Discrete-Time Zeroing Dynamics With Quadruplicate Error Pattern for Time-Varying Linear Inequality

Abstract

Linear inequality (LI) plays an important role in many fields of science and engineering. Recently, a typical neural dynamics called zeroing dynamics (ZD) has been reported for online solution of time-varying LI (TVLI). On the basis of the previous work, the discrete-time form of the ZD with superior computational property is studied in this paper. Specifically, a Taylor-type difference rule is first presented for the first-order derivative approximation. By utilizing such a difference rule to discrete the previous ZD model, the new discrete-time ZD (DTZD) algorithm is thus established and proposed for TVLI solving. Such an algorithm performs better computational performance than the existing DTZD algorithm. Theoretical results show that the proposed DTZD algorithm has a quadruplicate error pattern on solving the TVLI. Comparative numerical results with two illustrative examples further substantiate the efficacy and superiority of the proposed DTZD algorithm over the existing DTZD algorithm.

Keywords

• Zeroing dynamics (ZD)
• discrete-time algorithm
• time-varying linear inequality (TVLI)
• difference rule
• numerical validation