原文地址： Y. Song, “Consensus of heterogeneous agents with linear discrete dynamics,” 2015 34th Chinese Control Conference (CCC), 2015, pp. 7416-7422, doi: 10.1109/ChiCC.2015.7260815.

原文地址：Song, Yun-Zhong. “Consensus of agents with mixed linear discrete dynamics.” International Journal of Control, Automation and Systems 14.4 (2016): 1139-1143.

分享宋老師的兩篇文章，題目及引用格式如上所述。

Consensus of Heterogeneous Agents with Linear Discrete Dynamics

• Paper
• Codes
• Results

Paper

Second order agent dynamics:
$${\xi }_i(k+1)={\xi }_i(k)+u_i(k)\text{\hspace{1em}(8.1)}$$

$$\left[\begin{array}{c}{x}_i(k+1)\\ v_i(k+1)\end{array}\right]=\left[\begin{array}{c}{x}_i(k)+v_i(k)\\ v_i(k)+u_i(k)\end{array}\right]$$

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公式的一些展開和推論過程：

Codes

% Paper: Consensus of Heterogeneous Agents with Linear Discrete Dynamics % Protocol Simulation Results % Author: Zhao-Jichao % Date: 2021-04-15 % Update: 2021-05-15 重新考慮了二階的協議，為什么二階的速度最終為0，因為協議使用的是 vi，而不是 vj-vi。 clear clc%% Initial Parameters x1 = 3; x2 = [2; -2]; x3 = -1; x4 = [-2; 2]; x5 = -2; x6 = 4; X0 = [x1, x3, x5, x6, x2(1,1), x4(1,1), x2(2,1), x4(2,1)]; Xt(:,1) = X0; k = 1;% Time Params tBegin = 0; tFinal = 4; dT = 0.01; times = (tFinal - tBegin) / dT; t(1,1) = 0;%% Relation Matrix n1 = 4; n2 = 2;L_a = [2 0 0 -1 -1 0;0 2 0 0 -1 -1;0 0 2 -1 0 -1;-1 0 -1 2 0 0;-1 -1 0 0 2 0;0 -1 -1 0 0 2;];Pbar = L2P(L_a, dT, n1, n2);%% Iterations for i=1:timest(:,i+1) = t(:,i) + dT;Xt(:,i+1) = Pbar * Xt(:,i); end%% Draw Result Diagram subplot(1,2,1) plot(t,Xt(1,:), 'linewidth',1.5); hold on % x1 plot(t,Xt(2,:), 'linewidth',1.5); hold on % x3 plot(t,Xt(3,:), 'linewidth',1.5); hold on % x5 plot(t,Xt(4,:), 'linewidth',1.5); hold on % x6 plot(t,Xt(5,:), 'linewidth',1.5); hold on % x2 plot(t,Xt(6,:), 'linewidth',1.5); hold on % x4 title('Position Trajectory'); grid on; box on;subplot(1,2,2) plot(t,Xt(7,:), 'linewidth',1.5); hold on % v2 plot(t,Xt(8,:), 'linewidth',1.5); hold on % v4 title('Velocity Trajectory'); grid on; box on;%% Transformation SubFunction function Pbar = L2P(L, dT, n1, n2)L1 = L(1:n1, 1:n1);L2 = L(1:n1, (n1+1):(n1+n2));L3 = L((n1+1):(n1+n2),1:n1);L4 = L((n1+1):(n1+n2),(n1+1):(n1+n2));Pbar(1:n1, 1:n1) = eye(n1) - dT * L1;Pbar(1:n1, (n1+1):(n1+n2)) = -dT * L2;Pbar(1:n1, (n1+n2+1):(n1+n2+n2)) = zeros(n1,n2);Pbar((n1+1):(n1+n2), 1:n1) = zeros(n2,n1);Pbar((n1+1):(n1+n2), (n1+1):(n1+n2)) = eye(n2);Pbar((n1+1):(n1+n2), (n1+n2+1):(n1+n2+n2)) = eye(n2);Pbar((n1+n2+1):(n1+n2+n2), 1:n1) = -dT * L3;Pbar((n1+n2+1):(n1+n2+n2), (n1+1):(n1+n2)) = -dT * L4;Pbar((n1+n2+1):(n1+n2+n2), (n1+n2+1):(n1+n2+n2)) = zeros(n2); end

Results

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總結

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