Two New Discrete-Time Neurodynamic Algorithms Applied to Online Future Matrix Inversion With Nonsingular or...

Area of Science:

• Numerical Analysis
• Computational Neuroscience
• Robotics

Background:

• Continuous-time neurodynamic models are essential for solving complex dynamic problems.
• Existing discretization methods may lack precision, especially for time-varying systems.
• Online future matrix inversion (OFMI) is crucial in real-time control and signal processing.

Purpose of the Study:

• To propose a high-precision general discretization formula using six time instants (6ID).
• To develop and investigate novel discrete-time neurodynamic algorithms for OFMI.
• To address both nonsingular and sometimes-singular coefficient matrix scenarios in OFMI.

Main Methods:

• Development of a general six-instant discretization (6ID) formula for first-order derivatives.
• Discretization of continuous-time zeroing neurodynamic and gradient neurodynamic models using the 6ID formula.
• Formulation and analysis of 6ID-type discrete-time zeroing neurodynamic (DTZN) and gradient neurodynamic (DTGN) algorithms for OFMI.

Main Results:

• A specific 6ID formula is derived from the general one.
• The proposed 6ID-type DTZN and DTGN algorithms are shown to be effective for OFMI.
• The algorithms demonstrate robustness in handling both always-nonsingular and sometimes-singular coefficient matrices.

Conclusions:

• The proposed 6ID formula offers high-precision derivative approximation.
• The novel 6ID-type DTZN and DTGN algorithms provide efficient solutions for OFMI.
• These algorithms are validated through numerical examples, including robotic manipulator control, showcasing their practical advantages.