## 1 Introduction
Similarly, the angular velocity of each joint should not exceed its maximum related to the maximum rotational speed of the driving motor;
* For some existing controllers (e.g., [PERSON] _et al._ (2018); [PERSON] _et al._ (2018); [PERSON] _et al._ (2018); [PERSON] _et al._ (2018)), the tracking accuracy could be compromised due to the bounded result of tracking errors and uncertainty-estimation errors. Therefore, it is needed to avoid the loss of tracking accuracy caused by the lack of asymptotic convergence of tracking errors. To handle the above issues, this paper proposes a new adaptive control scheme that utilizes time delay estimation (TDE) and reinforcement learning (RL) for \(n\)-link robotic manipulators. In the proposed control scheme, the multiple-input-and-multiple-output (MIMO) robotic system is initially decomposed into \(n\) single-input-single-output (SISO) subsystems by TDE. Each subsystem is with an unknown bounded TDE error. After that, the novel virtual control law for each subsystem is designed, which can not only achieve the boundness of tracking errors for each joint in the presence of TDE error, but can also guarantee both the angular position and angular velocity for each joint to be not exceeding the preset constraints. To improve the tracking accuracy, an RL-based term in the virtual control law is designed, which automatically learns the optimal parameters of the controller in the different system states. RL is an artificial intelligence technique that gradually explores the optimal policy by interacting with the environment, which has attracted many interests in the control of robotic manipulators such as [PERSON] _et al._ (2018); [PERSON] _et al._ (2018); [PERSON] _et al._ (2018). Particularly, the RL-based term in this paper is designed to avoid the violation of the boundness of tracking errors, even if a bad policy is tried by RL, which ensures a safe environment for implementing RL. The tracking errors are proven to be uniformly ultimately bounded (UUB) via Lyapunov theory. Simulation results indicate the proposed control scheme can achieve a high tracking accuracy in the presence of model uncertainty and unknown disturbances. The major merits of this paper include the following points:  
* Compare with some existing research [PERSON] _et al._ (2018); [PERSON] _et al._ (2018); [PERSON] _et al._ (2018), in addition to the basic achievement of the uniformly ultimately bounded (UUB) tracking error for each joint in the presence of TDE error; the control scheme can guarantee both the angular position and angular velocity for each joint to be not exceeding the preset constraints;
* The novel adaptive gain in (13) results in the smooth control torques to reduce the chattering effect caused by switching term in (10). Meanwhile, an RL-based term can effectively improve the tracking accuracy, which thereby reduces the possible steady-state tracking errors caused by the lack of asymptotic convergence;
* The mathematical expression of the controller is simple, meanwhile, any prior knowledge of upper bounds caused by an imprecise model are unnecessary in our control scheme. The rest of this paper is organized as follows: in Section 2, the dynamics model of n-link robotic manipulators is given, and the control objective is described. In Section 3, the RL-based adaptive control scheme is proposed and the proof of stability is given. In Section 4, the numerical simulation is conducted to verify the effectiveness of the proposed controller. The conclusion is given in Section 5.