L¹ group consensus of multi-agent systems with stochastic inputs under directed interaction topology

Abstract

We address L ¹ group consensus problems of networked multi-agent systems with fixed directed information exchange in this article. A discrete-time protocol is designed to solve the L ¹ group consensus problems via general stochastic inputs. Under some mild assumptions, we derive sufficient conditions to guarantee the L ¹ group consensus based on algebraic graph theory and ergodicity theory for finite Markov chains. Moreover, the boundedness of the expected infinite sum of the inputs ensures the boundedness of the expected trajectory. Numerical simulations instantiating the inputs as varied independent and identically distributed random processes as well as autoregressive processes are presented to demonstrate the effectiveness of our theoretical results.

Keywords:

• group consensus
• multi-agent system
• directed graph
• L ¹ convergence