Different energy functions leading to different GDS models illustrated via square roots computing

The dynamic system, i.e., gradient dynamic system (GDS), is theoretically designed by defining a square-based nonnegative or at least lower-bounded error-monitoring function, which is termed the energy function (EF). Such a dynamic system is then cast in the form of a first-order differential equation. To compute scalar square roots, in this paper, different square-based nonnegative EFs, which lead to different GDS models, are proposed and developed as the error-monitoring functions. Towards the final purpose of field programmable gate array (FPGA) and application-specific integrated circuit (ASIC) realization, the MATLAB Simulink modeling and verification of such different GDS models are further investigated for the computation of scalar square roots. The modeling results with two illustrative examples substantiate the efficacy of the proposed GDS models for scalar square roots computing.