Abstract
This paper studies the consensus problem of multiagent system with packet losses and communication delays under directed communication channels. Different from previous research results, a novel control protocol is proposed depending only on periodic sampling and transmitting data in order to be convenient for practical implementation. Due to the randomicity of transmission delays and packet losses, each agent updates its input value asynchronously at discrete time instants with synchronized time stamped information and evolves in continuous time. Consensus conditions for multiagent system consists of three typical dynamics including single integrator, double integrator, and high-order integrator that are all discussed in this paper. It is proved that, for single integrator agents and double integrator systems with only communication delays, consensusability can be ensured through stochastic matrix theory if the designed communication topology contains a directed spanning tree. While, for double integrator agents and high-order integrator agents with packet losses and communication delays, the interval system theory is introduced to prove the consensus of multiagent system under the condition that the designed communication topology is a directed spanning tree. Finally, simulations are carried out to validate the effectiveness of the proposed solutions.
Highlights
Consensus of multiagent system has attracted increasing focuses of researchers from different areas including multiple robotics system, large-scale oceanographic survey, and wireless sensor networks [1,2,3,4]
We have proposed the conditions needed for consensusability of the multiagent system
For multiagent system consisting of high order agents, under Assumptions 13 and 18, the consensusability of the system can be guaranteed with transmission delays and packet losses if there exists a controller gain K such that the conditions in Lemma 22 can be satisfied for each Mg + NgK, g ∈ {1, 2, . . . , l}
Summary
Consensus of multiagent system has attracted increasing focuses of researchers from different areas including multiple robotics system, large-scale oceanographic survey, and wireless sensor networks [1,2,3,4]. The consensus can be reached as long as the designed communication topology contains a directed spanning tree When it comes to second order and high-order agent with packet losses and communication delays, stochastic theory is no longer applicable since the nonnegativity of the system matrix is not always guaranteed. Based on the theory of interval matrix, it will be proved that the consensus of the system can be reached as long as the designed communication topology is a directed spanning tree which is another contribution of this paper In this situation, the states of all agents will converge to the root node and average consensus cannot be obtained.
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