Title :
Reaching an Optimal Consensus: Dynamical Systems That Compute Intersections of Convex Sets
Author :
Guodong Shi ; Johansson, Karl H. ; Yiguang Hong
Author_Institution :
ACCESS Linnaeus Centre, R. Inst. of Technol., Stockholm, Sweden
Abstract :
In this paper, multi-agent systems minimizing a sum of objective functions, where each component is only known to a particular node, is considered for continuous-time dynamics with time-varying interconnection topologies. Assuming that each node can observe a convex solution set of its optimization component, and the intersection of all such sets is nonempty, the considered optimization problem is converted to an intersection computation problem. By a simple distributed control rule, the considered multi-agent system with continuous-time dynamics achieves not only a consensus, but also an optimal agreement within the optimal solution set of the overall optimization objective. Directed and bidirectional communications are studied, respectively, and connectivity conditions are given to ensure a global optimal consensus. In this way, the corresponding intersection computation problem is solved by the proposed decentralized continuous-time algorithm. We establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non-smooth analysis.
Keywords :
continuous time systems; convex programming; decentralised control; distributed control; multi-robot systems; optimal control; optimisation; set theory; time-varying systems; bidirectional communication; connectivity conditions; continuous-time dynamics; convex analysis; convex sets; convex solution set; decentralized continuous-time algorithm; directed communication; distance functions; distributed control rule; dynamical systems; global optimal consensus; global optimal solution set; intersection computation problem; invariant sets; multiagent systems; nonsmooth analysis; objective functions; optimization component; optimization problem; overall optimization objective; time-varying interconnection topology; Bidirectional control; Convergence; Distributed control; Multiagent systems; Optimization; Protocols; Topology; Connectivity conditions; distributed optimization; intersection computation; multi-agent systems; optimal consensus;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2012.2215261