| With the development of the modern control techniques,the amount of information that needs to be processed has increased dramatically.It is particularly difficult for centralized control to withstand such a heavy computational burden,so multi-agent distributed control strategy emerges as the times require.Distributed strategy can solve the large-scale problem of multiagent cooperation,increase the capacity of the system and improve the robustness of the network.Nowadays,the distributed optimization algorithm have been applied widely on deep learning,artificial intelligence,resource management,UAV formation and so on.With the development of multi-agent technology,distributed algorithm with better privacy and faster convergence rate has become a research hotspot.In view of recent research hotspots,the main research contents of this paper are as follows:A discrete-time distributed optimization algorithm is designed for a strongly connected weighted balanced digraph.The difficulty of step size selection is avoided by gradient restriction strategy,and the optimal solution of the optimization problem is transformed into the stability point problem of the system with linear transformation.The Lyapunov function is constructed to verify the convergence of the algorithm.The algorithm converges to the optimal solution with a linear rate.Furthermore,the proposed algorithm is combined with event triggering protocol to reduce the communication burden between agents at the expense of a part of convergence rate.For a strongly connected unbalanced digraph with network topology,a row stochastic optimization algorithm is designed by using the agent's information of in-degree.In the distributed optimization algorithm,the selection of step size is an important part of the algorithm,which is closely related to the convergence speed of the algorithm.By adding additional dynamic equations,the step size used by the agent at each time is allowed to be different.which makes the selection of step sizes easier.The diminishing step or constant step can be used in our algorithm.In addition,the diminishing step is different from the general diminishing step,so it is not necessary to require the diminishing step to 0.Furthermore,the equality constraints and set constraints in optimization problems are also considered.The correctness of the algorithm is verified by constructing appropriate matrix norm.For general distributed convex optimization problems,a multi-agent distributed optimization algorithm with independent step size is proposed.The algorithm uses a fixed step size,but unlike all agents using the same fixed step size,each agent uses a separate step size.The range of step size is independent of network topology and only related to the cost function of each agent itself.Compared with the existing methods,the local cost functions of each agent need only be convex rather than strongly convex.The requirement of cost function has been relaxed.Even if all agents use different step sizes,the proposed algorithm can ensure that the states of each agent converge to the exact optimal solution at a linear rate. |
