ggovind@uceng.UC.EDU (Girish Govind) (07/01/91)
I would like to get some help here about the different approaches of researchers to the control problem. I am familiar with the work done by Narendra, Miller, Jordan, Sutton, Werbos, and Anderson. But there are unanswered questions in my mind about the approach taken by Narendra in his IEEE Trans. on NN, March '90 paper and I am hoping that someone on the net could enlighten me. Basically, other researchers (besides Dr. Narendra) working on the control problem (using the supervised backpropagation learning or reinforcement learning) assume that only the input-output data of the plant or system is available. On the other hand in their 1990 paper Dr. Narendra has assumed that the internal structure of the plant is completely known. Thus the Model Reference Adaptive Control (MRAC) method converts the 'CONTROL PROBLEM' into a 'SYSTEM IDENTIFICATION PROBLEM' using some elementary algebra! In example 11 of their paper they have a plant of the form: y(k+1) = (y(k))/(1 + y(k)^2) + u(k)^3 and for first identifying the plant somehow they assume that the contribution of the two terms above is independently known and thus train two separate networks! How is that? I have read numerous papers on nonlinear system identification and structure detection etc. is not such a simple problem (one can look at the papers by Billings) for nonlinear systems. So, my questions are: 1) Is it commonplace to assume that the structure of the plant is completely known? If one knows the outputs of the individual terms then why can't one assume that the structure of the terms itself are known? That way one would not need a neural network at all! 2) In the above example, after the neural networks were used for identification an inverse model was used that would invert the cubic nonlinearity. Now what would one do if the second term above was u(k)^2 (The inverse is now a one to many mapping) ? I know that by Jordan's approach it would settle to a particular solution but how would one solve it using Dr. Narendra's approach? 2) I have always thought of the control problem as more involved than the system identification problem as one does not have a desired signal at the output of the controller (if one did, would one need a controller at all?) Am I wrong here? Why are the other researchers using a different approach? This is so convenient. Please respond to me by email. I promise to collect all the responses and summarize them here. Girish Govind Mail Location #30 Signal Processing and Computer Vision Group Department of Electrical and Computer Engineering University of Cincinnati Cincinnati, OH 45221-0030 (ggovind@uceng.uc.edu) (ggovind@nest.ece.uc.edu)