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

Cai, Jianhuang; Feng, Qingshan; Guo, Dongsheng

doi:10.1109/access.2021.3049244

Cited by 1 publication

(7 citation statements)

References 26 publications

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“…Thus, it is proven that the TVLES-SCF-I solution (6) to solve the TVLES problem (1) is effective, of which the solution error is O(τ 3 ). Similar to the above proven process, the TVLES-SCF-II solution (8) to solve the TVLES problem (1) is effective, of which the solution error is O(τ 4 ).…”

Section: Theoretical Analysismentioning

confidence: 99%

“…In this section, some numerical experimental results are shown to substantiate the effectiveness and advantages of the 6) and ( 8) and conventional stability-constraint solutions ( 13) and ( 14) when sampling gap τ = 0.01 s for solving TVLES with sometimes-ill-conditioned and even sometimes-singular matrix. (a) Solution trajectories of TVLES-SCF solution (6). (b) Residual errors of TVLES-SCF solutions ( 6) and ( 8).…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…− sin(0.1(i − j)t k )/(i − j), when i > j sin(0.1it k ) + 3, when i = j cos(0.1(j − i)t k )/(j − i), when i < j and b i (t k ) = cos(t k ), when i is odd sin(0.5t k ), when i is even, (15) where i, j = 1, 2, • • • , 9. First, to substantiate the effectiveness of the proposed solutions, we conduct a numerical experiment in which we employ the TVLES-SCF-I solution (6) and conventional solution (10) to solve the above TVLES problem (15). The sampling gap is set as 0.1 s and the coefficient h = 0.1.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…1, which displays all nine time-varying elements of the vector-form solution x(t k+1 ) generated by the TVLES-SCF-I solution (6) (i.e., blue lines), conventional solution (10) (i.e., green lines) and theoretical solution (i.e., red lines). It can be observed that all solution trajectories generated by the TVLES-SCF-I solution (6) and theoretical path always overlap during the process. Thus, the effectiveness of the TVLES-SCF-I solution (6) to solve the TVLES problem (15) is substantiated.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Linear equation systems are fundamental mathematical problems that are frequently encountered in engineering and scientific fields [1]- [6]. When coefficients in a linear equation system vary over time, the system becomes a time-varying linear equation system (TVLES) [7].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stability-Constraint-Free Solutions to Solve Time-Varying Linear Equation System

Fan

Zhu

et al. 2022

IEEE Access

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Time-varying linear equation systems have been solved by the traditional zeroing neural dynamics approach in recent years. However, this method has to satisfy the stability constraint, which is a very rigorous condition. For this reason, traditional Lagrange-type finite difference formulas fail to lead to effective solutions, and we have to utilize more instants and reduce accuracy so that this condition is satisfied. In this work, we develop a new method of solving a time-varying linear equation system, which is based on theoretical solution decomposition. As a result, the proposed solutions are stability-constraint-free. We do not have to meticulously search effective time-discretization formulas because traditional Lagrange-type formulas are sufficient and especially effective. In addition, the proposed solutions have other advantages. For example, they do not need convergence procedures; they do not have storage requirements for past calculative results; and they are still effective when the sampling gap value is relatively large. Detailed comparisons are presented in this paper. Comparative numerical experiments are also shown to substantiate the effectiveness and advantages of the proposed solutions.

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Section: Theoretical Analysismentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%