MATLAB C 生成编码器可以生成适合嵌入式系统的 C 代码吗？

Posted 2023-03-28

【中文标题】MATLAB C 生成编码器可以生成适合嵌入式系统的 C 代码吗？

【英文标题】：Can MATLAB C generation coder generate C-code that fits embedded system?

【发布时间】：2020-01-28 18:14:33

【问题描述】：

我需要将此代码转换为 C 代码。

问题：

MATLAB Coder 是否会生成内存安全的 C 代码，例如它们不使用 calloc 或 ma​​lloc。 Misra C 标准不允许编码器使用动态内存分配。由于内存泄漏，这对嵌入式系统很危险。 MATLAB Coder 是否会生成以动态矩阵为参数的 C 代码，例如带参数的函数 foo(float* A, int m, int n) 或 foo(int m, int n, float A[m][n]) 或已修复大小示例 foo(float A[3][5])，仅作为选项提供？ MATLAB Coder 是否会生成可嵌入嵌入式系统的 C 代码。 horzcat、size 和 vertcat 等 .m 文件中的内部 C++ 命令如何？它们会成为 100% 可移植的 C 代码吗？

MATLAB Coder 会生成通过引用调用的函数吗？示例 foo(float* input, float* output) 而不是 float* output = foo(float* input)

function [U] = mpc (A, B, C, x, N, r, lb)

  ## Find matrix
  PHI = phiMat(A, C, N);
  GAMMA = gammaMat(A, B, C, N);


  ## Solve first with no constraints
  U = solve(PHI, GAMMA, x, N, r, 0, 0, false);

  ## Then use the last U as upper bound
  U = solve(PHI, GAMMA, x, N, r, lb, U(end), true);

end

function U = solve(PHI, GAMMA, x, N, r, lb, ub, constraints)
  ## Set U
  U = zeros(N, 1);

  ## Iterate Gaussian Elimination
  for i = 1:N

    ## Solve u
    if(i == 1)
      u = (r - PHI(i,:)*x)/GAMMA(i,i)
    else
      u = (r - PHI(i,:)*x - GAMMA(i,1:i-1)*U(1:i-1) )/GAMMA(i,i)
    end

    ## Constraints 
    if(constraints == true)
      if(u > ub)
        u = ub;
      elseif(u < lb)
        u = lb;
      end
    end

    ## Save u
    U(i) = u
  end
end

function PHI = phiMat(A, C, N)

  ## Create the special Observabillity matrix
  PHI = [];
  for i = 1:N
    PHI = vertcat(PHI, C*A^i);
  end

end

function GAMMA = gammaMat(A, B, C, N)

  ## Create the lower triangular toeplitz matrix
  GAMMA = [];
  for i = 1:N
    GAMMA = horzcat(GAMMA, vertcat(zeros((i-1)*size(C*A*B, 1), size(C*A*B, 2)),cabMat(A, B, C, N-i+1)));
  end

end

function CAB = cabMat(A, B, C, N)

  ## Create the column for the GAMMA matrix
  CAB = [];
  for i = 0:N-1
    CAB = vertcat(CAB, C*A^i*B);
  end

end

我的 C 代码。是的，它的工作原理！

/*
 * Generalized_Predictive_Control.c
 *
 *  Created on: 
 *      Author:
 */

#include "Generalized_Predictive_Control.h"

/*
 * Parameters
 */
int adim;
int ydim;
int rdim;
int horizon;

/*
 * Deceleration
 */
static void obsv(float* PHI, const float* A, const float* C);
static void kalman(float* x, const float* A, const float* B, float* u, const float* K, float* y, const float* C);
static void mul(float* A, float* B, float* C, int row_a, int column_a, int column_b);
static void tran(float* A, int row, int column);
static void CAB(float* GAMMA, float* PHI, const float* A, const float* B, const float* C);
static void solve(float* GAMMA, float* PHI, float* x, float* u, float* r, float lb, float ub, int constraintsON);
static void print(float* A, int row, int column);


void GPC(int adim_, int ydim_, int rdim_, int horizon_, const float* A, const float* B, const float* C, const float* D, const float* K, float* u, float* r, float* y, float* x)
    /*
     * Set the dimensions
     */
    adim = adim_;
    ydim = ydim_;
    rdim = rdim_;
    horizon = horizon_;

    /*
     * Identify the model - Extended Least Square
     */
    int n = 5;
    float* phi;
    float* theta;
    //els(phi, theta, n, y, u, P);

    /*
     * Create a state space model with Observable canonical form
     */


    /*
     * Create the extended observability matrix
     */
    float PHI[horizon*ydim*adim];
    memset(PHI, 0, horizon*ydim*adim*sizeof(float));
    obsv(PHI, A, C);

    /*
     * Create the lower triangular toeplitz matrix
     */
    float GAMMA[horizon*rdim*horizon*ydim];
    memset(GAMMA, 0, horizon*rdim*horizon*ydim*sizeof(float));
    CAB(GAMMA, PHI, A, B, C);

    /*
     * Solve the best input value
     */
    solve(GAMMA, PHI, x, u, r, 0, 0, 0);
    solve(GAMMA, PHI, x, u, r, 0, *(u), 1);

    /*
     * Estimate the state vector
     */
    kalman(x, A, B, u, K, y, C);


/*
 * Identify the model
 */
static void els(float* P, float* phi, float* theta, int polyLength, int totalPolyLength, float* y, float* u, float* e)

    /*
     * move phi with the inputs, outputs, errors one step to right
     */
    for(int i = 0; i < polyLength; i++)
        *(phi + i+1 + totalPolyLength*0) = *(phi + i + totalPolyLength*0); // Move one to right for the y's
        *(phi + i+1 + totalPolyLength*1) = *(phi + i + totalPolyLength*1); // Move one to right for the u's
        *(phi + i+1 + totalPolyLength*2) = *(phi + i + totalPolyLength*2); // Move one to right for the e's
    

    /*
     * Add the current y, u and e

    (*phi + totalPolyLength*0) = -*(y + 0); // Need to be negative!
    (*phi + totalPolyLength*1) =  *(u + 0);
    (*phi + totalPolyLength*2) =  *(e + 0);
 */
    /*
     * phi'*theta
     */
    float y_est = 0;
    for(int i = 0; i < totalPolyLength; i++)
        y_est += *(phi + i) * *(theta + i);
    
    float epsilon = *(y + 0) - y_est; // In this case, y is only one element array

    /*
     * phi*epsilon
     */
    float phi_epsilon[totalPolyLength];
    memset(phi_epsilon, 0, totalPolyLength*sizeof(float));
    for(int i = 0; i < totalPolyLength; i++)
        *(phi_epsilon + i) = *(phi + i) * epsilon;
    

    /*
     * P_vec = P*phi_epsilon
     */
    float P_vec[totalPolyLength];
    memset(P_vec, 0, totalPolyLength*sizeof(float));
    mul(P, phi_epsilon, P_vec, totalPolyLength, totalPolyLength, 1);

    /*
     * Update our estimated vector theta = theta + P_vec
     */
    for(int i = 0; i < totalPolyLength; i++)
        *(theta + i) = *(theta + i) + *(P_vec + i);
    

    /*
     * Update P = P - (P*phi*phi'*P)/(1 + phi'*P*phi)
     */
    // Create phi'
    float phiT[totalPolyLength];
    memset(phiT, 0, totalPolyLength*sizeof(float));
    memcpy(phiT, phi, totalPolyLength*sizeof(float));
    tran(phiT, totalPolyLength, 1);

    // phi'*P
    float phiT_P[totalPolyLength];
    memset(phiT_P, 0, totalPolyLength*sizeof(float));
    mul(phiT, P, phiT_P, 1, totalPolyLength, totalPolyLength);

    // phi*phi'*P
    float phi_phiT_P[totalPolyLength*totalPolyLength];
    memset(phi_phiT_P, 0, totalPolyLength*totalPolyLength*sizeof(float));
    mul(phi, phiT_P, phi_phiT_P, totalPolyLength, 1, totalPolyLength);

    // P*phi*phi'*P
    float P_phi_phiT_P[totalPolyLength*totalPolyLength];
    memset(P_phi_phiT_P, 0, totalPolyLength*totalPolyLength*sizeof(float));
    mul(P, phi_phiT_P, P_phi_phiT_P, totalPolyLength, totalPolyLength, totalPolyLength);

    // P*phi
    float P_phi[totalPolyLength];
    memset(P_phi, 0, totalPolyLength*sizeof(float));
    mul(P, phi, P_phi, totalPolyLength, totalPolyLength, 1);

    // phi'*P*phi
    float phiT_P_phi[1];
    memset(phiT_P_phi, 0, 1*sizeof(float));
    mul(phiT, P_phi, phiT_P_phi, 1, totalPolyLength, 1);

    // P = P - (P_phi_phiT_P) / (1+phi'*P*phi)
    for(int i = 0; i < totalPolyLength*totalPolyLength; i++)
        *(P + i) = *(P + i) - *(P_phi_phiT_P + i) / (1 + *(phiT_P_phi));
    



/*
 * This will solve if GAMMA is square!
 */
static void solve(float* GAMMA, float* PHI, float* x, float* u, float* r, float lb, float ub, int constraintsON)
    /*
     * Now we are going to solve on the form
     * Ax=b, where b = (R*r-PHI*x) and A = GAMMA and x = U
     */

    /*
     * R_vec = R*r
     */
    float R_vec[horizon*ydim];
    memset(R_vec, 0, horizon*ydim*sizeof(float));
    for(int i = 0; i < horizon*ydim; i++)
        for (int j = 0; j < rdim; j++) 
            *(R_vec + i + j) = *(r + j);
        
        i += rdim-1;
    

    /*
     * PHI_vec = PHI*x
     */
    float PHI_vec[horizon*ydim];
    memset(PHI_vec, 0, horizon * ydim * sizeof(float));
    mul(PHI, x, PHI_vec, horizon*ydim, adim, 1);

    /*
     * Solve now (R_vec - PHI_vec) = GAMMA*U
     * Notice that this is ONLY for Square GAMMA with lower triangular toeplitz matrix e.g SISO case
     * This using Gaussian Elimination backward substitution
     */
    float U[horizon];
    float sum = 0.0;
    memset(U, 0, horizon*sizeof(float));
    for(int i = 0; i < horizon; i++)
        for(int j = 0; j < i; j++)
            sum += *(GAMMA + i*horizon + j) * *(U + j);
        
        float newU = (*(R_vec + i) - *(PHI_vec + i) - sum) / (*(GAMMA + i*horizon + i));
        if(constraintsON == 1)
            if(newU > ub)
                newU = ub;
            if(newU < lb)
                newU = lb;
        
        *(U + i) = newU;
        sum = 0.0;
    
    //print(U, horizon, 1);

    /*
     * Set last U to u
     */
    if(constraintsON == 0)
        *(u + 0) = *(U + horizon - 1);
    else
        *(u + 0) = *(U + 0);
    




/*
 * Lower traingular toeplitz of extended observability matrix
 */
static void CAB(float* GAMMA, float* PHI, const float* A, const float* B, const float* C)
    /*
     * First create the initial C*A^0*B == C*I*B == C*B
     */
    float CB[ydim*rdim];
    memset(CB, 0, ydim*rdim*sizeof(float));
    mul((float*)C, (float*)B, CB, ydim, adim, rdim);

    /*
     * Take the transpose of CB so it will have dimension rdim*ydim instead
     */
    tran(CB, ydim, rdim);

    /*
     * Create the CAB matrix from PHI*B
     */
    float PHIB[horizon*ydim*rdim];
    mul(PHI, (float*) B, PHIB, horizon*ydim, adim, rdim); // CAB = PHI*B
    tran(PHIB, horizon*ydim, rdim);

    /*
     * We insert GAMMA = [CB PHI;
     *                    0  CB PHI;
     *                    0   0  CB PHI;
     *                    0   0   0  CB PHI] from left to right
     */
    for(int i = 0; i < horizon; i++) 
        for(int j = 0; j < rdim; j++) 
            memcpy(GAMMA + horizon*ydim*(i*rdim+j) + ydim*i, CB + ydim*j, ydim*sizeof(float)); // Add CB
            memcpy(GAMMA + horizon*ydim*(i*rdim+j) + ydim*i + ydim, PHIB + horizon*ydim*j, (horizon-i-1)*ydim*sizeof(float)); // Add PHI*B
        
    
    /*
     * Transpose of gamma
     */
    tran(GAMMA, horizon*rdim, horizon*ydim);
    //print(CB, rdim, ydim);
    //print(PHIB, rdim, horizon*ydim);
    //print(GAMMA, horizon*ydim, horizon*rdim);


/*
 * Transpose
 */
static void tran(float* A, int row, int column) 

    float B[row*column];
    float* transpose;
    float* ptr_A = A;

    for (int i = 0; i < row; i++) 
        transpose = &B[i];
        for (int j = 0; j < column; j++) 
            *transpose = *ptr_A;
            ptr_A++;
            transpose += row;
        
    

    // Copy!
    memcpy(A, B, row*column*sizeof(float));



/*
 * [C*A^1; C*A^2; C*A^3; ... ; C*A^horizon] % Extended observability matrix
 */
static void obsv(float* PHI, const float* A, const float* C)

    /*
     * This matrix will A^(i+1) all the time
     */
    float A_pow[adim*adim];
    memset(A_pow, 0, adim * adim * sizeof(float));
    float A_copy[adim*adim];
    memcpy(A_copy, (float*) A, adim * adim * sizeof(float));

    /*
     * Temporary matrix
     */
    float T[ydim*adim];
    memset(T, 0, ydim * adim * sizeof(float));

    /*
     * Regular T = C*A^(1+i)
     */
    mul((float*) C, (float*) A, T, ydim, adim, adim);

    /*
     * Insert temporary T into PHI
     */
    memcpy(PHI, T, ydim*adim*sizeof(float));

    /*
     * Do the rest C*A^(i+1) because we have already done i = 0
     */
    for(int i = 1; i < horizon; i++)
        mul((float*) A, A_copy, A_pow, adim, adim, adim); //  Matrix power A_pow = A*A_copy
        mul((float*) C, A_pow, T, ydim, adim, adim); // T = C*A^(1+i)
        memcpy(PHI + i*ydim*adim, T, ydim*adim*sizeof(float)); // Insert temporary T into PHI
        memcpy(A_copy, A_pow, adim * adim * sizeof(float)); // A_copy <- A_pow
    


/*
 *   x = Ax - KCx + Bu + Ky % Kalman filter
 */
static void kalman(float* x, const float* A, const float* B, float* u, const float* K, float* y, const float* C) 
    /*
     * Compute the vector A_vec = A*x
     */
    float A_vec[adim*1];
    memset(A_vec, 0, adim*sizeof(float));
    mul((float*) A, x, A_vec, adim, adim, 1);

    /*
     * Compute the vector B_vec = B*u
     */
    float B_vec[adim*1];
    memset(B_vec, 0, adim*sizeof(float));
    mul((float*) B, u, B_vec, adim, rdim, 1);

    /*
     * Compute the vector C_vec = C*x
     */
    float C_vec[ydim*1];
    memset(C_vec, 0, ydim*sizeof(float));
    mul((float*) C, x, C_vec, ydim, adim, 1);

    /*
     * Compute the vector KC_vec = K*C_vec
     */
    float KC_vec[adim*1];
    memset(KC_vec, 0, adim*sizeof(float));
    mul((float*) K, C_vec, KC_vec, adim, ydim, 1);

    /*
     * Compute the vector Ky_vec = K*y
     */
    float Ky_vec[adim*1];
    memset(Ky_vec, 0, adim*sizeof(float));
    mul((float*) K, y, Ky_vec, adim, ydim, 1);

    /*
     * Now add x = A_vec - KC_vec + B_vec + Ky_vec
     */
    for(int i = 0; i < adim; i++)
        *(x + i) = *(A_vec + i) - *(KC_vec + i) + *(B_vec + i) + *(Ky_vec + i);
    



/*
 * C = A*B
 */
static void mul(float* A, float* B, float* C, int row_a, int column_a, int column_b) 

    // Data matrix
    float* data_a = A;
    float* data_b = B;

    for (int i = 0; i < row_a; i++) 
        // Then we go through every column of b
        for (int j = 0; j < column_b; j++) 
            data_a = &A[i * column_a];
            data_b = &B[j];

            *C = 0; // Reset
            // And we multiply rows from a with columns of b
            for (int k = 0; k < column_a; k++) 
                *C += *data_a * *data_b;
                data_a++;
                data_b += column_b;
            
            C++; // ;)
        
    


/*
 * Print matrix or vector - Just for error check
 */
static void print(float* A, int row, int column) 
    for (int i = 0; i < row; i++) 
        for (int j = 0; j < column; j++) 
            printf("%0.18f ", *(A++));
        
        printf("\n");
    
    printf("\n");

【问题讨论】：

Misra 并没有说你不能分配内存。您使用 Misra 的 matlab 函数是否经过认证？使用手动内存分配编写符合 ASIL D 的代码通常并不容易 - 但是 - 在这里转储 Matlab 代码以希望得到答案可能会浪费您的时间。向（合同）交付 matlab 模块的人索取证书。如果您是编写模块的人，请询问 matllab。如果他们不能提供该证书，你也不能。

...如果您从事汽车行业，通常有基础技术类型的组织可以提供指导。

【参考方案1】：

免责声明：我在 MATLAB Coder 上工作

有一个configuration setting 告诉 MATLAB Coder 在不使用动态分配的内存的情况下生成代码，或者发出一个错误来告诉你为什么它不能这样做。

cfg = coder.config('lib');
cfg.DynamicMemoryAllocation = 'Off';
codegen -config cfg ...

MATLAB Coder 支持使用固定大小的数组、可变大小的数组和动态分配的数组生成代码。各种生成的签名格式显示在the documentation 中。对于非动态分配的可变大小数组，常见的签名类似于：foo(x_data[100], x_size[2])

是的，对于您在生成代码时指定的硬件，生成的代码通常是可移植的并且独立于 MATLAB。代码生成支持的可用函数和类的完整列表是listed here。在极少数情况下，生成的代码需要依赖于 MATLAB 中的库。这些案例将在文档中列出。 horzcat 和 vertcat 等基本操作生成独立于 MATLAB 的可移植代码。

是的。对于数组输出和具有多个输出的 MATLAB 函数，生成的代码将通过引用返回输出。在某些情况下，当相应的 MATLAB 函数具有 same variable as an input and output 时，它还支持通过引用传递参数：function A = foo(A,B) 调用如下：y = foo(y,z); 可以产生类似 void foo(double A[100], const double B[20]); 的内容，其中 A 是输入和输出。

【讨论】：

太棒了！还有一个问题！ C 代码的优化程度如何？

许多核心计算可选地支持使用高性能库，并且 Embedded Coder 提供了其他硬件特定优化的能力。我建议获取trial 并自己测量。