. Unlike conventional consensus protocols where a network of agents reach an agreement on certain quantities of interest, agents under the general biased min‐consensus protocol will converge to different states but can generate various design results pertaining to complex combinatorial optimization problems, such as the shortest path problem and its variants.

Keywords

• Optimisation techniques
• Interpolation and function approximation (numerical analysis)
• Optimisation techniques
• Combinatorial mathematics
• Stability in control theory