Consensus And Network Node-localization Under Uncertain Information

Consensus problem as an essential problem in coordination control of multi-agent systems(MASs),has received more and more attention from researchers,due to the reason that many practical problems,such as the time synchronization and node localization over wireless sensor networks(WSNs),distributed formation control and distributed optimization,can be transformed into the consensus problem under proper transformations.The study of the consensus problem is significant for both theory and practical applications.For the study of the consensus problem under the ideal environment,such as the noise-free case and delay-free case,many results have been obtained with the help of the property of the Laplacian matrix or stochastic matrix.However,in practice,the ideal environment does not exist.The unreliable communication of the network usually leads to the interruption of the link between nodes,and the collection and transmission of information is inevitably subject to various kinds of noises,such as the measurement noise and communication noise.These uncertainties make the analysis of consensus more difficult and challenging.Although the study of the consensus problem under uncertain information has received much concern,it still has many problems to be solved.This thesis studies the consensus problem of discrete-time single-integrator and double-integrator MASs under uncertain information.During the analysis of the consensus,the consensus problem is transformed into a stability problem by using a transformation matrix to reduce the dimension of the system.Then,combined with the stability theory,graph theory and stochastic convergence analysis tools,the consensus result is finally obtained.In addition,this thesis presents an application with respect to the design and convergence analysis of consensus protocol under uncertain information in relative-position-based network node localization.The main work of this thesis is summarized as follows:1.The consensus problem of single-integrator discrete-time MASs under the directed switching topology under uncertain information(more specifically,the information corrupted by additive noises or relative-statedependent(RSD)multiplicative noises or non-relative-state-dependent(non-RSD)multiplicative noises is studied.Different consensus protocols are designed for different noise types.In order to obtain consensus result,the consensus problem of MASs under the switching topology is transformed into a stability problem of switching systems.Under the obtained stability result,the consensus condition is finally presented.When the additive noise or RSD multiplicative noise is involved,it is pointed out that the system can achieve the mean square(m.s.)and almost sure(a.s.)consensus under the weakly periodic switching topology together with a Hurwitz constraint.This conclusion does not require all digraphs be balanced and all edge weights be non-negative.When the exponentially or polynomially decaying non-RSD multiplicative noise is involved,it is pointed out that for any bounded communication delay and uniformly rooted switching topology,the system can achieve the consensus under a precondition that the system state is bounded.2.The consensus problem of discrete-time double-integrator MASs under the directed switching topology with RSD multiplicative noises is studied.In order to obtain the consensus result,similar to the study of the discrete-time single-integrator MASs,the consensus problem is also transformed into a stability problem to do the convergence analysis.Firstly,for a kind of switching topology with each digraph containing a spanning tree,based on mode-dependent average dwell time method,it is pointed out that if the topology switching satisfies a certain dwell time constraint,the system can always achieve the weak consensus under the designed consensus protocol.Then,for another kind of switching topology of which all digraphs are strongly connected and the corresponding Laplacian matrices have a common left eigenvector for zero eigenvalue,it is pointed out that for an arbitrary switching sequence,the system can always achieve the m.s.and a.s.consensus under the designed protocol.3.An application of the design and convergence analysis of consensus protocol under uncertain information to relative-position-based reference-frame-free network node localization is presented.In order to solve the accurate node localization problem under the measurement noise and communication noise,a robust distributed orientation estimate algorithm and distributed node-localization algorithm are respectively designed based on the consensus protocol under uncertain information,where unbiased estimators are constructed based on the historical measurement information to inhibit the measurement noise and the stochastic approximation method is adopted to inhibit the communication noise.Under the zero-mean and independence assumption on the measurement/communication noise,a sufficient and necessary topology condition that can guarantee that all position-unknown nodes can asymptotically determine their own orientation angles and positions almost surely under the designed algorithms is presented.Besides,if only one kind of the noise is involved,the convergence rate is quantified.