时变koopman预测器的设计流程及其matlab代码
时间: 2023-11-29 07:05:43 浏览: 27
时变Koopman预测器的设计流程已经在上一个回答中概括了,下面提供一个简单的Matlab代码实现示例:
```matlab
% Step 1: Collect data
data = load('system_data.mat');
u = data.u; % system inputs
y = data.y; % system outputs
% Step 2: Choose features
X = [y, u]; % use output and input as features
% Step 3: Build Koopman operator
n = size(X, 2); % number of features
m = 10; % number of modes
K = zeros(m*n, m*n);
for i = 1:m
for j = 1:m
K((i-1)*n+1:i*n, (j-1)*n+1:j*n) = X.'*X^(i+j-2);
end
end
% Step 4: Choose time-varying function
t = data.t; % time vector
f = sin(t); % example time-varying function
% Step 5: Train model
S = diag(f); % time-varying scaling matrix
A = pinv(S)*K*S; % scaled Koopman operator
lambda = eig(A); % eigenvalues of A
phi = pinv(S)*real(eigvecs(A)); % scaled Koopman modes
x0 = X(1,:).'; % initial condition
tspan = [0, max(t)]; % time span for simulation
[t, x] = ode45(@(t, x) A*x, tspan, x0); % simulate system
% Step 6: Validate model
x_true = X.';
x_pred = phi.'*(S*x(1,:).');
figure;
plot(t, x_true, 'b', t, x_pred, 'r--');
legend('True', 'Predicted');
% Step 7: Apply model
x0 = X(1,:).'; % initial condition
tspan = [0, max(t)]; % time span for prediction
[t, x] = ode45(@(t, x) A*x, tspan, x0); % predict system
y_pred = x(:,1:size(y, 2)); % predicted output
```
请注意,这只是一个简单的示例,实际的应用可能需要更复杂的模型和更大的数据集。