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

Abstract

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.

Keywords:

• nonlinear inequalities
• time-varying
• Zhang dynamics (ZD)
• discrete-time model
• exponential convergence

2010 AMS Subject Classifications:

• 60-08
• 65C20

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants 61075121, 60935001 and 60775050, and also by the Fundamental Research Funds for the Central Universities of China.