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.

分享宋老师的两篇文章，题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:
ξi(k+1)=ξi(k)+ui(k)(8.1)\xi_i(k+1) = \xi_i(k) + u_i(k) \tag{8.1} ξi(k+1)=ξi(k)+ui(k)(8.1)

[xi(k+1)vi(k+1)]=[xi(k)+vi(k)vi(k)+ui(k)]\left[\begin{matrix} x_{i}(k+1) \\ v_{i}(k+1) \\ \end{matrix}\right] = \left[\begin{matrix} {x}_{i}(k) + v_i(k) \\ {v}_{i}(k) + u_i(k) \\ \end{matrix}\right][xi(k+1)vi(k+1)]=[xi(k)+vi(k)vi(k)+ui(k)]

公式的一些展开和推论过程：

Codes

% Paper: Consensus of Heterogeneous Agents with Linear Discrete Dynamics
% Protocol Simulation Results
% Author: Zhao-Jichao
% Date: 2021-04-15
% Update: 2021-05-15 重新考虑了二阶的协议，为什么二阶的速度最终为0，因为协议使用的是 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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【Paper】2015_Song_Consensus of Heterogeneous Agents with Linear Discrete Dynamics

Consensus of Heterogeneous Agents with Linear Discrete Dynamics

Paper

Codes

Results

【Paper】2015_Song_Consensus of Heterogeneous Agents with Linear Discrete Dynamics相关推荐

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