On Stochastic Seeking Via Stochastic Approximation Algorithms

Stochastic seeking refers to seeking the source of signal or extremum of objec-tive function with single or multiple agents(vehicles or robots)controlled by some stochastic mechanism.It exists widely in nature and human life,which achieves intensive attention and is studied by many scholars.Stochastic seeking in discrete time is of greater significance than that in continuous time because of the compu-tation requirement.Lots of stochastic seeking utilize the information of objective function(e.g.,functional form or gradient information).Existing stochastic seeking without objective function knowledge mainly focus on Stochastic Extremum Seeking(SES)and a few scholars use stochastic approximation idea,but the boundedness of estimated sequence is often assumed.In addition,owing to the neighbor relationship among the agents,data transmission and delay,distributed stochastic seeking is far from full research.In this thesis,based on stochastic approximation idea with expanding trun-cations,we propose discrete-time stochastic seeking algorithms to tune single or multiple agents toward the maximum(or minimum)point of the objective function,and remove the boundedness hypothesis and weaken the noise conditions.The main work includes:1.Stochastic source seeking with two types of vehicle models(velocity actuated vehicle and force actuated vehicle)are studied.By the division of time interval and discrete sampling,the discrete-time motion model is obtained.Based on the existing stochastic approximation idea with expanding truncations,we give discrete-time stochastic source seeking algorithm and conditions of convergence.Finally,the effectiveness is verified by numerical simulations.2.Distributed stochastic source seeking is investigated.Namely,N vehicles seek the source by exchanging the measurements of signal.Furthermore,we consider distributed stochastic extremum seeking,i.e.,N vehicles seek the extremum of global objective function(the sum of N local cost functions)using noisy measurements.First of all,N vehicles(velocity actuated vehicles or force actuated vehicles)are treated as nodes and a network is formed.The dynamic models of each vehicle are discretized by the same time interval division.Then the definition of distance is given.The neighborhood relationship between agents is decided and the weight matrix is constructed.After that the distributed source seeking algorithm is proposed and the convergence is proved.By strengthening the hypothesis and modifying the distributed source seeking algorithm,we can seek the extremum in a distributed manner.Finally,the effectiveness is verified by numerical simulations.