Abstract
AbstractIn this paper, an optimal consensus problem for continuous-time multi-agent systems is formulated and solved with time-varying interconnection topologies. Based on a sharp connectivity assumption, the considered multi-agent network with simple nonlinear distributed control rules achieves not only a consensus, but also an optimal one by agreeing within the global optimal solution set of a sum of objective functions corresponding to multiple agents. Convergence analysis is presented, by establishing several key properties of a class of distance functions and invariant sets with the help of convex analysis and non-smooth analysis.
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