Design Of Distributed Cooperative Controllers For Multi-Agent Systems With Multi-Input Multi-Output Individual

In recent years,for the multi-agent systems with single-input single-output individual,some important results have obtained.However,there are few studies on the multi-input multi-output individual.Thus,based on the frequency domain analysis method,a distributed low-order controllers and time-delay controllers design method for multi-agent systems with multi-input multi-output individual is proposed.Based on the theory of equivalent transfer function(ETF),a distributed PID controller design method is proposed for the high-dimensional multivariable square and non-square systems with time delay.By exploiting the relationship between ETF and the transfer function of multivariable systems,an ETF algorithm is proposed and an analytical expression of ETF model is derived.Based on the Hermite-Biehler generalization theorem,the range of the proportional gain(k_p)for each equivalent transfer function with multi-time delay complex coefficients is analytically obtained.For each value of k_p in the entire range,the stabilizing region of the subsystem in the space of integral(k_i)and derivative(k_d)gains is determined and the linear programming characteristic of the stabilizing region is obtained.By sweeping over the entire ranges of the proportional gain(k_p),the stabilizing region of distributed PID controllers for multi-agent systems can be determined.Based on the stabilizing results of PID controllers for multivariable systems,the method of designing distributed controllers for multi-agent systems with multi-input multi-output individual is proposed.For the multi-agent systems with two-input two-output individual,a method of designing distributed tracking controller is presented.Based on the theory of matrix theory,the multi-agent system is decomposed into several subsystems with respect to the eigenvalues of the Laplacian matrix,which reduces the complexity of the system.The stabilizing region of PID controller for the multi-agent system is given by solving the intersection of the stabilizing regions of the control parameters of all improved subsystems.The two outputs of the multi-agent systems can achieve consensus by selecting the parameters in the stabilizing region.For the multi-agent system with multi-input multi-output individual(the number of input and output are greater than 2),a method of designing distributed tracking controller is further presented.In addition,the necessary and sufficient conditions of the tracking controllers for the linear multi-agent system are given.The stabilization problem of multi-agent systems can be transformed into the one of zero steady-state error control for a group of independent subsystems.The stabilizing region of PID controller for the multi-agent system is given by solving the intersection of the stabilizing regions of the control parameters of all improved subsystems.The multiple outputs of the multi-agent systems can achieve tracking consensus by selecting the parameters in the stabilizing region.For the multi-agent systems with multi-input multi-output individual,the DPR(Double Proportional Retarded)controllers are proposed.Based on the network topology matrix and equivalent transfer function theory,independent single-input single-output systems can be derived from the multi-agent systems with multi-input multi-output individual.The closed-loop feature polynomials of the system are regarded as the sum of vectors and constitute triangles.Based on the triangle feature,the stabilizing region of DPR controller can be obtained.The outputs of multi-agent systems can achieve consensus by selecting appropriate parameters in the stabilizing region.The problem of distributed cooperative controller designed for the multi-agent systems with multi-input multi-output individual is solved and the stabilizing range of the corresponding control parameters is given.Since the distributed PID controller and the DPR controller have the advantages of simple structure,low computational complexity and easy implementation,the proposed design method of the cooperative controller provides a theoretical basis for the cooperative control of multi-agent systems in industrial applications.