Adaptive Error-Related Zeroing Neurodynamics Models for Handling Temporally-Varying System of Linear Equation and Inequation With Applications

While zeroing neurodynamics (ZN) method stands out in handling various temporally-varying problems, the deficiencies of self-adaptivity and intelligence make ZN models be less mature. Aiming at this point, in this paper we propose three adaptive ZN models, i.e., adaptive error-related ZN (AERZN) model, AERZN with power-sum (AERZN-PS) model, and AERZN with modified sign-bi-power (AERZN-MSBP) model, to solve the more challenging temporally-varying system of linear equation and inequation (TVSLEI). Three models are respectively provided with globally exponential, super-exponential, and finite-time convergence properties, which are theoretically proved via rigorous mathematical deduction. Moreover, numerical comparative experiments are conducted to illustrate the correctness of theoretical analyses, the effectiveness of three models, as well as the superiority of AERZN-MSBP model over AERZN-PS model and AERZN-PS model over AERZN model. Finally, with the aid of the AERZN-PS and AERZN-MSBP models, the path-following tasks about two different types of robot arms (i.e., PUMA560 and four-link robot arms) with physical limits are successfully conducted, verifying the potential feasibility and practicality of the models.