The ball-and-beam problem is a benchmark for testing control algorithms. Zadeh proposed (1994) a twist to the problem, which, he suggested, would require 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 this 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. Our best 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 respond to Zadeh's challenge. We do not claim this neural network control algorithm is the best approach to this problem, nor do we claim it is better than a fuzzy controller. It is instead a contribution to the scientific dialogue about the boundary between the two overlapping disciplines.


Electrical and Computer Engineering

Second Department

Computer Science

Keywords and Phrases

DHP; Kalman Filters; NDEKF Algorithm; Adaptive Critic Design; Approximate Dynamic Programming; Backpropagation; Control Algorithm Testing; Dual Heuristic Programming; Duality (Mathematics); Dynamic Programming; Filtering Theory; Friction; Fuzzy Ball-And-Beam Systems; Fuzzy Control; Fuzzy Logic Controller; Heuristic Programming; Neurocontroller; Neurocontrollers; Node-Decoupled Extended Kalman Filter; Nonlinear Control Systems; Nonuniform Nonlinear Friction; Recurrent Neural Networks; Sticky Beam; Sticky Coating; Truncated Backpropagation; Upper-Level Design

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2000 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 2000