Event-triggered differentially private average consensus for multi-agent network

This paper investigates the differentially private problem of the average consensus for a class of discrete-time multi-agent network systems ( MANSs ). Based on the MANSs, a new distributed differentially private consensus algorithm ( DPCA ) is developed. To avoid continuous communication between neighboring agents, a kind of intermittent communication strategy depending on an event-triggered function is established in our DPCA. Based on our algorithm, we carry out the detailed analysis including its convergence, its accuracy, its privacy and the trade-off between the accuracy and the privacy level, respectively. It is found that our algorithm preserves the privacy of initial states of all agents in the whole process of consensus computation. The trade-off motivates us to find the best achievable accuracy of our algorithm under the free parameters and the fixed privacy level. Finally, numerical experiment results testify the validity of our theoretical analysis.

[1]  J. Cortés,et al.  Differentially Private Average Consensus with Optimal Noise Selection , 2015 .

[2]  Haibo He,et al.  Event-Driven Nonlinear Discounted Optimal Regulation Involving a Power System Application , 2017, IEEE Transactions on Industrial Electronics.

[3]  Wei Xing Zheng,et al.  On the Bipartite Consensus for Generic Linear Multiagent Systems With Input Saturation , 2017, IEEE Transactions on Cybernetics.

[4]  Derong Liu,et al.  Learning and Guaranteed Cost Control With Event-Based Adaptive Critic Implementation , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[5]  George J. Pappas,et al.  Differentially Private Filtering , 2012, IEEE Transactions on Automatic Control.

[6]  Haibo Ji,et al.  A continuous leader-following consensus control strategy for a class of uncertain multi-agent systems , 2014, IEEE/CAA Journal of Automatica Sinica.

[7]  Tao Dong,et al.  Event-driven optimal control for uncertain nonlinear systems with external disturbance via adaptive dynamic programming , 2017, Neurocomputing.

[8]  Guangming Xie,et al.  Event-triggered tracking consensus with packet losses and time-varying delays , 2016, IEEE/CAA Journal of Automatica Sinica.

[9]  Timothy W. McLain,et al.  Coordinated target assignment and intercept for unmanned air vehicles , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[10]  Yilin Mo,et al.  Privacy Preserving Maximum Consensus , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[11]  Guanghui Wen,et al.  Distributed Position-Based Consensus of Second-Order Multiagent Systems With Continuous/Intermittent Communication , 2017, IEEE Transactions on Cybernetics.

[12]  Gang Feng,et al.  Output Consensus of Heterogeneous Linear Multi-Agent Systems by Distributed Event-Triggered/Self-Triggered Strategy , 2017, IEEE Transactions on Cybernetics.

[13]  Jinde Cao,et al.  Leader-Following Consensus of Nonlinear Multiagent Systems With Stochastic Sampling , 2017, IEEE Transactions on Cybernetics.

[14]  Tongwen Chen,et al.  Event based agreement protocols for multi-agent networks , 2013, Autom..

[15]  Frank Allgöwer,et al.  Cooperative Estimation and Robust Synchronization of Heterogeneous Multiagent Systems With Coupled Measurements , 2018, IEEE Transactions on Control of Network Systems.

[16]  Geir E. Dullerud,et al.  Differentially private iterative synchronous consensus , 2012, WPES '12.

[17]  Yasaman Khazaeni,et al.  Event-Driven Trajectory Optimization for Data Harvesting in Multiagent Systems , 2018, IEEE Transactions on Control of Network Systems.

[18]  Shaojiang Deng,et al.  Differentially Private Consensus With an Event-Triggered Mechanism , 2019, IEEE Transactions on Control of Network Systems.

[19]  M. Degroot.  Reaching a Consensus , 1974 .

[20]  Huaguang Zhang,et al.  Distributed Cooperative Optimal Control for Multiagent Systems on Directed Graphs: An Inverse Optimal Approach , 2015, IEEE Transactions on Cybernetics.

[21]  Qichao Zhang,et al.  Event-Triggered $H_\infty $ Control for Continuous-Time Nonlinear System via Concurrent Learning , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[22]  Magdi S. Mahmoud,et al.  LMI consensus condition for discrete-time multi-agent systems , 2018, IEEE/CAA Journal of Automatica Sinica.

[23]  Qingshan Liu,et al.  A Second-Order Multi-Agent Network for Bound-Constrained Distributed Optimization , 2015, IEEE Transactions on Automatic Control.

[24]  Richard M. Murray,et al.  Privacy preserving average consensus , 2014, 53rd IEEE Conference on Decision and Control.

[25]  Tao Dong,et al.  Event‐Triggered Consensus of Nonlinear Multi‐Agent Systems with Unknown External Disturbance , 2018 .

[26]  Dongbin Zhao,et al.  Event-Based Robust Control for Uncertain Nonlinear Systems Using Adaptive Dynamic Programming. , 2018, IEEE transactions on neural networks and learning systems.

[27]  Huaguang Zhang,et al.  Data-Driven Optimal Consensus Control for Discrete-Time Multi-Agent Systems With Unknown Dynamics Using Reinforcement Learning Method , 2017, IEEE Transactions on Industrial Electronics.

[28]  Jorge Cortés,et al.  Differentially private average consensus: Obstructions, trade-offs, and optimal algorithm design , 2015, Autom..

[29]  Xinghuo Yu,et al.  Iterative learning control for discrete-time systems with event-triggered transmission strategy and quantization , 2016, Autom..

[30]  Jiming Chen,et al.  Differentially Private Maximum Consensus , 2017 .

[31]  Gang Feng,et al.  Consensus of Heterogeneous Linear Multiagent Systems With Communication Time-Delays. , 2017 .

[32]  Christoforos N. Hadjicostis,et al.  Privacy-preserving asymptotic average consensus , 2013, 2013 European Control Conference (ECC).

[33]  Qing Zhao,et al.  Robust leader-following output regulation of uncertain multi-agent systems with time-varying delay , 2018, IEEE/CAA Journal of Automatica Sinica.

[34]  E.M. Atkins,et al.  A survey of consensus problems in multi-agent coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

[35]  Qichao Zhang,et al.  Event-Triggered H ∞ Control for Continuous-Time Nonlinear System , 2015, ISNN.

[36]  Hai Lin,et al.  Protocols Design and Uncontrollable Topologies Construction for Multi-Agent Networks , 2015, IEEE Transactions on Automatic Control.

[37]  Tongwen Chen,et al.  Event detection and control co-design of sampled-data systems , 2014, Int. J. Control.

[38]  Richard M. Murray,et al.  INFORMATION FLOW AND COOPERATIVE CONTROL OF VEHICLE FORMATIONS , 2002 .

[39]  Qingshan Liu,et al.  Distributed Optimization Based on a Multiagent System in the Presence of Communication Delays , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[40]  Haibo He,et al.  Event-Triggered Optimal Control for Partially Unknown Constrained-Input Systems via Adaptive Dynamic Programming , 2017, IEEE Transactions on Industrial Electronics.

[41]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[42]  Xiaofeng Liao,et al.  On the general consensus protocol in multi-agent networks with second-order dynamics and sampled data , 2016 .

[43]  Guanghui Wen,et al.  Neuro-Adaptive Consensus Tracking of Multiagent Systems With a High-Dimensional Leader , 2017, IEEE Transactions on Cybernetics.

[44]  Eloy García,et al.  Model-Based Event-Triggered Control for Systems With Quantization and Time-Varying Network Delays , 2013, IEEE Transactions on Automatic Control.

[45]  Tao Dong,et al.  Event-triggered synchronization strategy for complex dynamical networks with the Markovian switching topologies , 2016, Neural Networks.

[46]  R. Durrett.  Probability: Theory and Examples , 1993 .