Dünaamiliste süsteemide modelleerimine Identification for control in a non- linear system world Eduard Petlenkov, Automaatikainstituut, 2013

Control Design Nominal Model Regulator © Lennart Ljung

Control Design True System Regulator © Lennart Ljung

Control Design Nominal Model Regulator Model error model © Lennart Ljung

Control Design Nominal Model Regulator Model error model True system © Lennart Ljung

Control Design Nominal Model Regulator Model error model Nominal closed loop system © Lennart Ljung

Model Error Models   = y – y model u  © Lennart Ljung

Identification for Control Identifiction for control is the art and technique to design identification experiments and regulator design methods so that the model error model matches the nominal closed loop system in a suitable way © Lennart Ljung

A Data Set/ nonlinear process Output Input © Lennart Ljung

Feedback Neural Networks. Identification of dynamic systems (1) Eduard Petlenkov, Automaatikainstituut, 2013 External feedback:

11 Eduard Petlenkov, Automaatikainstituut, 2013 Elman’i võrk Internal feedback: where r is the number of neurons on the recurrent layer; Feedback Neural Networks. Identification of dynamic systems (2)

Identification with ANNs (1) Eduard Petlenkov, Automaatikainstituut, 2013 is the input of the system is the output of the system is the output of the model

Identification with ANNs (2) Eduard Petlenkov, Automaatikainstituut, 2013

Identification with ANNs (3) Eduard Petlenkov, Automaatikainstituut, Getting experimental training data: Input signal is given to the system and the corresponding output reaction is measured. Obtained input-output data is used to train a NN-based model; 2. Choosing NN’s structure: number of inputs, outputs, hidden layers, neurons; activation functions; 3. Choosing initial weighting coefficients (usually random).

Identification with ANNs (3) Eduard Petlenkov, Automaatikainstituut, Calculation of NN outputs corresponding to the training input set; 5. Comparison of outputs with reference outputs from the training set – calculation of model error; 6. Calculation of uptadeted weighting coefficients using selected training algorithm; Repeat steps 4-6 untill a predefined number of iterations (epochs) is reached or until the desire accuracy is achieved.

Dünaamiliste süsteemide juhtimine tehisnärvivõrkudega NN-based control of dynamic systems Eduard Petlenkov, Automaatikainstituut, 2013

Predictive Control

Inverse model Eduard Petlenkov, Automaatikainstituut, 2013

Inverse model Eduard Petlenkov, Automaatikainstituut, 2013

Inverse model based control Here Eduard Petlenkov, Automaatikainstituut, 2013

Adaptive inverse model based control Eduard Petlenkov, Automaatikainstituut, 2013

Adaptive Predictive Control

Mustrite tuvastamine ja klassifitseerimine tehisnärvivõrkudega NN-based pattern recognition and classification Eduard Petlenkov, Automaatikainstituut, 2013

24 Self-organizing networks Self-orgamizing network is capable of adjusting its parameters on the basis of inputs and chosen optimization criteria. It doesn’t have any reference outputs Kohonen map Eduard Petlenkov, Automaatikainstituut, 2013

Näide 1: Character recognition(1)

Näide 1: Character recognition (2)

Näide 2: number recognition

Etalon_1=[ ]'; Etalon_2=[ ]'; Etalon_3=[ ]'; Etalon_4=[ ]'; Etalon_5=[ ]'; Etalon_6=[ ]'; Etalon_7=[ ]'; Etalon_8=[ ]'; Etalon_9=[ ]'; Etalon_0=[ ]'; net = newff(minmax(P),[25 10],{'logsig' 'logsig'},'traingda') net.trainParam.goal = 0 net.trainParam.epochs=10000 Näide 2: Number recognition– NN structure

Näide 2: Number recognition– testing on the training set

Näide 2: Number recognition– testing on the validation set ,06680,00060,00660,00260,00890,01520,00340,00000,00500, ,00190,15480,00140,00050,01080,00050,00440,00010,00000, ,01450,00020,14950,00010,00320,03430,00810,00010,00390, ,00030,00260,00010,01020,00040,00000,00140,00470,00080, ,00000,00030,0000 0,01770, ,00010,00130,00200,00020,00050,06110,00020,00000,00650, ,00020,00000,00020,00030,00010,00000,01540,00090, ,10300,0000 0,58680, ,0002 0,00030,00080,05800,00560,00060,00100,27990, ,0000 0,0186

Databases for benchmark problems  MNIST database of handwritten digits  26x26px  labeled images and test images  Semeion handwritten digits from around 80 persons  16x16px