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Solving time-varying nonlinear inequalities using continuous and discrete-time Zhang dynamics

A special kind of neural dynamics, termed Zhang dynamics (ZD), is proposed, generalized and investigated for the online solution of time-varying scalar-valued nonlinear inequalities by following Zhang et al.’s design method. The continuous-time ZD (CTZD) model based on an exponent-type design formula can be guaranteed to exponentially converge to the time-varying solution set of the problem in an error-free manner. For potential hardware implementation on digital circuits, the corresponding discrete-time ZD (DTZD) model is generated through the well-known Euler forward difference rule. Newton-type algorithm is also developed for comparison purposes. In addition, the simplified CTZD (S-CTZD) and DTZD (S-DTZD) models are developed for solving static scalar-valued nonlinear inequalities. Numerical simulative examples further demonstrate and verify the efficacy of the ZD models for solving time-varying and static scalar-valued nonlinear inequalities. Besides, the DTZD model possesses the lower complexity and higher accuracy, as compared with the Newton-type algorithm.