Distributed constrained optimization by singular perturbation method and its application to energy networks by real-time implementation

This paper proposes a new algorithm to a distributed constrained optimization problem with an undirected and connected network. The singular perturbation, dynamic average consensus, and saddle point dynamics methods are utilized to construct a dynamical system to seek global optimality. The theoretical guarantee on the optimality of the solutions is provided as it is proved that the constructed system is semi-globally practically asymptotically stable. The algorithm is further validated by an experiment on controller boards with real-time communication to apply the proposed algorithm to the IEEE 5 bus system. The experimental results demonstrate the efficiency and practical usage of the new algorithm.