# Nonlinear Nonsingular Fast Terminal Sliding Mode Control Using Deep Deterministic Policy Gradient
## 1 Introduction  
In recent years, with the development of industrial robots, nonlinear, external interference, a variety of uncertainty problems appear, and the performance requirements of the control system are more and more strict. At present, there are many control methods of general nonlinear systems--e.g., adaptive control, fuzzy control, neural network control, sliding mode control (SMC) [1, 2, 3, 4], etc. Among them, in the dynamic process, sliding mode control (SMC) is subject to the continuous changes of the system according to the current state of the system, which forces the system to move according to the state trajectory of the predetermined sliding mode, the hypersurface in state space is defined as sliding surface [5], which has strong robustness to the external interference and uncertainty of the nonlinear system [6, 7]. Therefore, SMC is usually used in the control system of industrial robots and manipulators [8, 9, 10, 11]. However, the traditional sliding mode variable structure controls have some disadvantages, such as singularity, uncertain convergence time,and the error is difficult to converge on 0. When the state trajectory reaches the sliding surface, it is difficult to slide strictly into the sliding surface to the equilibrium point, it passes back and forth on both sides of the sliding surface, which is called chattering [5; 12], and it needs an accurate dynamic model for the control object. To solve these problems, some research effects propose a series of solutions to eliminate the uncertainty, chatter, and error of the system as much as possible [13; 14; 15; 16; 17; 18; 19; 20; 21]. For the uncertain dynamic model, neural network [13; 14; 15], fuzzy logic system [16; 17; 18], RBF [19; 20] are used to approach the uncertainty infinitely. In [21; 22], the TSMC is introduced, and the nonlinear function is led into the sliding surface to construct the terminal sliding surface, so that the sliding surface's tracking error converges on 0 in finite time T. However, the convergence speed of TSMC is slow, and the singularity still exists. Therefore, the authors of [23; 24] proposed fast terminal sliding mode control (FTSMC) to solve the convergence rate problem, while [25; 26] proposed NTSMC to solve the singularity problem. On these bases, the authors of [9; 27] proposed nonsingular fast terminal sliding mode control (NFTSMC), which overcomes the single problem that [21; 22; 23; 24; 25; 26] proposed a solution only for one of the shortcomings of SMC. However, the above TSMC, FTSMC and NFFTSMC have not eliminated the chattering of the system. Therefore, some scholars proposed global terminal sliding mode control technology [24; 28]. The control law is continuous and does not contain switching term (control transformation parameter) [5; 12], so the chattering of the system is eliminated, but the tracking accuracy is less precise. Deep reinforcement learning has been developed rapidly and applied to the field of control in recent years. For example, in [29; 30] the authors applied the reinforcement learning neural network algorithm to the control of flexible manipulator and multi-body system with unknown dynamic model, inspired by [29; 30], this paper combined deep reinforcement learning algorithm with SMC, proposed DDPG-NNFTSMC. It had the following characteristics:  
* It is proved that NNFTSMC has the characteristics of nonsingularity and finite time convergence by mathematical derivation, and the robustness and stability of the system are verified by Lyapunov theorem;
* DDPG is used to adaptively approximate the uncertainty of the system model, and the chattering is eliminated to realize the control system's smooth input, to improve the anti-interference ability which ensures the robustness of the system in various environments such as quality change, friction factor, external disturbance, and modeling uncertainty of the system [5; 6; 12];
* On the basis of eliminating chattering with DDPG, it brings the advantages of low steady-state error and high-precision position tracking.