# Improved Sliding Mode Finite-Time Synchronization of Chaotic Systems with Unknown Parameters
## 1 Introduction  
The chaos system is a special kind of nonlinear system, and chaos will occur in many aspects. The chaos phenomenon is generally caused by disturbances and the system parameters satisfying certain conditions. Thus, to improve the operation reliability of the system, sometimes this chaos phenomenon should be avoided. Discussions on the relation between the chaos and bifurcation phenomenon, and the non-linear oscillation of the system are very popular. Most scholars study how to ensure the stable operation of the system. This research is also of significance for the above-mentioned chaos control of one class of system in practice. In most cases, the control of chaotic system refers to the synchronization control of the system. Therefore, in recent years, chaotic system synchronization control has attracted significant attention within the fields of mathematics, physics and, engineering science. The research findings on chaotic system synchronization are widely applied in securing communication, power conversion, biological systems, information processing, and chemical reactions [1]. The primary approach to two chaotic systems' synchronization relies on designing an appropriate controller that controls the slave system, making the slave system state asymptotically track the main system state. Numerous control techniques (e.g., in differential dynamics and bifurcation theory) of chaotic systems synchronization have emerged [2]. Specific methods include classical Proportional-Integral-Derivative (PID) control [3], adaptive fuzzy control, adaptive pulseperturbation [4], random Melnikov method [5], negative feedback algorithm [6], and chaotic synchronization based on the ant colony algorithm [7]. [PERSON] et al. [8] used the Melnikov method to study the bifurcation phenomenon of chaotic motion, while [PERSON] [9] utilized it in researching the fractal state of rolling chaotic motion. Path tracking technique was used in [10], where the authors found a nonlinear bifurcation set with six degrees of freedom and obtained the chaotic attractors generated by periodical system multiplication. [PERSON] et al. [11] used the optimization algorithm to explain the phase spectrum's influence on resonance phenomenon development, given the mixed nonlinear model of six degrees of freedom. In early research works, the chaotic system's parameters were commonly assumed to be known in advance. However, in the majority of real-world systems, external natural factors inevitably disturb the chaotic system parameters, thus changing the parameter values. Consequently, the synchronization of chaotic systems' unknown parameters has become an important research direction in recent years. The chaotic systems unknown parameters' synchronization methods include a sliding mode control [12; 13], backstepping design [14], optimum control [15], adaptive control [16], linear balanced feedback control [17], active control [18], pulse control, and fuzzy control [19]. In most cases, the parameters inside the system model are directly selected as unknown parameters, which has certain limitations, because of the parameters outside the system model cannot be identified. The listed studies on the synchronization of unknown parameters in chaotic systems pose no time requirements and guarantee asymptotic stability. In other words, the time approaches infinity until the system synchronization is achieved. However, practical applications require achieving system synchronization within finite time. In addition, the finite-time control approaches were shown to result in better robustness and anti-interference performance. Several researchers realized the chaotic synchronization control using the finite-time control techniques, such as finite-time stochastic method [20], CLF-based method [21], sliding mode control [22], and pure finite-time control method [23]. As mentioned above, the unknown parameters of a chaotic system are usually selected in a system model.