Time delay Chebyshev functional link artificial neural network

Abstract In real applications, a time delay in the parameter update of the neural network is sometimes required. In this paper, motivated by the Chebyshev functional link artificial neural network (CFLANN), a new structure based on the time delay adaptation is developed for nonlinear system identification. Particularly, we present a new CFLANN-delayed recursive least square (CFLANN-DRLS), as an online learning algorithm for parameter adaptation in CFLANN. The CFLANN-DRLS algorithm exploits the time delayed error signal with the gain vector delayed by D cycles to form the weight increment term, which provides potential implementation in the filter with pipelined structure. However, it suffers from the instability problems under imperfect network delay estimate. To overcome this problem, we further propose a modified CFLANN-DRLS (CFLANN-MDRLS) algorithm by including a compensation term to the error signal. We analyze the stability and convergence of the proposed algorithm. Simulations in nonlinear system identification contexts reveal that the newly proposed CFLANN-MDRLS algorithm can effectively compensate the time delay of system and it is even superior to the algorithm without delay in some cases.