An Arbitrarily Predefined-Time Convergent RNN for Dynamic LMVE With Its Applications in UR3 Robotic Arm Control and...

Area of Science:

• * Control Systems Engineering
• * Computational Neuroscience
• * Robotics and Automation

Background:

• * Recurrent neural networks (RNNs), particularly Zeroing Neural Networks (ZNNs), excel at solving time-varying linear matrix-vector equations.
• * Existing ZNNs with predefined-time convergence (PTC) require complex parameter tuning for convergence time, posing challenges in practical applications.

Purpose of the Study:

• * To introduce a novel arbitrarily predefined-time convergent RNN (APTC-RNN) that eliminates the need for parameter adjustments to set convergence time.
• * To develop an APTC-RNN utilizing a new nonlinear piecewise activation function (NPAF) for enhanced efficiency and robustness.

Main Methods:

• * Design of a novel arbitrarily predefined-time convergent RNN (APTC-RNN) incorporating a nonlinear piecewise activation function (NPAF).
• * Rigorous theoretical analysis and mathematical derivation to prove the stability and arbitrarily predefined-time convergence (APTC) capabilities.
• * Numerical simulations comparing APTC-RNN performance against existing state-of-the-art RNNs.

Main Results:

• * The proposed APTC-RNN achieves arbitrarily predefined-time convergence (APTC) without requiring explicit upper bound parameter tuning.
• * APTC-RNN demonstrates superior convergence speed and accuracy compared to three benchmark RNNs.
• * The NPAF results in reduced computational cost and faster computation times.

Conclusions:

• * The novel APTC-RNN with NPAF provides a robust and efficient solution for solving time-varying linear matrix-vector equations with arbitrary predefined convergence times.
• * The model's practicality is validated through successful application to UR3 robotic arm control and multiagent systems.
• * This advancement offers significant potential for real-time control applications in robotics and complex systems.