TRAJECTORY PRODUCTION WITH THE ADAPTIVE TIME-DELAY NEURAL-NETWORK

The adaptive time-delay neural network (ATNN), a paradigm for training a nonlinear neural network with adaptive time delays, has a rich repe rtoire of capabilities that are characterized in this paper. This netw ork, in which both time delays and weights are adapted, is used to gen erate circular and figure-eight trajectories, to perform signal produc tion, and to learn repetitive spatial motions, Spatiotemporal signal p roduction has the property that initial segments of signals that conta in large amounts of noise can be ''cleaned up'' to result in trained t rajectory motions. Spatiotemporal features are learned as opposed to a point-by-point memorization of the trajectory. Closed-loop, repetitiv e trajectories that are learned result from training the network to pr oduce attractors consistent with those trajectories. Widely varying st arting motions will result in the network being attracted to the repet itive attractor for which it is trained. The network also displays tra ining position invariance, and noise removal when only part of the pat tern is trained. Sampling rate effects versus training speed and perfo rmance were measured. A comparison between the ATNN and related networ ks (BP and the TDNN) is reviewed in an example with successful time se ries prediction of a chaotic series.