Consensus Control And Privacy-Preserving Of The Multi-Agent Systems

With the rapid development of computer science,multi-agent system is becoming more and more important in control theory and control science.Multi-agent system has broad application prospects in many fields,such as UAV coordinated control,formation control,congestion control of communication network and distributed sensor network.Among them,the research on multi-agent consensus and its privacy protection has attracted more and more attention from researchers.This thesis focuses on the consensus and privacy-preserving problem of multi-agent systems,whose main contributions are the following aspects:(1)The consensus problem of second-order multi-agents in a directed network via a general distributed sample-data control is studied.By employing the algebra graph theory and analysing matrix characteristics,necessary and sufficient conditions to guarantee the second-order consensus are established.Besides,we discuss the impact of sampling period,the control parameters and the spectra of the Laplacian matrix on the system consensus,respectively.Finally,a simulation example is given to verify the theoretical results.(2)The tracking consensus problem for the second-order leader systems by designing a kind of fractional-order observer is investigated with a periodic sampled-based data event-triggered control.Compared with the sampled-data control employed in (1),our event-triggered control reduces the overall load of the network.In our proposed event-triggered strategy,the event detection only works at every sampling time instant which determines whether the sampled-data should be discarded or used.Under this control strategy,the Zeno-behavior is absolutely excluded since the minimum of inter-event times is inherently lower bounded by one sampling period.By using the generalized Nyquist stability criterion,a necessary and sufficient condition for the observer tracking consensus of the second-order leader systems is derived.The results show that the real and imaginary parts of the eigenvalues of the augmented Laplacian matrix,and fractional-order ? of observer play a vital role in reaching consensus.Finally,a simulation example is given to verify the theoretical analysis.(3)In order to extend the results obtained in the above (1) and (2),the consensus problem of nonlinear multi-agent systems with unknown external disturbance is investigated.A distributed observer is proposed to estimate the state and unknown disturbance of each agent simultaneously.Then,a novel event-triggered control scheme based on the agent state estimation and disturbance estimation is proposed.Under this observer and control strategy,some sufficient conditions are derived to ensure the consensus of multi-agent system with unknown external disturbance.Moreover,the Zeno-behavior of triggering time sequences is also excluded.Finally,a simulation example is given to verify the theoretical analysis.(4)The differentially private problem of the average consensus for a class of discrete-time multi-agent network systems is studied.On the basis of multi-agent consensus (1),(2)and (3),the privacy-preserving problem of initial state of multi-agent system is discussed.Based on the MANSs,a new distributed differentially private consensus algorithm(D-PCA)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,accuracy,privacy and the tradeoff between the accuracy and the privacy level,respectively.Finally,numerical experiment results testify the validity of our theoretical analysis.(5)The privacy-preserving consensus problem for the general continuous-time multi-agent network systems(MANSs)with time delay via the event-triggered communication scheme is investigated.Different from the privacy-preserving approach used in (4) adding random noises to the update law of agents' states,a new privacy-preserving approach is that we construct an output mask to make agents' internal states indiscernible by others.Moreover,the privacy-preserving approach used in (4) only applies to the discrete-time multi-agent systems and makes all agents in MANSs converge to the same value in mean square.Based on the proposed privacy-preserving method,a novel consensus algorithm based on event-triggered strategy is developed.Based on the proposed algorithm,we carry out the detailed theoretical consensus analysis of the network agents,from which it is shown that the upper bound of the communication time delay between neighbors' agents can be estimated approximately.Moreover,the Zeno-behavior of event-triggered time sequences for each agent is excluded.Finally,a numerical simulation is performed to demonstrate the effectiveness of our theoretical results.