Optimal topology for consensus of heterogeneous multi-agent systems

Consensus can be achieved under various topologies for multi-agent systems. Then, which one is the optimal? In this paper, we consider the problem of optimal topology for consensus of heterogeneous multi-agent systems. We assume that the system consists of a leader and several followers with heterogeneous dynamics. Firstly, we define a quadratic cost function composed of consensus error and control effort for the heterogeneous multi-agent system. Secondly, by using linear-quadratic regulator theory and matrix theory, we prove that the optimal position topology and the optimal velocity topology are star graphs. Finally, simulations are carried out to illustrate the effectiveness of the theoretical results.

[1]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[2]  Li Wang,et al.  Adaptive second-order consensus of multi-agent systems with heterogeneous nonlinear dynamics and time-varying delays , 2013, Neurocomputing.

[3]  Long Wang,et al.  Consensus of heterogeneous multi-agent systems , 2011 .

[4]  Yongcan Cao,et al.  Optimal Linear-Consensus Algorithms: An LQR Perspective , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[6]  Jean-Charles Delvenne,et al.  Optimal strategies in the average consensus problem , 2007, 2007 46th IEEE Conference on Decision and Control.

[7]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[8]  Long Wang,et al.  Finite-time consensus of multiple second-order dynamic agents without velocity measurements , 2014, Int. J. Syst. Sci..

[9]  Long Wang,et al.  LQR‐based optimal topology of leader‐following consensus , 2015 .

[10]  Housheng Su,et al.  Multi-agent containment control with input saturation on switching topologies , 2015 .

[11]  Bo Liu,et al.  Controllability of switching networks of multi‐agent systems , 2012 .

[12]  Long Wang,et al.  Consensus of switched multi-agent systems , 2014, ArXiv.

[13]  Guangming Xie,et al.  Consensus control for a class of networks of dynamic agents , 2007 .

[14]  Long Wang,et al.  Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements , 2012, Syst. Control. Lett..

[15]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[16]  Long Wang,et al.  Finite-Time Consensus Problems for Networks of Dynamic Agents , 2007, IEEE Transactions on Automatic Control.

[17]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[18]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[19]  Long Wang,et al.  Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies , 2012, Int. J. Control.

[20]  Long Wang,et al.  Containment control of heterogeneous multi-agent systems , 2014, Int. J. Control.

[21]  James Lam,et al.  Semiglobal Observer-Based Leader-Following Consensus With Input Saturation , 2014, IEEE Transactions on Industrial Electronics.