Distributed constrained optimization for multi-agent systems over a directed graph with piecewise stepsize

Abstract In this paper, the distributed constrained optimization problem over a directed graph is considered. We assume that the digraph has a row-stochastic adjacency matrix, which corresponds to the case when agents assign weights to the received information individually. We present an algorithm that converges to the optimal solution even with a time-varying stepsize which is not attenuated to zero. The choice of stepsizes is relatively easy. The usable type of stepsizes is added. The diminishing or constant stepsizes can be used in our algorithm. Equality constraints and set constraints are also considered in this paper. Convergence analysis of the proposed algorithm relies on a conversion theorem between column-stochastic and row-stochastic matrices. Finally, the results of the numerical simulation are provided to verify the effectiveness of the proposed algorithm.

[1]  Junbo Wang,et al.  Time-varying output formation tracking of heterogeneous linear multi-agent systems with multiple leaders and switching topologies , 2019, J. Frankl. Inst..

[2]  Huijun Gao,et al.  Distributed H∞ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks , 2013, IEEE Transactions on Industrial Electronics.

[3]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[4]  Ya-Jun Pan,et al.  Event-Triggered Control for Consensus Problem in Multi-Agent Systems With Quantized Relative State Measurements and External Disturbance , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  Qing Ling,et al.  EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization , 2014, 1404.6264.

[6]  C. Peng,et al.  State feedback controller design of networked control systems with interval time‐varying delay and nonlinearity , 2008 .

[7]  Peng Shi,et al.  Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data , 2013, IEEE Transactions on Cybernetics.

[8]  Zheng-Guang Wu,et al.  Observer-Based Distributed Mean-Square Consensus Design for Leader-Following Multiagent Markov Jump Systems , 2019, IEEE Transactions on Cybernetics.

[9]  Usman A. Khan,et al.  A Linear Algorithm for Optimization Over Directed Graphs With Geometric Convergence , 2018, IEEE Control Systems Letters.

[10]  Ya Zhang,et al.  Leader-following-based distributed Kalman filtering in sensor networks with communication delay , 2017, J. Frankl. Inst..

[11]  Qingshan Liu,et al.  A Multi-Agent System With a Proportional-Integral Protocol for Distributed Constrained Optimization , 2017, IEEE Transactions on Automatic Control.

[12]  David J. Hill,et al.  Global Uniform Synchronization With Estimated Error Under Transmission Channel Noise , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Zhigang Zeng,et al.  Robust probabilistic sampling H∞ output tracking control for a class of nonlinear networked systems with multiplicative noises , 2013, J. Frankl. Inst..

[14]  Angelia Nedic,et al.  Distributed Optimization Over Time-Varying Directed Graphs , 2015, IEEE Trans. Autom. Control..

[15]  Asuman E. Ozdaglar,et al.  Distributed Subgradient Methods for Multi-Agent Optimization , 2009, IEEE Transactions on Automatic Control.

[16]  Changyin Sun,et al.  Q-learning solution for optimal consensus control of discrete-time multiagent systems using reinforcement learning , 2019, J. Frankl. Inst..

[17]  Maojiao Ye,et al.  Distributed Extremum Seeking for Constrained Networked Optimization and Its Application to Energy Consumption Control in Smart Grid , 2016, IEEE Transactions on Control Systems Technology.

[18]  Housheng Su,et al.  Second-order consensus of multiple agents with coupling delay , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[19]  Martin J. Wainwright,et al.  Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling , 2010, IEEE Transactions on Automatic Control.

[20]  Yuanqing Xia,et al.  Networked Predictive Control for Nonlinear Systems With Arbitrary Region Quantizers , 2017, IEEE Transactions on Cybernetics.

[21]  Yiguang Hong,et al.  Constrained Consensus Algorithms With Fixed Step Size for Distributed Convex Optimization Over Multiagent Networks , 2017, IEEE Transactions on Automatic Control.

[22]  Aryan Mokhtari,et al.  Network Newton Distributed Optimization Methods , 2017, IEEE Transactions on Signal Processing.

[23]  Derong Liu,et al.  Multibattery Optimal Coordination Control for Home Energy Management Systems via Distributed Iterative Adaptive Dynamic Programming , 2015, IEEE Transactions on Industrial Electronics.

[24]  Yiguang Hong,et al.  Distributed Algorithm for Robust Resource Allocation with Polyhedral Uncertain Allocation Parameters , 2018, J. Syst. Sci. Complex..

[25]  Wei Shi,et al.  A Push-Pull Gradient Method for Distributed Optimization in Networks , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[26]  Van Sy Mai,et al.  Distributed optimization over weighted directed graphs using row stochastic matrix , 2016, 2016 American Control Conference (ACC).

[27]  Chenguang Xi,et al.  On the Linear Convergence of Distributed Optimization over Directed Graphs , 2015, 1510.02149.

[28]  Ming Liu,et al.  Event-triggered fault tolerant control for spacecraft formation attitude synchronization with limited data communication , 2019, Eur. J. Control.

[29]  Wei Ren,et al.  Information consensus in multivehicle cooperative control , 2007, IEEE Control Systems.

[30]  Usman A. Khan,et al.  FROST—Fast row-stochastic optimization with uncoordinated step-sizes , 2018, EURASIP Journal on Advances in Signal Processing.

[31]  Kok Lay Teo,et al.  Two-Channel Linear Phase FIR QMF Bank Minimax Design via Global Nonconvex Optimization Programming , 2010, IEEE Transactions on Signal Processing.

[32]  Qing Ling,et al.  On the Convergence of Decentralized Gradient Descent , 2013, SIAM J. Optim..

[33]  Min Wu,et al.  Improved stabilisation method for networked control systems , 2007 .

[34]  F. Chung.  Laplacians and the Cheeger Inequality for Directed Graphs , 2005 .

[35]  Feng Liu,et al.  Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems , 2015, Autom..