A new variant of the Zhang neural network for solving online time-varying linear inequalities

Abstract

Since March 2001, a special class of recurrent neural networks termed the Zhang neural network (ZNN) has been proposed by Zhang and co-workers for solving online a rich repertoire of time-varying problems. By extending Zhang et al.'s design formula (or say, the ZNN design formula), a (new) variant of the ZNN design formula is proposed and investigated in this paper, which is also based on a matrix/vector-valued indefinite error function. In addition, by employing such a novel design formula, a new variant of the ZNN (NVZNN) is proposed, developed and investigated for online solution of time-varying linear inequalities (LIs). The resultant NVZNN models are depicted in implicit dynamics and methodologically exploit the time-derivative information of time-varying coefficients.Computer simulation results further demonstrate the novelty, efficacy and superiority of the proposed NVZNN models for solving online time-varying LIs.

Zhang neuronet solving complex-valued time-varying linear inequalities

“…By contrast, from Fig. 6(b), we can see that the energy function 0"(t) synthesized by GN model (7) always oscillates. This also means that the solution via (7) does not guarantee the convergence to the time-varying theoretical-solution set of (8), even if the initial state v(O) is inside Q 2 (0) .…”

“…More importantly, these comparative results show the great superiority of ZN model (6) for CVTVLI solving, as compared to GN model (7).…”

“…Case 1: in itial state is outside the in itial solution set If initial state v(O) is outside the initial solution set Q2(O) of (8), by applying ZN model (6) and GN model (7) with y= 10 to solving (8), the corresponding dynamic performance of state vector v(t) is shown in Fig. 2.…”

“…For illustration and comparison, both ZN model (6) and GN model (7) are exploited for online solution of (8). Consid ering that different initial states of the proposed ZN model result in different performance, we discuss the following two cases.…”

Common nature of learning between BP-type and Hopfield-type neural networks

“…Nowadays, the BPNN is one of the most widely used neural-network models in the computational-intelligence research and engineering fields [13][14][15][21][22][23][24][25][26][27][28][29]. Thus, lots of Hopfield-type neural networks (HNNs) have been proposed, developed and investigated [4,5,10,[15][16][17][30][31][32][33], e.g., the one shown in the right of Fig. In [26], a BPNN improved by genetic algorithm (GA) was established by Zhang et al to model the relation between welding appearance and the characteristics of the molten-pool-shadows.…”