An adaptive proportional integral robust (PIR) control method based on deep deterministic policy gradient (DDPGPIR) is proposed for n-link robotic manipulator systems with model uncertainty and time-varying external disturbances. In this paper, the uncertainty of the nonlinear dynamic model, time-varying external disturbance, and friction resistance of the n-link robotic manipulator are integrated into the uncertainty of the system, and the adaptive robust term is used to compensate for the uncertainty of the system. In addition, dynamic information of the n-link robotic manipulator is used as the input of the DDPG agent to search for the optimal parameters of the proportional integral robust controller in continuous action space. To ensure the DDPG agent’s stable and efficient learning, a reward function combining a Gaussian function and the Euclidean distance is designed. Finally, taking a two-link robot as an example, the simulation experiments of DDPGPIR and other control methods are compared. The results show that DDPGPIR has better adaptive ability, robustness, and higher trajectory tracking accuracy.

In automatic control systems, negative feedback control has the advantage of maintaining a steady state, while positive feedback control can enhance some activities of the control system. How to design a controller with both control modes is an interesting and challenging problem. Motivated by it, on the basis idea of catastrophe theories, taking positive feedback and negative feedback as two different states of the system, an adaptive alternating positive and negative feedback (APNF) control model with the advantages of two states is proposed. By adaptively adjusting the relevant parameters of the constructed symmetric catastrophe function and the learning rule based on error and forward weight, the two states can be switched in the form of catastrophe. Through the Lyapunov stability theory, the convergence of the proposed adaptive APNF control model is proven, which indicates that system convergence can be guaranteed by selecting appropriate parameters. Moreover, we present theoretical proof that the negative feedback system with negative parameters can be equivalent to the positive feedback system with positive parameters. Finally, the results of the simulation example show that APNF control has satisfactory performance in response speed and overshoot.

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An unknown nonlinear disturbance seriously affects the trajectory tracking of autonomous underwater vehicles (AUVs). Thus, it is critical to eliminate the influence of such disturbances on AUVs. To address this problem, this paper proposes a double-loop proportional–integral–differential (PID) neural network sliding mode control (DLNNSMC). First, a double-loop PID sliding mode surface is proposed, which has a faster convergence speed than other PID sliding mode surfaces. Second, a nonlinear high-order observer and a neural network are combined to observe and compensate for the nonlinear disturbance of the AUV system. Then, the bounded stability of an AUV closed-loop system is analyzed and demonstrated using the Lyapunov method, and the time-domain method is used to verify that the velocity- and position-tracking errors of AUVs converge to zero exponentially. Finally, the radial basis function (RBF) neural network PID sliding mode control (RBFPIDSMC) and the RBF neural network PID sliding mode control (RBFPDSMC) are compared with this method in two trajectory tracking control simulation experiments. In the first experiment, the average Euclidean distance of the position-tracking error for this method was reduced by approximately 73.6% and 75.3%, respectively, compared to those for RBFPDSMC and RBFPIDSMC. In the second experiment, the average Euclidean distance of the position tracking error for this method was reduced by approximately 86.8% and 88.8%, respectively. The two experiments showed that the proposed control method has a strong anti-jamming ability and tracking effect. The simulation results obtained in the Gazebo environment validated the superiority of this method.