上述关于非线性系统有限时间控制的matlab代码,未定义函数或变量‘U’,重新给出代码
时间: 2023-06-15 17:03:16 浏览: 62
抱歉,之前的回答中可能有误,请参考以下代码:
```matlab
clear all;
clc;
%% System parameters
a = 1;
b = 1;
c = 1;
d = 1;
%% State feedback controller design
Q = [1 0 0 0;
0 1 0 0;
0 0 1 0;
0 0 0 1];
R = 1;
[K,S,e] = dlqr([0 1 0 0;
a b c 0;
0 0 0 1;
0 0 d 0], [0;0;0;1], Q, R);
Acl = [0 1 0 0;
a-b*K(1) b-c*K(2) c-d*K(3) -d*K(4);
0 0 0 1;
0 0 -d*K(1) -d*K(2)];
Bcl = [0; 0; 0; d];
C = [1 0 0 0; 0 0 1 0];
%% Observer design
L = place(Acl',C',[0.1 0.2 0.3 0.4])';
%% Simulation
tspan = 0:0.01:10;
x0 = [1; 0; 1; 0];
xhat0 = [0; 0; 0; 0];
x = zeros(4,length(tspan));
xhat = zeros(4,length(tspan));
u = zeros(1,length(tspan));
for i=1:length(tspan)
x(:,i) = expm([(a-b*K(1)) b-c*K(2) c-d*K(3) -d*K(4);
0 0 0 1;
0 0 0 0;
0 0 -d*K(1) -d*K(2)]*tspan(i))*x0;
xhat(:,i) = expm([(a-b*K(1)+L(1,1)*c) (b-c*K(2)+L(2,1)*d) c-d*K(3) (-d*K(4)+L(4,1)*d);
L(1,2) L(2,2) 0 L(4,2);
0 0 0 0;
(L(1,1)-K(1)*L(3,1)) (L(2,1)-K(2)*L(3,1)) 0 (L(4,1)-K(1)*L(3,1))]*tspan(i))*xhat0 + ...
expm([(a-b*K(1)+L(1,1)*c) (b-c*K(2)+L(2,1)*d) c-d*K(3) (-d*K(4)+L(4,1)*d);
L(1,2) L(2,2) 0 L(4,2);
0 0 0 0;
(L(1,1)-K(1)*L(3,1)) (L(2,1)-K(2)*L(3,1)) 0 (L(4,1)-K(1)*L(3,1))]*tspan(i))*(-L*[xhat(1,i);xhat(3,i)]) + ...
expm([(a-b*K(1)+L(1,1)*c) (b-c*K(2)+L(2,1)*d) c-d*K(3) (-d*K(4)+L(4,1)*d);
L(1,2) L(2,2) 0 L(4,2);
0 0 0 0;
(L(1,1)-K(1)*L(3,1)) (L(2,1)-K(2)*L(3,1)) 0 (L(4,1)-K(1)*L(3,1))]*tspan(i))*u(1);
u(:,i) = -K*xhat(:,i);
end
%% Plot results
figure(1)
plot(tspan,x(1,:),'LineWidth',2)
hold on
plot(tspan,xhat(1,:),'--','LineWidth',2)
title('State 1')
xlabel('Time')
ylabel('Value')
legend('True','Estimated')
figure(2)
plot(tspan,x(2,:),'LineWidth',2)
title('State 2')
xlabel('Time')
ylabel('Value')
figure(3)
plot(tspan,x(3,:),'LineWidth',2)
hold on
plot(tspan,xhat(3,:),'--','LineWidth',2)
title('State 3')
xlabel('Time')
ylabel('Value')
legend('True','Estimated')
figure(4)
plot(tspan,x(4,:),'LineWidth',2)
title('State 4')
xlabel('Time')
ylabel('Value')
figure(5)
plot(tspan,u,'LineWidth',2)
title('Control Input')
xlabel('Time')
ylabel('Value')
```