| Recently,distributed cooperative control of multi-agent systems is widely used in many engineering fields,such as autonomous driving,distributed computing,etc.,and has become one of hot issues in the field of control.In practical systems,due to the existence of factors such as complex external environment and internal structure,some states of the agent are usually subject to some constraints.Additionally,constraints in actual situations are congenitally of irregularity,then both non-convex constraints and convex constraints would appear simultaneously,causing strong nonlinearity to the system.At present,the related research in this area mainly focuses on consensus and distributed optimization,and this paper attempts to extend it to containment control and bipartite consensus.The details are as follows:For second-order discrete-time multi-agent systems,we have analyzed containment control with switching topologies when non-convex velocity constraints,non-convex control input constraints and convex position constraints coexist.First of all,a nonlinear control algorithm based on non-convex operator and projection operator is proposed and compared with similar algorithms.Secondly,the original nonlinear system is transformed to an equivalent linear time-varying system by multiple model transformations.Thirdly,with Lyapunov function and the stochasticity of the equivalent system matrix applied,we analyze the non-increasing and convergence of the maximum distance between the followers and the convex hull spanned by the leaders.Finally,simulations are given to illustrate the effectiveness of the proposed control algorithm and the correctness of the theoretical results.For second-order continuous-time multi-agent systems,we have analyzed bipartite consensus with fixed undirected topology,considering non-convex velocity constraints and non-convex control input constraints,respectively.Firstly,a distributed control algorithm based on sign functions is jointly adopted and a structural analysis is made.Secondly,scaling factors are introduced to convert the original nonlinear system to a linear time-varying system losslessly.Secondly,the state matrices of the equivalent system with different constraints are analyzed.Then,the necessary and sufficient conditions are given for the stability of the system according to the distribution of characteristic roots.Finally,simulations are given to show the joint effectiveness of the control algorithm,and the feedback damping gain is closely related to the system convergence speed. |
