A Fixed-Time Convergent Distributed Algorithm for Strongly Convex Functions in a Time-Varying Network

This paper presents a novel distributed nonlinear protocol for minimizing the sum of convex objective functions in a fixed time under time-varying communication topology. In a distributed setting, each node in the network has access only to its private objective function, while exchange of local information, such as, state and gradient values, is permitted between the immediate neighbors. Earlier work in literature considers distributed optimization protocols that achieve convergence of the estimation error in a finite time for static communication topology, or under specific set of initial conditions. This study investigates first such protocol for achieving distributed optimization in a fixed time that is independent of the initial conditions, for time-varying communication topology. Numerical examples corroborate our theoretical analysis.

[1]  Jiong Jin,et al.  Fixed-time consensus for multi-agent systems with discontinuous inherent dynamics over switching topology , 2017, Int. J. Syst. Sci..

[2]  Wei Zhu,et al.  Finite-time Consensus of Leader-following Multi-agent Systems with Multiple Time Delays over Time-varying Topology , 2020, International Journal of Control, Automation and Systems.

[3]  Guoqiang Hu,et al.  Finite-time distributed optimization with quadratic objective functions under uncertain information , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[4]  Angelia Nedic,et al.  Distributed optimization over time-varying directed graphs , 2013, 52nd IEEE Conference on Decision and Control.

[5]  Zongyu Zuo,et al.  Nonsingular fixed-time consensus tracking for second-order multi-agent networks , 2015, Autom..

[6]  Angelia Nedic,et al.  Distributed Optimization for Control , 2018, Annu. Rev. Control. Robotics Auton. Syst..

[7]  Stephen P. Boyd,et al.  Distributed optimization for cooperative agents: application to formation flight , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[8]  Alfred O. Hero,et al.  Robust Distributed Fixed-Time Economic Dispatch Under Time-Varying Topology , 2019, IEEE Control Systems Letters.

[9]  Qing-Long Han,et al.  Distributed Optimization for Multiagent Systems: An Edge-Based Fixed-Time Consensus Approach , 2019, IEEE Transactions on Cybernetics.

[10]  Alfred O. Hero,et al.  Fixed-time Distributed Optimization under Time-Varying Communication Topology , 2019 .

[11]  Huai-Ning Wu,et al.  Leader-following formation control of multi-agent systems under fixed and switching topologies , 2012, Int. J. Control.

[12]  Minghui Zhu,et al.  Distributed Optimization-Based Control of Multi-Agent Networks in Complex Environments , 2015 .

[13]  Andrey Polyakov,et al.  Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems , 2012, IEEE Transactions on Automatic Control.

[14]  Asuman E. Ozdaglar,et al.  Constrained Consensus and Optimization in Multi-Agent Networks , 2008, IEEE Transactions on Automatic Control.

[15]  Jing Wang,et al.  A control perspective for centralized and distributed convex optimization , 2011, IEEE Conference on Decision and Control and European Control Conference.

[16]  Choon Yik Tang,et al.  Zero-Gradient-Sum Algorithms for Distributed Convex Optimization: The Continuous-Time Case , 2011, IEEE Transactions on Automatic Control.

[17]  Robert Nowak,et al.  Distributed optimization in sensor networks , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.

[18]  Diego Klabjan,et al.  Optimization for Large-Scale Machine Learning with Distributed Features and Observations , 2017, MLDM.

[19]  Lei Wang,et al.  Finite-time consensus of multi-agent systems with continuous time-varying interaction topology , 2018, Neurocomputing.

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

[21]  Gang Chen,et al.  A fixed-time convergent algorithm for distributed convex optimization in multi-agent systems , 2018, Autom..

[22]  Jay A. Farrell,et al.  Distributed Continuous-Time Optimization: Nonuniform Gradient Gains, Finite-Time Convergence, and Convex Constraint Set , 2017, IEEE Transactions on Automatic Control.

[23]  Lihua Xie,et al.  Continuous-time Distributed Convex Optimization with Set Constraints , 2014 .

[24]  R. Srikant,et al.  Network Optimization and Control , 2008, Found. Trends Netw..

[25]  Jianying Yang,et al.  Distributed finite-time optimization for second order continuous-time multiple agents systems with time-varying cost function , 2018, Neurocomputing.

[26]  Zengqiang Chen,et al.  Distributed Optimization with Finite-Time Convergence via Discontinuous Dynamics , 2018, 2018 37th Chinese Control Conference (CCC).

[27]  Zhengtao Ding,et al.  Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics , 2018, IEEE Transactions on Automatic Control.

[28]  Eduardo Camponogara,et al.  Distributed Optimization for Model Predictive Control of Linear Dynamic Networks With Control-Input and Output Constraints , 2011, IEEE Transactions on Automation Science and Engineering.

[29]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[30]  Zongyu Zuo,et al.  Distributed robust finite-time nonlinear consensus protocols for multi-agent systems , 2016, Int. J. Syst. Sci..

[31]  Takatoshi Ito,et al.  A Filippov solution of a system of differential equations with discontinuous right-hand sides , 1979 .