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Description:
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The ball -and -beam problem is a benchmark for testing new control algorithms . In the Worid Congress On Neural Networks , 1994 , Prof Lotfi Zadeh proposed a more difficult version which he claimed required a fuzzy logic controller . This experiment uses a beam , partially covered with a sticky substance , increasing the difficulty of predicting the ball's motion . We complicated the problem even more by not using any information concerning the ball's velocity . Although it is common to use the first differences of the ball's consecutive positions as a measure of velocity and explicit input to the controller , we preferred to exploit recurrent neural networks inputting only consecutive positions instead . We have used truncated backpropagation through time with the Node -Decoupled Extended Kalman Filter (NDEKF ) algorithm to update the weights in the networks . The neurocontroller uses a form of approximate dynamic programming called an adaptive critic design . A hierarchy of such designs exists . Our system uses Dual Heuristic Programming (DHP ) , an upper -level design . To our best knowledge , our results are the first use of DHP to control a physical system . It is also the first system we know of to meet Zadeh's challenge . |