Different-Value Parameters (DVP) Based Zhang Equivalency (ZE) Generalized from Equal-Value Parameters (EVP) Situation with Mechanical Arm Application

Equivalency is a prevalent concept as well as approach for general problems solving in both academia and industry, and the Zhang neuronet dynamics (ZND) based Zhang equivalency (ZE) is an important equivalent method for time-variant problems solving. In this paper, the first-order and higher-order formulas for equal-value parameters based Zhang equivalency of the equation kind (EVP-ZE-EK) are introduced. Subsequently, the first-order through fourth-order formulas for the differentvalue parameters based Zhang equivalency of equation kind (DVP-ZE-EK) are derived, accompanied by the general formula and its proof. Following this, the equal-value parameters based Zhang equivalency of inequation kind (EVP-ZE-IK) are introduced. Then, the general formula for the different-value parameters based Zhang equivalency of inequation kind (DVP-ZE-IK) is proposed. Utilizing the ZND formulas mentioned above, simulations concerning the minimum motion planning and control (MMPC) scheme for a mechanical arm are conducted, verifying the great performance of ZE with different design parameters.