Optimal Cooperative Control Scheme Of Multi-agent Systems With Time Delay Based On PSO Algorithm

In recent years,the research on the cooperative control methods for multi-agent systems has been one of the hottest issues that attract the domestic and foreign scholars.The optimal control method is an important branch of the cooperative control method.Although there are some achievements in the optimal control for multi-agent systems,the research on it is still not enough.Especially for the multi-agent systems with communication delay and input delay,the current feedback control methods for single system are not effective.Therefore,it has significant theory and practice values to design the optimal cooperative controller for such the time-delayed multi-agent system.In the dissertation,the optimal controller design problem for different multi-agent systems with time delay is studied based on the control theory and graph theory.The main contributions of the dissertation are concluded as follows.(1)Considering the universality of the first-order system,an optimal distributed PID control scheme is proposed for first-order multi-agent systems with time delay based on the PSO algorithm.Firstly,a multi-input multi-output framework based on transfer function is introduced to describe the multi-agent system.Based on the matrix theory,the multi-agent system is decomposed into several subsystems with respect to the eigenvalues of the Laplacian matrix.Thus,the consensus problem of the multi-agent system is transformed into the stabilizing problem of the subsystems with complex coefficients.For each subsystem,the stabilizing region of the PID controller is calculated.The global stabilizing region of the distributed PID controller can be derived by intersecting all the stabilizing regions.Finally,the optimal control parameter satisfying a certain performance index can be determined by the PSO algorithm.(2)Considering the universality of the nonlinear system,it is indeed to design controllers for the nonlinear multi-agent systems.Thus,for a kind of second-order nonlinear multi-agent system,an optimal distributed PID control scheme is presented based on the characteristic model.By using the characteristic model,the control problem of the nonlinear system is changed into the problem of the linear system,which reduces the complexity of the problem.For the characteristic model,the global stabilizing region is calculated.The optimal control parameters is finally derived based on the improved PSO algorithm.(3)If the agent is under some particular cases,such as flopping on the grass,it is better to use the fractional-order model to describe the model.When the model of the agent is fractional-order,it is difficult to reach good performance using the distributed control scheme.Therefore,a two-degree-of-freedom optimal consensus scheme is investigated,in which the individual controller and the coupling controller are both designed.The individual controller guarantees the robustness of the single agent and the coupling controller is designed to ensure fast consensus.The two-degree-of-freedom structure is applicable to arbitrary-order multi-agent systems with time delay,including the integer-order system and the fractional-order system.