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Matlab 仿真含时滞多智体一致性分析，附代码

系统结构如下图所示：

clear;
clc;
% 2014_多智能体网络的一致性问题研究_纪良浩
% 此为Paper中的示例代码
% 例2.1:
A = [0,   0,    0.1, 0, 0;
     0.1, 0,    0,   0, 0;
     0,   0.15, 0,   0, 0;
     0,   0.25, 0,   0, 0;
     0.2, 0,    0,   0, 0;];

D = [0, 0, 0, 0, 0;
     0, 0, 0, 0, 0;
     0, 0, 0, 0, 0;
     0, 0, 0, 0, 0;
     0, 0, 0, 0, 0;];

% 各节点间的通信时滞如下
T13 = 1.0;
T21 = 0.75;
T32 = 1.8;
T42 = 2.0;
T51 = 0.8;
% 输入时滞如下
T = 0.3;
% 各节点的随机初始状态如下
X = [2, 3.5, 2.5, 3, 5;]';
U = [0, 0, 0, 0, 0;]';

%% 更改时滞格式
% 各节点间的通信时滞如下
T13 = 10;
T21 = 7;
T32 = 18;
T42 = 20;
T51 = 8;
% 输入时滞如下
T = 3;
% 为了防止开始收敛前无状态，特扩充收敛前的状态
t = 0;
for i = 1:20
   X(:, i+1) = X(:, i);
   U(:, i+1) = U(:, i);
   t(:, i+1) = t(:, i)+0.1;
   i = i + 1;
end

%%
% 仿真相关参数如下
tBegin = 0;
tEnd   = 60;
dt     = 0.1;
times  = (tEnd - tBegin)/dt;
time   = 1;


% 计算过程如下
while (time <= times)
    % 时间记录
    t(1, time+20) = tBegin + dt * time + 19*0.1;
    % 控制输入分别为
    j = X(3, time+20-T13);
    i = X(1, time+20-T);
    a = A(1,3);
    U(1, time+20) = sum( a * (j-i) );
    U(2, time+20) = sum( A(2,1) * (X(1, time+20-T21)-X(2, time+20-T)) );
    U(3, time+20) = sum( A(3,2) * (X(2, time+20-T32)-X(3, time+20-T)) );
    U(4, time+20) = sum( A(4,2) * (X(2, time+20-T42)-X(4, time+20-T)) );
    U(5, time+20) = sum( A(5,1) * (X(2, time+20-T51)-X(5, time+20-T)) );
    % 状态更新为
    X(1, time+21) = X(1, time+20) + U(1, time+20) * dt;
    X(2, time+21) = X(2, time+20) + U(2, time+20) * dt;
    X(3, time+21) = X(3, time+20) + U(3, time+20) * dt;
    X(4, time+21) = X(4, time+20) + U(4, time+20) * dt;
    X(5, time+21) = X(5, time+20) + U(5, time+20) * dt;
    
    time  = time + 1;
end

%% 绘制结果图
subplot(2,1,1);
plot(t,X(1,1:620), t,X(2,1:620), t,X(3,1:620), t,X(4,1:620), t,X(5,1:620), "linewidth",2);
legend("x_1", "x_2", "x_3", "x_4", "x_5");

subplot(2,1,2);
plot(t,U(1,:), t,U(2,:), t,U(3,:), t,U(4,:), t,U(5,:), "linewidth",2);
legend("u_1", "u_2", "u_3", "u_4", "u_5");

下图为默认输入时滞T=0.3s的收敛情况：

下图为输入时滞T=2.0s的收敛情况：

Ref:

1. 2014_多智能体网络的一致性问题研究_纪良浩