Output sign-consensus of heterogeneous multiagent systems over fixed and switching signed graphs

Distributed control of multiagent systems has been extensively studied over the past years. For most practical scenarios, the coexistence of cooperative and antagonistic interactions among individual groups is common. For such cases, using a signed graph has been identified as a more appropriate approach for modeling the interactions between the agents. However, analyzing collective behaviors over signed graphs is difficult than analyzing distributed control of multiagent systems over nonnegative graphs. This can be partly attributed to the absence of important properties of nonnegative graphs due to the general nature of a signed graph. The emergence of new collective behaviors owing to competitive interactions has been recently observed. A good example is a bipartite consensus where the whole agent group is divided into two subgroups, with the consensus values of agents in each subgroup having the same magnitude but opposite signs.

The signed graphs used for problems related to bipartite consensus are usually structurally balanced. However, condition on structural balanceness is rather restricted, which motivates researches on structurally unbalanced signed graphs, among which is the topic of sign-consensus. Existing work on sign-consensus focuses on homogenous multiagent systems, which is inadequate considering that majority of multiagent systems involved in practical circumstances are heterogeneous in nature. Previous results revealed that the output of individual agents in heterogeneous multiagent systems could realize output sign-consensus. Notably, the distributed feature of these heterogenous systems is a critical factor in the design of control laws. Because multiagent systems are based on the assumption that agents can obtain the dynamics of exosystem that is usually unavailable in most practical circumstance, distributed observers have been developed to remove this restriction. Nevertheless, the available distributed observer design techniques consider nonnegative graph configurations that are limited in many circumstances.

To address these challenges, Mr. Zhenyu Sun from Southwest Jiaotong University (who is now a PhD student of Northwestern University, IL), Professor Hongwei Zhang from Harbin Institute of Technology，Shenzhen, and Professor Frank L. Lewis from University of Texas at Arlington studied the output sign-consensus of heterogeneous multiagent systems over fixed and switching signed graphs. A distributed observer was adopted to remove the restriction requiring all the agents to know the dynamics of the exosystem. The observer was designed for all the follower agents to estimate the exosystem’s dynamics and signals. A structurally unbalanced and time-varying communication graph was considered. Observer-based control laws were proposed and analyzed. The effectiveness of the proposed laws was validated through simulation examples. The work is currently published in the International Journal of Robust and Nonlinear Control.

The research team reported that the inclusion of distributed observer for all the following agents was useful in eliminating the common assumption that the dynamics of the exosystem are always available for all the following agents. This is of great benefit to practical applications considering that the assumption limited the practical application of heterogeneous multiagent systems. Moreover, the effectiveness of the proposed control laws was successfully verified using the simulation examples of fixed and switching topologies.

In summary, the authors extended the study of output sign-consensus to heterogeneous multiagent systems where the output of the agents is expected to eventually have the same sign. The distributed observer controller was designed over fixed and switching topologies. The analysis of the distributed observer produced remarkable results, suggesting the practicability of the observer-based approach. In a statement to Advances in Engineering, the authors said their findings provide more insights into the output sign-consensus of heterogeneous multiagent systems, thereby enhancing their practical applications.