Abstract
This paper studies the distributed convex optimization problem, where the global utility function is the sum of local cost functions associated to the individual agents. Only using the local information, a novel continuous-time distributed algorithm based on proportional-integral-differential (PID) control strategy is proposed. Under the assumption that the global utility function is strictly convex and local utility functions have locally Lipschitz gradients, the exponential convergence of the proposed algorithm is established with undirected and connected graph among these agents. Finally, numerical simulations are presented to illustrate the effectiveness of theoretical results.
Highlights
Recent years have witnessed an increasing interest in distributed optimization and its widely applications in various fields, including energy internet, intelligent manufacturing and machine learning.1–4 The aim of distributed optimization problem is to minimize global objective function with a sum of individual objective function, which computes and exchanges information among neighboring agents
The discrete-time algorithm has attracted much attention since the distributed gradient descent (DGD) algorithm was proposed by Nedicand Ozdaglar
Shi et al.8 proposed an exact first-order algorithm (EXTRA) with fixed step-size, which converges to the optimal solution precisely
Summary
Recent years have witnessed an increasing interest in distributed optimization and its widely applications in various fields, including energy internet, intelligent manufacturing and machine learning. The aim of distributed optimization problem is to minimize global objective function with a sum of individual objective function, which computes and exchanges information among neighboring agents. Measurement and Control networks, a double-integrator distributed optimization algorithm under the undirected graph was presented in Zhang and Hong.. Due to the progressive control techniques, various of algorithms based on proportional-integral (PI) control strategy for distributed optimization have attracted an increasing attention recently. Wang and Elia proposed a distributed optimization algorithm based on PI control strategy, where each agent used an auxiliary state to correct the error caused by different local gradient. Based on the above discussions, a new continuoustime algorithm with PID control strategy for distributed optimization under an undirected communication graph is studied in this paper. We focus on designing a distributed proportional-integral-differential (PID) algorithm such that each agent obtains the global minimizer xà 2 ( À ‘, ‘) of the feasible optimization problem xà = arg min f(x) ð5Þ x2Rn only using its own and its neighbors’ information.
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