%改变了Laplacian函数里面的FAI矩阵，使得状态收敛至静态值，
clc
;
clear;
% 初始化
X0
= [-3, 2, 1, -1,4
]'; % 初始位置
DX0 = [0.3, 0.1, 0.5, 0.2, 0.4]'; % 初始速度
Y1
= [X0
; DX0
]; % 积分初值
n
= 5
;
n
= length
(X0
);
A
=[0 1 0 -1 1
;
0 0 1 0 0
;
1 0 0 0 0
;
0 0 0 0 1
;
0 0 0 1 0
]; % 邻接矩阵，有向拓扑结构
D
=[1 0 0 0 0
;
0 1 0 0 0
;
0 0 1 0 0
;
0 0 0 1 0
;
0 0 0 0 1
]; % 度矩阵，有向拓扑结构
L
= D - A
;
gama
= 1.2547
;
k
= 0.5
;
% 构造矩阵FAI
FAI
= [zeros
(n,n
), eye
(n
);
-L, -k*eye
(n
)-gama*L
];
tBegin
= 0
;
tEnd
= 10
;
h
= 0.1
;
times = (tEnd-tBegin
) / h
;
Y
(:,1
) = Y1
;
t
(1
) = tBegin
;
i
= 1
;
% 从1到100循环了100次
while
(i
<= times
)
K1
= h * FAI * Y
(1:10,i
);
K2
= h * FAI * Y
(1:10,i
) + K1/2
;
K3
= h * FAI * Y
(1:10,i
) + K2/2
;
K4
= h * FAI * Y
(1:10,i
) + K3
;
t
(i+1
) = t
(i
) + h
;
Val
= (K1+2*K2+2*K3+K4
)/6
;
Y
(1:10,i+1
) = Y
(1:10,i
) + Val
;
i
= i+1
;
end
% 显示
subplot
(2,1,1
)
plot
(t,Y
(1,:
), t,Y
(2,:
), t,Y
(3,:
), t,Y
(4,:
), t,Y
(5,:
))%位置
subplot
(2,1,2
)
plot
(t,Y
(6,:
), t,Y
(7,:
), t,Y
(8,:
), t,Y
(9,:
), t,Y
(10,:
))%速度
