From Euclid division of constant integers to Zhang division of time-varying variables

A novel complex varying‐parameter finite‐time zeroing neural network (VPFTZNN) for finding a solution to the time‐dependent division problem is introduced. A comparative study in relation to the zeroing neural network (ZNN) and finite‐time zeroing neural network (FTZNN) is established in terms of the error function and the convergence speed. The error graphs of the VPFTZNN design show promising results and perform better than corresponding ZNN and FTZNN graphs. The proposed dynamical systems are suitable tools for overcoming the division by zero difficulty, which appears in the time‐varying division. An application of the introduced VPFTZNN model in an output tracking control time‐varying linear system is demonstrated.

show abstract

“…Example Consider the following TV complex division from Ref. 43 that does not have the DBZ issue:

x false(t false) = \frac{\sin (2 t) + i \cos (3 t)}{\cos (4 t) + i \sin (5 t)} .

In Figure 4A and B, we compare the theoretical solution with the graphs generated by applying the VPFTZNN model () with the parameters

b = a_{1} = a_{2} = 1

q = 1, p = 2

γ = 10

, and

x (0) = 1

. Specifically, Figure 4A presents the real part of the theoretical solution and the real part of the VPFTZNN solution, while Fig.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The evolution from the Euclidean division of constant integers to the Zhang division of TV variables was discussed in Ref. 43. Four different Zhangian error function and induced ZNN models for solving the TV division problem were proposed in Refs.…”

Section: Introductionmentioning

confidence: 99%