Stability Analysis of Neutral Fractional Stochastic Differential Equations Driven by Mixed Brownian Motion and Subfractional Brownian Motion With Applications in the I-Cub Robot

Abstract

Exponential stability is often used to barricade stochastic disturbance in visual trajectory tracking of a robotic system. In this work, a nonlinear mathematical model to deal with the exponential stability of visual trajectory in the I-cub robot is developed. The main contributions of this article are: 1) exponential stability is studied for the first time in the literature for the neutral fractional stochastic differential equations (NFSDEs) driven by mixed Brownian motion (Bm) and subfractional Bm (sub-fBm); 2) existence and stability results are derived based on the Banach contraction principle, semi-group theory, and fractional calculus in stochastic settings; 3) stability results of mixed Bm and sub-fBm are established and applied to avoid dense environment stochastic disturbance in the visual trajectory of the I-cub robot; and 4) stability of sub-fBm is entrusted in the dense environment even in small particles from the shorter length. A weak solution of the proposed result ensures a sufficiently smooth solution of the considered robotic system. The obtained results are new and innovative in the sense that the proposed algorithms have several advantages for gaze shift framed to the I-cub robot, including helping to maintain the fixation of eye movement in the microscopic laboratory. Furthermore, the results are used to enhance the performance of decreasing rendering gaze shift to achieve high-quality visual tracking.