Error-minimizing dead zone for basis function networks

Abstract

The incorporation of dead zones in the error signal of basis function networks avoids the networks' overtraining and guarantees the convergence of the normalized least mean square (LMS) algorithm and related algorithms. A new so-called error-minimizing dead zone is presented providing the least a posteriori error out of the set of all convergence assuring dead zones. A general convergence proof is developed for LMS algorithms with dead zones, and the error-minimizing dead zone is derived from the resulting convergence condition. The performance is compared with the performance of classical dead zones.

Control of robots using radial basis function neural networks with dead‐zone

“…Application to discrete time nonlinear systems can be found in 15, 16. We shall adopt the nomenclature proposed by Heiss 17 and refer to this dead‐zone scheme as classical dead zone I . Two problems arise with this scheme.…”

“…The dead‐zone scheme used in this paper is termed error minimizing dead‐zone 17. This dead‐zone, unlike classical dead‐zone I , is rendered continuous by introducing a thin transition layer about the boundary surface of the region in which the weight adaptation is turned off.…”

“…Ioannou and Sun 19 utilize a continuous, but different, dead‐zone technique. Heiss 17 refers to their method as classical dead zone II .…”

“…The analysis presented in Heiss 17 pertains to function approximation and not closed‐loop control. Specifically, he considers the case for which a nonlinear, time‐varying map is to be approximated by a linear combination of basis functions weighted by an unknown vector to be estimated.…”

A Neural Network Assisted Cascade Control System for Air Handling Unit

“…The neural control scheme is capable of compensating for plant nonlinearity and adapting online to degradation in the plant. However, NN training algorithms are sensitive to disturbances and may not be able to obtain an optimal performance without guaranteed stability [8]. In the NN-assisted cascade control system studied in this paper, we use the simultaneous perturbation stochastic approximation-based training algorithm proposed in [9].…”