当D=1.5,Nm=3,用c++代码写一个拉格朗日插值算法实现的分数阶控制
时间: 2024-01-21 18:17:59 浏览: 28
下面是用C++代码实现的拉格朗日插值算法实现的分数阶控制:
```cpp
#include <iostream>
#include <vector>
using namespace std;
double lagrange_interp(vector<double> x, vector<double> y, double xi)
{
int n = x.size();
double res = 0;
for (int i = 0; i < n; i++) {
double term = y[i];
for (int j = 0; j < n; j++) {
if (i != j) {
term *= (xi - x[j]) / (x[i] - x[j]);
}
}
res += term;
}
return res;
}
double frac_ctrl(double u, double D, double Nm)
{
double alpha = 1.0 - D;
vector<double> x(Nm + 1), y(Nm + 1);
for (int i = 0; i <= Nm; i++) {
x[i] = i;
y[i] = pow(x[i], alpha) / (1 + pow(x[i], D));
}
double y_interp = lagrange_interp(x, y, u);
return pow(u, alpha) * y_interp;
}
int main()
{
double D = 1.5;
int Nm = 3;
double u = 2.5;
double y = frac_ctrl(u, D, Nm);
cout << "u = " << u << ", y = " << y << endl;
return 0;
}
```
其中,`lagrange_interp`函数实现拉格朗日插值算法,`frac_ctrl`函数实现分数阶控制,`main`函数测试了该函数在`u=2.5`时的输出。注意,此处的分数阶控制函数只是一个简单的示例,实际应用中需要根据具体问题进行调整。