Saturation Function-Based Finite-Time Synchronization Control for Fractional-Order Coupled Neural Networks

Abstract

In the existing research on finite-time synchronization (FTS) control for fractional-order coupled neural networks (FOCNNs), signum function plays a crucial role in controller design. The discontinuity of the signum function causes the chattering phenomenon to worsen the performance of controlled system. In this paper, a saturation function is utilized instead of signum function in controller design, overcoming the shortcomings of previous control schemes. Due to the introduction of the saturation function, the system exhibits different dynamic behaviors within and outside the boundary of the saturation function. To further analyze this effect, the two-stage fractional-order nonlinear differential inequalities (TFNDIs) are established, which provides an effective tool for handling saturation function-based FTS control for FOCNNs. At last, the validity of proposed theoretical results is demonstrated through numerical simulations, which show that the chattering has been significantly suppressed.Note to Practitioners—The FTS problems have practical applications in control and engineering, such as multi-robot collaboration, microgrid synchronization and satellite formation flight, etc. However, there is a fact that signum function may cause chattering phenomenon in finite-time control, which makes it difficult to implement in the engineering application of high precision systems. In this paper, a saturation function-based finite-time control scheme has been constructed for FOCNNs to suppress the chattering, but it is difficult to apply the stability method based on integer-order systems directly to fractional-order ones. Therefore, we propose a new TFNDIs method, and give a rigorous proof for FTS. The superiority of proposed method has been demonstrated in the numerical example.