|On Stability and Inverse Optimality for a Class of Multi-agent Linear Consensus Protocols
Keun Uk Lee, Jae Young Lee, Yoon Ho Choi*, and Jin Bae Park
International Journal of Control, Automation, and Systems, vol. 16, no. 3, pp.1194-1206, 2018
Abstract : "This paper studies stability and inverse optimality for a class of linear consensus protocols applied to
the identical linear time-invariant multi-agent systems, where communications among the agents are described
by a fixed digraph, containing a spanning tree, whose scaled Laplacian is diagonalizable. The concept of the
scaled Laplacian, normal Laplacian multiplied by a positive diagonal matrix, allows a more general graph topology
to be handled. First, we show that partial stability and, even more, inverse optimality hold if either the scaling
factors in each protocol are sufficiently large depending on graph properties, or the system matrix A satisfies the
Lyapunov inequality. Then, duality principles between the agents’ and the consensus error dynamics are presented,
which provide additional properties regarding consensus-related stability and inverse optimality. And the results
are characterized in terms of the related symmetric Laplacian and its algebraic connectivity when the given graph is
scaled undirected. Finally, through formation control simulation of a multi-agent mobile robot system for G-scaled
undirected and G-scaled directed graphs, we have verified the theory of this paper on the partial stability and the
inverse optimality conditions."
Consensus, cooperative control, inverse optimality, multi-agent system, optimal control, partial stability.