Different modified zeroing neural dynamics with inherent tolerance to noises for time-varying reciprocal problems: A control-theoretic approach.

With reciprocal problem widely arising in various scientific computation and engineering fields in recent decades, it is always assumed that the computing process is free of measurement noises. However, time is precious for time-varying reciprocal problem, which is considered to be an important operation in a floating-point divider in practice and optimization. Therefore, mathematical models with inherent noise tolerance are needed to compute reciprocal problem in real time. In this paper, different modified zeroing neural dynamics models are proposed, analyzed and investigated for the solution of time-varying reciprocal problem with inherent tolerance to noises. Moreover, theoretical analyses show that the modified zeroing neural dynamics globally/exponentially converge to the exact solution of the time-varying reciprocal problem with measurement noises. Furthermore, the zeroing neural dynamic models with different activation functions are employed for comparison with the modified zeroing neural dynamic model. Finally, some numerical simulations are reported and analyzed to substantiate the feasibility and superiority of the developed zeroing neural dynamic for time-varying reciprocal problem with inherent tolerance to noises. This paper develops a systematic approach on exploiting control techniques to design zeroing neural dynamic models for robustly and accurately solving time-varying reciprocal problems.