Different Zhang functions leading to different ZD models illustrated via time-varying square roots finding

Zhang dynamics (ZD) has been proved a powerful alternative for solving online time-varying problems. Such a dynamic system is elegantly designed by defining an indefinite error-monitoring function, called Zhang function (ZF). The dynamic system is then cast in the form of a first-order differential equation. In this paper, different ZFs, which lead to different ZD models, are proposed and developed as the error-monitoring functions for time-varying scalar square roots finding (TVSSRF). Towards the final purpose of field programmable gate array (FPGA) and application-specific integrated circuit (ASIC) realization, the MATLAB Simulink modelings and verifications of such different ZD models are further investigated for online solution of time-varying scalar square roots. Both theoretical analysis and modeling results substantiate the efficacy of the proposed ZD models for TVSSRF.