Noise-Resistant Discrete-Time Neural Dynamics for Computing Time-Dependent Lyapunov Equation

Abstract

Z-type neural dynamics, which is a powerful calculating tool, is widely used to compute various time-dependent problems. Most Z-type neural dynamics models are usually investigated in a noise-free situation. However, noises will inevitably exist in the implementation process of a neural dynamics model. To deal with such an issue, this paper considers a new discrete-time Z-type neural dynamics model, which is analyzed and investigated to calculate the real-time-dependent Lyapunov equation in the form $A^{T}(t)X(t)+X(t)A(t)+C(t)=0$ in different types of noisy circumstances. Related theoretical analyses are provided to illustrate that, the proposed neural dynamics model is intrinsically noise-resistant and has the advantage of high precision in real-time calculation. This model is called the noise-resistant discrete-time Z-type neural dynamics (NRDTZND) model. For comparison, the conventional discrete-time Z-type neural dynamics model is also proposed and used for solving the same time-dependent problem in noisy environments. Finally, three illustrative examples, including a real-life application to the inverse kinematics motion planning of a robot arm, are performed and analyzed to prove the validity and superiority of the proposed NRDTZND model in computing the real-time-dependent Lyapunov equation under various types of noisy situations.