PROGRAM LIST. 1* Backpropagation Neuro-Control*1 #include <stdio.h> #include <math.h> #include <string.h> #include <stdlib.h>

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Nathaniel Roberts
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1 PROGRAM LIST 1* This program can be used to train a neural network model with *1 1* one hidden layer to learn the inverse dynamics of the plant *1 1* Once trained the neural network model can *1 1* be used as a direct controller to the plant *1 1* The plant input-output characteristics must first be *1 1* generated and kept in a file called in-out.dat *1 1* This program runs under the Borland C++ Version 3.1 Environment *1 1* Backpropagation Neuro-Control*1 #include <stdio.h> #include <math.h> #include <string.h> #include <stdlib.h> 1* Declare the total number of nodes and pattern *1 #define No_oCInpuCUnits 3 1* No. of nodes of input layer i *1 #define No_oCHidden_Units 15 1* No. of nodes of hidden layer j *1 #define No_oCOutpuCUnits 1 1* No. of node s of output layer k *1 #define No_oCPatterns 8 1* Total no. of patterns p *1 #define Eta #define Alpha #define Beta #define ErrorFunc #define W min #define Wmax #define No_oCData * The learning rate * * Momentum constant * * Acceleration constant * * Maximum error allowed * * For use in random function * * to generate random values *1 101 I*Total number of plant input-output data *1 1* Functions *1 #define f(x) #define rnd( ) (1/(1 +exp( -(x)))) 1* Sigmoid function where x = net + bias*1 «float)rand( )/Ox7fff * (Wmax-Wmin) + Wmin) 1* This function is used to generate random values *1 1* Declare outputs, weights, and biases *1 float 01 [No_oCPatterns][No_oCInpuCUnits]; 1* Output of Input layer i *1 float 02[No_oCHidden_Units]; 1* Output of Hidden laye r j *1 float 03 [No_oCOutpucUnits]; 1* Output of Output layer k *1 float t[no_ocpatterns] [No_oCOutpucUnits];

2 246 Neuro-Control and Its Applications 1* Desired Output or target value *1 float w21[no_ochidden_units][no_oclnpucunits]; 1* Weights from i to j layer *1 float dw21 [No_oCHidden_Units][No_oClnpuCUnits][3]; 1* Change in the above weights *1 float w32[no_ocoutpucunits] [No_oCHidden_Units]; 1* Weights fromj to k layer *1 float dw32[no_ocoutpucunits] [No_oCHidden_Units][3]; 1* Change in the above weights *1 float bias2[no_ochidden_units]; 1* Bias to nodes in layer j (thetaj) *1 float dbias2[no_ochidden_units][3]; 1* Change in the above bias j *1 float bias3[no_ocoutpucunits]; 1* Bias to nodes in layer k (theta k) *1 float dbias3[no_ocoutpucunits][3]; 1* Change in the above bias j *1 float increase, erorfunc, er[3], u[no_ocdata], y[no_ocdata]; float Errorfunction int count, iterations; 1* Main Program *1 void main 0 I*begin main program*1 unsigned long i,j,k; static float errorfunc; void propagation(int); void back_propagation(int); void forward(int); void void read_input-outpucdata( ); initialize( ); void save_weight( ); void NN_inputs(); initialize( ); read_input-output_data( ); increase=o.o; for (errorfunc = 0.0, i=o; kno_ocpattems;i++) forward(i); for(j=o; j<no_ocoutpucunits; j++) errorfunc += pow(t[i][j] - o3[j], 2.0); printf("error Function is: %.5f\n", errorfunc); 1* error is the square oftarget - output *1 } errorfunc 1= 2; erorfunc=errorfunc;

3 Program List 247 printf("error Value is : %.3t\n", errorfunc); 1* print the error value *1 er[o]=errorfunc; fore i=o; errorfunc>errorfunc;) fore j=o; j<no_ocpatterns; j++ ) propagation(j); back_propagation(j); } fore errorfunc=o.o, j=o; j<no_ocpatterns;j++) forward(j); for(k=o; k<no_ocoutpucunits; k++) errorfunc += pow(t[j][k] - o3[k], 2.0); iterations= 1; ++i; increase+=(float)iterations; errorfunc 1= 2; erorfunc=errorfunc; printf(" 1= %f ",increase); printf("e = %.7t\n", errorfunc); er[1 ]=er[o]; er[o]=errorfunc; if( er[ 1 ]<er[o))break; }; printf("\o After Learning \0"); fore i=o; i<no_ocpatterns; i++) forward(i); save_ weighto; 1* To save tbe adapted weights in a data file *1 void save_weighto int I,J; FILE *fp; fp = fopen("weight.dat","w"); 1* To save the weights in layer j *1 fore i=o; i<no_ochidden_units; i++) fore j=o; j<no_ocinpucunits; j++) fprintf(fp, II %t\n",w21 [i][j)); fprintf(fp, "%t\n",bias2[i)); 1* To save tbe weights in layer k *1 fore i=o; i<no_ocoutpucunits; i++)

4 248 Neuro-Control and Its Applications for( j=o; j<no_ochidden_ Units; j++) fprintf(fp, "%t\n", w32[i] [j]); fprintf(fp, "%t\n",bias3[i]); } fc1ose(fp); 1* Procedure Propagation *1 1* To propagate the network forward */ void propagation(int p) int i,j; float net; for( i=o; i<no_ochidden_units; 1* layer j */ i++) for( net=o.o, j=o; j<no_oclnpucunits; j++) net += w21[i][j] * 01 [p][j]; 02[i] = f(net+bias2[i]); 1* sigmoid function *1 for( i=o; kno_ocoutpucunits; 1* layer k *1 i++) for( net=o.o, j=o; j<no_ochidden_ Units; j++) net += w32[i][j] * 02[j]; 03[i] = (net+bias3[i]); 1* output of NN not bounded by sigmoid function *1 1* Procedure Back Propagation *1 1* To backpropagate error through the network *1 void back_propagation (int p) int i,j; float d2[no_ochidden_units]; /* d2 is deltaj */ float d3[no_ocoutput_units]; 1* d3 is delta k *1 float sum; /* sum is add. of delta k * Wkj */ 1* to calculate delta k */ for( i=o; i < No_oCOutpuCUnits; i++ ) d3[i] = (t[p][i] - 03[i]); for( i=o; i<no_ochidden_units; i++) 1* to calculate the weights, w and dw, between layer j and k */ for(sum=o.o, j=o; j<no_ocoutpucunits; j++)

5 Program List 249 dw32[j][i][o] = Eta * d3[j] * 02[i] + Alpha * dw32[j][i][1] + Beta * dw32[j][i][2]; w32[j][i] += dw32[j][i][o]; sum += d3[j] * w32[j][i]; dw32[j][i][2] = dw32[j][i][1]; dw32[j][i][l] = dw32[j][i][o]; 1* to calculate delta j *1 d2[i] = 02[i] * (1-02[i]) * sum; 1* to calculate bias k *1 for( i=o; kno_ocoutpucunits; i++) dbias3[i][o] = Eta * d3[i] + Alpha * dbias3[i][l] + Beta * dbias3[i][2]; bias3[i] += dbias3[i][o]; dbias3[i][2] = dbias3[i][i]; dbias3[i][l] = dbias3[i][o]; 1* to calculate the weights, w and dw, between layer j and i *1 for( i=o; kno_ocinpucunits; i++) for( j=o; j<no_ochidden_units; j++ ) dw21 [j][i][o] = Eta * d2[j] * 01 [p][i] + Alpha * dw21[j][i][l] + Beta * dw21 [j][i][2]; w21 [j][i] += dw21 [j][i][o]; dw21[j][i][2] = dw21 [j][i][i]; dw21[j][i][1] = dw21[j][i][o]; 1* to calculate bias j *1 for (i=o; i<no_ochidden_units; i++) dbias2[i][o] = Eta * d2[i] + Alpha * dbias2[i][1] + Beta * dbias2[i][2]; bias2[i] += dbias2[i][o]; dbias2[i][2] = dbias2[i][1]; dbias2[i][1] = dbias2[i][o]; 1* Procedure to read input-output characteristics of systems *1 void read_input-outpucdata( ) int j,k; FILE *file; file = fopen("in-out.dat","r");

6 250 Neuro-Control and Its Applications 1* this file must be generated which consists of plant input-output characteristics *1 } for(j=o; j < No_oCData; j++) fscanf(file,"%f %f\n",&u[j],&y[j]); for(j=o; j < No_oCData; j++) printf("u[%d]=%f y[%d]=%f\n",j,u[j],j,y[j]); fclose(file ); 1* Procedure to equate NN inputs *1 void NN_inputsO 1* to select the patterns over entire input-output plant characteristics *1 int i, j, k; for(i=o,j=o; j < No_oCPatterns; j++) for(k=o; k <No_oCOutput_Units; k++) t[j][k]=u[i+2]; for(j=o; j < No_oCPatterns; j++) for(k=o; k <No_oCOutput_Units; k++) printf("t[%d][%d]=%f\n", j, k, t[j][k]); for(i=o, j=o; j < No_oCPatterns; j++) I*example for 3 NN input vectors *1 01 [j][0]=y[i+2]; 01 [j][i]=y[i+ 1]; 01 [j][2]=y[i]; for(j=o; j < No_oCPatterns; j++) for(k=o; k <No_oCInpuCUnits; k++) printf(" 1 [%d][%d]=%f\n",j,k,o 1 [j][k]); 1* Procedure forward*1 void forward(int p) int i; printf("\t%d ->", p+ 1); propagation(p ); for( i=o; kno_ocoutpucunits; i++)

7 Program List 251 printf (" o3[%d]=%2.5tm",p+ 1, o3[i]); 1* Procedure Initialize *1 1* To randomly initialize the weights *1 void initialize( ) int i,j; 1* To initialize the weights between layer j and i */ for (i=o; kno_ochidden_units; i++) for( j=o; j<no_ocinpuc Units; j++) w21[i][j] = mdo; bias2[i] = 1.0; 1* To initialize the weights between layer k and j *1 for (i=o; i<no_ocoutpucunits; i++) for( j=o; j<no_ochidden_units; j++) w32[i][j] = mdo; bias3[i] = 1.0; }

8 INDEX adaptive control , 82 adaptive critic ARMA model associative memory auto-tuning... 30, 77 axon backpropagation algorithm ,87,90-92,94,96,99,103,112,116, 117, 124, 166, 174, 176 backpropagation-through-time... 94, 95, 161 Boltzmann machine CARMA model CARIMA model... 34, 63 CASSIS... 1,3 certainty equivalent competitive learning control horizon cybernetics dendrites... 7, 8 derivative gain derivative time... 35, 152,210,211 direct inverse control/model... 89, 91, 108, 114, , distributed memory... 2 disturbance... 30, 39, 40, 63 electric vehicle , ,239 extended least squares feedback-error learning... 92,93, furnace , fuzzy associative memories fuzzy logic control , , fuzzy sets Gaussian noise generalized learning... 91, 92

9 254 Neuro-Control and Its Applications generalized minimum variance control generalized predictive control , Hopfield network INSPEC... 1,2 integral gain integral time , 187,210,211,214,215 intelligent control... 5 intelligent systems... 1, 2 inverted pendulum , Kohonen feature map learning machine... 12,13 learning rate... 17, 21, 24, 25,129, 142, 163, 179,213,225 least squares estimation , 56, 57, 66 load disturbances... 63, , 195, local minimum... 17,22-23 long range prediction , 79 maximum costing McCulloch-Pitts neuron m~~bership f~nctions... 69,70,71-73, 184, 185, 194, 199 InlnlmUm costing minimal order observer minimum variance control model reduction momentum term... 21, 24, 25, 129, 136,225 multivariable self-tuning PID control neuro-emulator ,95, , 112, 116, 136, 157, , 179,226 nonlinear observer , non-minimum phase... 38, 39 on-line learning , , , optimal control optimum prediction... 41, 54 overfitting parallel architecture... 2 parallel neuro-control... 95, parameter estimation ,37,56-57, 78 parameterization parameter variations , 191, 221 perceptron... 13, 14 PI, PID control , 29-31, 34-36, 86, 152, , ,221, pole-placement , 77

10 Index 255 predicted output error proportional gain Purkinje cell...,... 7,8 receding horizon control... 33,62 saturation... 35, 43 self-tuning control... 31,32,36-40 self-tuning neuro-control... 95, self-tuning PIIPID control... 32, self-tuning PID-type neuro-control , 208, series neuro-control... 95, sigmoid... 13,23,88,103, 112, 129, 137, 194,218 specialized inverse mapping/learning... 92, 99, 115 stability... 32,39,62,63, 172 steady-state error... 32,44 step-wise disturbance steepest descent , 100, 112, 114, 136, 140, 154 soma... 7 synapse... 7, 8 supervised control... 89,90 time-delay ,47,62-63,96,97,103,105,108,136,174, 177, ,237 UD factorization Von Neumann computers... 1 water bath , 130, , ,239

Supervised Learning in Neural Networks (Part 2)

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