This paper describes the adaptive control design to solve the trajectory tracking problem of a Delta robot with uncertain dynamical model. This robot is a fully actuated, parallel closed-chain device. The output-based adaptive control was designed within the active disturbance rejection framework. An adaptive nonparametric representation for the uncertain section of the robot model was obtained using an adaptive least mean squares procedure. The adaptive algorithm was designed without considering the velocity measurements of the robot joints. Therefore, a simultaneous observer-identifier scheme was the core of the control design. A set of experimental tests were developed to prove the performance of the algorithm presented in this paper. Some reference trajectories were proposed which were successfully tracked by the robot. In all the experiments, the adaptive scheme showed a better performance than the regular proportional-integral-derivative (PID) controller with feed-forward actions as well as a nonadaptive active disturbance rejection controller. A set of numerical simulations was developed to show that even under five times faster reference trajectories, the adaptive controller showed better results than the PID controller.

This study presents the design of a robust control based on the sliding-mode theory to solve both; the stabilization and the trajectory tracking problems of nonlinear systems subjected to a class of full-state restrictions. The selected nonlinear system satisfies a standard Lagrangian structure affected by nonparametric uncertainties. A barrier Lyapunov function is used to ensure the state constraints by designing a time-varying gain, which guarantees the fulfillment of the predefined state constraints even under external perturbations. The proposed design methodology for the barrier sliding-mode control (BSMC) ensures the convergence of the sliding surface in finite time to the origin. Consequently, the asymptotic convergence of the states to the corresponding equilibrium point is achieved. The finite-time stability of the origin in the closed-loop system with the proposed controller has been demonstrated using the second Lyapunov stability method. The suggested controller was evaluated on a two-link robotic manipulator. Then, the obtained results showed better stabilization and tracking performances (while the restrictions are satisfied) than the traditional first-order sliding-mode or linear state feedback controllers.

The identification problem incorporated in feedback control of uncertain nonlinear systems exhibiting complex behavior has been solved in different ways. Some of these solutions have used artificial intelligence methods like fuzzy logic and neural networks. However, their individual implementation suffers from certain drawbacks, such as the black-box nature of neural network and the problem of finding suitable membership functions for fuzzy systems. These weaknesses can be avoided by implementing a hybrid structure combining these two approaches, the so-called neuro-fuzzy system. In this paper, a neuro-fuzzy system that implements differential neural networks (DNNs) as consequences of Takagi–Sugeno (T–S) fuzzy inference rules is proposed. The DNNs substitute the local linear systems that are used in the common T–S method. In this paper, DNNs are used to provide an effective instrument for dealing with the identification of the uncertain nonlinear system, while the T–S rules are used to provide the framework of previous knowledge of the system. The main idea is to carry out an online identification process of an uncertain nonlinear system with the aim to design a closed-loop trajectory tracking controller. The methodology developed in this study that supports the identification and trajectory control designs is based on the Lyapunov formalism. The DNN implementation results in a time-varying T–S system. As a consequence, the solution of two time-varying Riccati equations was used to adjust the learning laws in the DNN as well as to adjust the gains of the controller. Two results were provided to justify the existence of positive-definite solutions for the class of Riccati equations used in the learning laws of DNNs. A complete description of the learning laws used for the set of DNN identifiers is also obtained. An autonomous underwater vehicle system is used to demonstrate the performance of the controller on tracking a desired 3-D path by this combination of the DNN and the T–S system.