Distributed Continuous Time Optimization With Different Types Of Constraints

With the rapid development of large-scale network systems,the research on distributed optimization of multi-agent systems has received widespread attention from many scholars,and related research results have also been widely used in engineering and scientific fields such as machine learning,smart grids,and unmanned aerial vehicles.However,in practical applications,due to the limitations of realistic physical conditions and communication environments,agents are subject to various constraints,such as control inputs and communication information are constrained by non-convex sets,and positions are constrained by convex sets.Solving distributed optimization problems with heterogeneous constraints is more challenging due to the coupling of multiple constraints and strong nonlinearity.This paper mainly studies distributed optimization problems with non-convex input constraints and non-convex interaction constraints for continuous-time multi-agent systems.The details are as follows:Firstly,a distributed optimization problem with nonuniform state constraints and switching communication graphs is studied for non-convex input-constrained first-order continuous multi-agent systems,and a nonuniform gradient step-size distributed optimization algorithm is designed,and the destruction of the communication graph balance caused by the non-convex input constraint and the objective function is analyzed.Based on the property of the joint-strongly-connected graph,a chain recursion method is introduced and it is obtained that the maximum distance from the agent states to the intersection of the convex constraint state set decreases as time evolves.On this basis,combined with the contradiction analysis method,convex optimization theory and Lyapunov stability theory,the convergence analysis of the system is carried out.Finally,it is proved that the system can converge to the optimal consensus point in the case of jointly-strongly-connected communication graphs.Secondly,a coupled-constrained distributed optimization problem is studied for non-convex interaction and input simultaneous constrained continuous-time multi-agent systems,a gradient-based projection optimization algorithm is designed,and the nonlinear multi-coupling relations caused by non-convex interaction and input constraints and nonuniform state constraint are analyzed.Through the projection vector transformation,the original system is transformed into an equivalent linear time-varying system with a disturbance-like term and the angular relationship between the projection vectors is studied by a geometric method,thereby decoupling the couple of strong nonlinear.Then the optimal convergence of the system is obtained under the condition of jointly strongly connected by a contradiction method and the Lyapunov function approach.