Distributed Parameter Estimation And Optimization Based On Stochastic Multi-agent Systems

In recent years,stochastic multi-agent systems have attracted great attentions from scholars in various fields and become an active interdisciplinary research subject.In multi-agent systems,the communication structure often randomly changes due to packet dropouts and link failures;the communication channels between agents inevitably suffer from time delays and are corrupted by additive and multiplicative noises when transmitting information;nodes are prone to sensing failures or measurement losses due to limited power;These uncertain factors can seriously affect the information interaction and fusion among the agents and bring great challenges to the design and analysis of distributed consensus,estimation and optimization algorithms.By the tools of algebraic graph,probability,matrix,martingale convergence,time-varying system and convex optimization theories,we study the problems of distributed average consensus,parameter estimation and convex optimization in an uncertain environment.In detail,the contents include the following four aspects.1.The problem of distributed average consensus for discrete multi-agent systems with compound communication noises and random network graphs is studied.The communication model contains both additive and multiplicative noises.The network structure is modeled by a sequence of time-varying random digraphs.The time-varying algorithm gain is introduced to attenuate the additive noises.By stochastic Lyapunov method,sufficient conditions for stochastic approximation type algorithms to achieve mean square and almost sure average consensus are obtained.It is proved that states of all the agents converge to a common random variable,whose mathematical expectation is the average of initial values,in mean square and almost surely if the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected.An upper bound of the variance of the limit random variable is given,which quantitatively reflects the effects of the timevarying algorithm gain,the number of agents,the agents' initial values,the second-order moment of the noises,the random weights and unbalance of the digraphs on the mean square steady-state error.2.The problem of distributed online parameter estimation with time-varying random observation matrices and communication delays under the sequence of random communication graphs is studied.By the binomial expansion of random matrix products,the convergence analysis of the algorithm is transformed into that of the mathematical expectation of random matrix products.Firstly,for the delay-free case,it is shown that all nodes' local estimates converge to the true parameter in mean square and almost surely if the observation matrices and communication graphs satisfy the stochastic spatio-temporal persistence of excitation condition.Especially,this condition holds for Markovian switching communication graphs and observation matrices,if the stationary graph is balanced with a spanning tree and the measurement model is spatio-temporally jointly observable.Secondly,for the case with time delays,delay matrices are introduced to model the random time-varying communication delays among the nodes.It is shown that under the stochastic spatio-temporal persistence of excitation condition,for any given bounded delays,proper algorithm gains can be designed to guarantee mean square convergence for the case with conditionally balanced digraphs.3.The problem of distributed multi-area state estimation for power systems with switching communication graphs is studied.By the binomial expansion of matrix products,it is proved that the algorithm gains can be designed properly such that all areaslocal estimates converge almost surely to the global least square estimate if the measurement system is jointly observable and the communication graphs are balanced and jointly strongly connected.4.Convergence of the distributed gradient-tracking-based optimization algorithm with random graphs is analyzed.The communication networks are modelled as a sequence of balanced random graphs.It is proved that the algorithm achieves convergence to the global solution at an exponential rate if the digraphs are uniformly conditionally strongly connected,the global cost function is strongly convex and the step sizes don't exceed some upper bounds.