1. Neural Network Based Control Dan Simon Cleveland State University 1

2. Neural Control Architectures 1.Inverse model approach 2.Direct control (derivative-free training) 3.Reference control learning 4.Direct model reference adaptive control 5.Indirect model reference adaptive control 6.Fixed stabilizing control 2

3. Inverse Model Approach Two-step approach: 1.Train a neural dynamic system model 2.Train an inverse model to be the controller First we train a neural network to model the dynamic system. 3 Input  + System Neural Model Error Learning Step 1

4. Inverse Model Approach Two neural nets in series  one neural network Backprop: Compute derivative of error w/r to controller weights Backprop: Change controller weights to minimize tracking error Although we backpropagate derivatives through the neural model, we do not modify the weights of the neural model 4 ErrorReference  + Neural Model Neural Controller Learning Step 2

5. Direct Control Derivative-free training to minimize tracking error e 5 e Reference  + System Neural Controller Learning

6. Reference Control Learning The ANN learns to mimic the optimal controller. Then the ANN can replace the optimal controller. 6 We already have an optimal controller, so why would we want to train the ANN? Because ANN’s often have the built- in ability to generalize. So the ANN may be more robust than the optimal controller. +  e Ref. + System Neural Controller Optimal Controller  Learning

7. Direct Model Reference Adaptive Control Use derivative-free optimization to adjust the controller parameters so the closed loop system behaves like the model (desired rise time, overshoot, etc.) 7 +  e Ref. + System Model Reference Neural Controller  Learning

8. Indirect Model Reference Adaptive Control System: y k +a 1 y k  1 +…+a n y k  n = b 1 u k  1 +…+b m u k  m 8 System structure is given. ANN estimates parameters. Parameters used in controller. u +  e Ref. + System ANN Model and System ID Standard Controller  y Learning

9. Indirect Model Reference Adaptive Control ANN Model and System ID: 9 +  uk1…ukmyk1…yknuk1…ukmyk1…ykn + ykyk Weight adjustment … …

10. e Fixed Stabilizing Control The standard controller stabilizes the system The ANN (inverse model) adjusts its weights until the standard controller output is zero, which means that tracking error e = 0. The ANN gradually “takes over” the control function. Reference  + System Inverse Model Standard Controller + 10 Learning

11. References M. Hagan and H. Demuth, Neural Networks for Control K. Astrom and B. Wittenmark, Adaptive Control W. Zhang, System Identification Based on Generalized ADALINE Neural Network B. Kosko, Neural Networks and Fuzzy Systems 11