Inverse-Free Discrete ZNN Models Solving for Future Matrix Pseudoinverse via Combination of Extrapolation and ZeaD...

Area of Science:

• Numerical analysis
• Matrix theory
• Robotics

Background:

• The time-varying matrix pseudoinverse (TVMP) is well-studied, but new matrix types like Zhang matrices pose challenges.
• Future matrix pseudoinverse (FMP) problems are critical for engineering applications like redundant manipulators but remain difficult.

Purpose of the Study:

• Design novel discrete zeroing neural network (ZNN) models for computing future matrix pseudoinverses (FMPs).
• Address the computation of FMPs for all full-rank matrices, including Zhang matrices.
• Evaluate the performance of new models against existing methods.

Main Methods:

• Derivation of an inverse-free continuous ZNN model for TVMP.
• Discretization of the continuous ZNN model using Zhang et al. discretization (ZeaD) and equidistant extrapolation formulas.
• Development of two discrete ZNN models for FMP computation with varying truncation errors.

Main Results:

• Numerical experiments demonstrated the superior effectiveness of the two new discrete ZNN models compared to five conventional models.
• The proposed models successfully computed FMPs for full-rank matrices, including Zhang matrices.
• One new model was validated through simulations and physical implementation on robot manipulators.

Conclusions:

• The newly proposed discrete ZNN models offer an effective and preferable approach for computing future matrix pseudoinverses.
• These models are practical for real-world applications, as evidenced by their successful implementation in robotic manipulator systems.