Distributed Optimization And Control For Multi-agent Systems Under Different Kinds Of Constraints

With the development of the networked system,it becomes more difficult to obtain the global information of the centralized algorithm.More attention has been concentrated on the distributed control strategy due to its distributive data,robustness and extendibility.People always expect to achieve the goal with the minimum cost in the network system.The distributed optimization algorithms have been applied widely on smart grid,transportation,cloud computing,UAVs and so on.So the study on distributed optimization algorithms gradually becomes a hotspot.The main topic in this paper is to study the designing of the distributed optimization algorithms with different external conditions.The main contributions of this paper are described as follows:The designing of the distributed optimization algorithm under Markov switching topologies for multi-agent systems is discussed in this paper.The distributed optimization algorithms based on the compensation-feedback method for continuous-time and discrete-time multi-agent systems are provided.The problem is transformed to the stability of the multi-agent system with the linear transformation.The sufficient conditions for asymptotic convergence and exponential convergence are obtained through the Lyapunov method,respectively.The case that the transition rates matrix is partly unknown is also discussed.We study the distributed optimization problem over general strongly connected graphs.Most of the existing results design the algorithm over undirected or weight-balanced graphs,which simplifies the design of the algorithm and obtains a good convergence result.However,it is hard to achieve the undirected graph and the weight-balanced graph in the realistic applications.This paper proposes the algorithm over directed graphs based on the out-degree and in-degree information,which makes the algorithm overcome the disadvantages.Utilizing the coordinate transformation and Lyapunov method,the sufficient condition for convergence is also obtained.The protocol to decrease the communication among agents for the multi-agent systems is discussed.The computation of the frequent communication between agents and agents itself consume a lot of energy.By simplifying and improving the control strategy,the numbers of communication and calculation between agents can be reduced effectively,so that the energy consumption of agents is decreased,which prolongs the lifetime of the whole multi-agent system.At the same time,input saturation is also a very common phenomenon in the design of the controller.If the input saturation is not taken into account in the design of the controller,the system may fail and even collapse.The necessary and sufficient conditions for average consensus and containment control in discrete multi-agent systems are studied.By using matrix iterative analysis and the properties of the eigenvalues,the necessary and sufficient conditions for achieving average consensus and containment control are given,which is important for the design of the step-size,stability analysis and system stabilization.