Analysis of minimal radial basis function network algorithm for real-time identification of nonlinear dynamic systems

Abstract

This paper presents first a performance analysis of the recently developed Minimal Resource Allocating Network (MRAN) algorithm for on-line identification of nonlinear dynamic systems. Using nonlinear time invariant and time varying identification benchmark problems, MRAN's performance is compared with the recently proposed On-line Structural Adaptive Hybrid Learning (ONSAHL) algorithm of Junge and Unbehauen. The results indicate that MRAN realizes networks using fewer hidden neurons than ONSAHL algorithm with better approximation accuracy. Next, methods for improving the run time performance of MRAN for real time identification of the nonlinear systems are developed. An extension to MRAN referred to as the Extended Minimum Resource Allocating Network (EMRAN) which utilizes a winner neuron strategy is highlighted. This modification reduces the computation load for MRAN and leads to considerable reduction in the learning time with only a slight increase in the approximation error. Using the same benchmark problems, the results show that EMRAN is well suited for fast on-line identification of nonlinear plants.

Dynamic Threshold Selection for Sequential Learning in Radial Basis Function Networks

“…Ever since the pruning algorithm in MRAN was introduced, the MRAN algorithm has been successfully applied and furthermore, improvised to attain optimal neuron configurations in the hidden layer as in EMRAN and HMRAN developed by Li et al and Nishida et al in [9], [10] respectively. By removing unnecessary neurons in the hidden layer of the network, minimal computation power is required in the actual implementation of the system.…”

Sequential Adaptive RBF-Fuzzy Variable Structure Control Applied to Robotics Systems

“…If the growing criteria in (17) and (18) are not met, only the network parameters of the nearest node to the current inputs are updated using the extended Kalman filter (EKF) as follows [9] …”

“…To obtain the desired behavior i y responding to the input i x , where i is the sample index, the neural network is trained using a sequential algorith m with a Growing and Pruning strategy (GAP) [9] …”

“…To train the proposed networks, a sequential training algorith m based on Gro wing-Pruning (GAP) strategy and Kalman filter is imp lemented [9]. A similar approach in [12] was applied to control two degrees of freedom robot man ipulator where we ignored the frictions.…”

“…Radial basis function (RBF) neural networks with their approximation capabilit ies [9] are very emergent powerful tools for system identification, so they can estimate any complex nonlinear system parameters even in presence of disturbances [10] [11].…”