Adaptive finite‐time neural network control for redundant parallel manipulators

In this paper, a finite-time adaptive fuzzy tracking control scheme is proposed for parallel manipulators with unbounded uncertainties. The proposed approach is based on fuzzy logic systems (FLS), nonsingular fast terminal sliding mode control (NFTSMC) and adaptive sliding compensation from nonlinearities in output feedback. FLS are adopted to handle system uncertainties and external disturbances. This learning approach does not require knowledge of parallel manipulator dynamics. The proposed control scheme can possess several advantages over other state-of-the-art approaches such as rapid response, robustness, higher precision, nonsingular, and finite-time converge. Besides, since the proposed approach is a hybrid scheme of NFTSMC and FLS, the proposed controller can have much better tracking control performance. The finite-time convergence and stability of the closed-loop robotic system are ensured by the Lyapunov theory. Finally, from the simulation results, it is clearly evident that the proposed approach can indeed outperform previous existing methods.

A manipulator often cannot converge rapidly within finite time and has low tracking accuracy owing to factors such as manipulator model errors and external disturbances. To address these problems, this paper proposes a time-varying non-singular fast terminal sliding mode control scheme based on an improved variable power–power reaching law. First, three radial basis function neural networks (RBFNNs) are employed to approximate the dynamic parameters of the manipulator model and thus realize model-free control. Second, to achieve faster finite-time convergence of the system state, a time-varying non-singular fast terminal sliding-mode (NFTSM) surface is designed according to the system state change. In addition, an improved variable power–power reaching law is adopted to avoid chatter and eliminate approximation errors. Finally, comparative simulation experiments are conducted using a 2-DOF manipulator as the research object. The results show that the proposed control scheme facilitates fast convergence, high-precision trajectory tracking, and effective suppression of system chatter under complex uncertainties, thereby confirming its utility and superiority.

Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems

This work proposes a non-singular fast terminal sliding mode control (NFTSMC) strategy based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and a nonlinear disturbance observer (NDO) to address the issues of modeling errors, motion disturbances, and transmission friction in robotic manipulators. Firstly, a novel modular serial 5-DOF robotic manipulator configuration is designed, and its kinematic and dynamic models are established. Secondly, a nonlinear disturbance observer is employed to estimate the total disturbance of the system and apply feedforward compensation. Based on boundary layer technology, an improved NFTSMC method is proposed to accelerate the convergence of tracking errors, reduce chattering, and avoid singularity issues inherent in traditional terminal sliding mode control. The stability of the designed control system is proved using Lyapunov stability theory. Subsequently, a deep reinforcement learning (DRL) agent based on the TD3 algorithm is trained to adaptively adjust the control gains of the non-singular fast terminal sliding mode controller. The dynamic information of the robotic manipulator is used as the input to the TD3 agent, which searches for optimal controller parameters within a continuous action space. A composite reward function is designed to ensure the stable and efficient learning of the TD3 agent. Finally, the motion characteristics of three joints for the designed 5-DOF robotic manipulator are analyzed. The results show that compared to the non-singular fast terminal sliding mode control algorithm based on a nonlinear disturbance observer (NDONFT), the non-singular fast terminal sliding mode control algorithm integrating a nonlinear disturbance observer and the Twin Delayed Deep Deterministic Policy Gradient algorithm (TD3NDONFT) reduces the mean absolute error of position tracking for the three joints by 7.14%, 19.94%, and 6.14%, respectively, and reduces the mean absolute error of velocity tracking by 1.78%, 9.10%, and 2.11%, respectively. These results verify the effectiveness of the proposed algorithm in enhancing the trajectory tracking accuracy of the robotic manipulator under unknown time-varying disturbances and demonstrate its strong robustness against sudden disturbances.

Diseases such as cerebral palsy can lead to lower limb dysfunction in children. Lower limb rehabilitation exoskeletons have been clinically validated as effective interventions for gait rehabilitation of children. This study proposes a novel lower-limb gait rehabilitation exoskeleton design and its corresponding control method for pediatric applications. A dynamic model was established, and a nonsingular fast terminal sliding mode control (NFTSMC) strategy was developed to achieve precise trajectory tracking. The curve fitting was performed on a publicly available children’s gait dataset to generate reference hip and knee joint trajectories. The Lagrange method was subsequently employed to derive the dynamic model of the lower-limb exoskeleton. Control simulations were conducted using the proposed NFTSMC algorithm. Comparative analysis with traditional sliding mode control (SMC) demonstrated that NFTSMC reduced root mean square error (RMSE) by 75% (hip) and 67.4% (knee), while integral of time-weighted absolute error (ITAE) decreased by 77.3% and 92.3%, respectively. These results confirm that NFTSMC significantly enhances joint trajectory tracking accuracy, system response speed, and tracking precision.

This paper proposes a non-singular fast terminal sliding mode control strategy based on the self-organizing radial basis function neural network (RBFNN) approximation for the train key network system to realize the safe and reliable operation of the train. In order to improve the RBFNN approximation performance and speed, an improved multi-strategy particle swarm optimization (IMPSO) algorithm, which utilizes multi-strategy evolution ways with a nonlinear deceasing inertia weight to improve the global optimizing performance of particle swarm, is proposed to optimize the structure and parameters for better mapping the highly nonlinear characteristics of train traction braking. In addition, the IMPSO is also introduced into a non-singular fast terminal sliding mode (NFTSM) controller to obtain the most appropriate tuning parameters of the controller and suppresses the chattering phenomenon from sliding mode controller. The stability characteristic of the system under the proposed NFTSM controller is studied based on the Lyapunov theory. Further combined with effective delay prediction and delay compensation methods, the NFTSM high-precision control of the train key nonlinear network system is implemented. The simulation results show that the proposed method has more efficient and robust tracking performance and real-time performance compared with other control methods, which can provide effective means for realizing the symmetrical bus control by automatic train operation (ATO) at both ends of the train, with the safe operation of the train under every complex motion condition.

For accurate trajectory tracking of robotic manipulators with actuators, a novel nonsingular fast terminal sliding mode control (NFTSMC) strategy based on radial basis function neural network (RBFNN) is put forward and investigated in this paper. Because of the existence of nonsingular fast terminal sliding mode (NFTSM) manifold, the controller possesses high precision and fast convergence. Considering that it is difficult to obtain accurate model parameters owing to modeling errors or external disturbances, RBFNN is used to approximate the nonlinear uncertainties due to its simple structure and great generalization ability. A new adaptive law is designed to adjust RBFNN. In order to compensate the estimation errors and suppress other unstable factors, a robust term is introduced. A new adaptive law is developed to flexibly adjust the robust term. Then, Lyapunov theory is applied to prove the system stability and finite-time convergence. Finally, a small-sized industrial robotic manipulator Epson LS3-401S with its first two joints is taken as the simulation plant, and several simulations between the proposed controller and the other two controllers are performed. External disturbances and other two conditions are considered to simulate the real environment, and the corresponding results verify the effectiveness and superiority of the proposed controller.

A Non-singular Fast Terminal Sliding Mode Approach to Improve the Network Stability of Wind Rich Power Grids

A novel adaptive non-singular fast terminal sliding mode control (NFTSMC) scheme is developed for a highly nonlinear two-link robotic manipulator (TLRM) system subject to system uncertainties and unknown disturbances. First, to compensate for the system uncertainties, neural network (NN) is employed to approximate the unknown nonlinear dynamic function. Subsequently, to address the challenges of disturbance compensation and unmeasured joint angular velocity, a nonlinear NN-based extended state observer (NN-based ESO) is introduced. The NN-based ESO facilitates accurate disturbance estimation and compensation, while also enabling simultaneous estimation of the joint angular velocity. Through the integration of these techniques, the closed-loop system’s stability is proven using the direct Lyapunov method, demonstrating remarkable tracking performance within finite time. Simulation results validate the effectiveness of the NFTSMC with the NN-based ESO, showcasing superior performance compared to alternative control strategies.

This paper proposes a non-singular fast terminal sliding mode control (NFTSMC) method for micro gyroscopes with unknown uncertainty based on gated recurrent fuzzy neural networks (GRFNNs). First, taking advantage of non-singular fast terminal sliding control, a sliding hyperplane is designed with a nonlinear function to ensure that the tracking error of the system converges to zero within a specified finite time. Then, the unknown model parameters of the micro gyroscope are estimated using a GRFNN. Since the GRFNN can adaptively adjust the base width, center vector, gated recurrent unit parameters, and outer gains, it can achieve accurate approximation to unknown models, enhancing the robustness and accuracy. In addition, due to the introduction of gated recurrent units, The GRFNN can effectively utilize the previous data and avoid the problem of gradient disappearance. The comparison of the simulation results with traditional neural sliding mode control shows that the proposed method can achieve better tracking performance and more accurate estimation of unknown models.

Steering angle and driving force saturations are inevitable in autonomous vehicle motions, which will degrade the motion control performance and even deteriorate the driving safety. In addition, the strong coupling of lateral and longitudinal motions of autonomous vehicles also contributes to the saturations damage and increases the control difficulty. To reduce these negative impacts on motion control, a novel motion controller for automated vehicles is presented in this paper. Firstly, an extended 3 degree of freedom vehicle dynamic model is built with the unknown saturations, strong-coupled motion characteristics and external disturbance considered simultaneously. Then, a coordinated controller is designed to complete motion control task based on sliding-mode control (SMC) and non-singular fast terminal sliding-mode control (NFTSM). Moreover, a three-layer radial basis function neural network (RBFNN) is adopted as a compensator to approximate modelling uncertainties. Based on Lyapunov stability theory, the uniform ultimate boundednesses of motion control errors are guaranteed. Simulation results show that the proposed controller owns smaller steady-state errors and faster convergence speed.

We propose a radial basis function (RBF) neural network controller for ship control. The main feature of the controller is to combine a fuzzy controller with neural networks. We transform a set of fuzzy inference rules into an RBF neural-network controller, utilizing the nonlinear mapping and learning ability of the neural networks. We present the design method of the controller based on the RBF neural networks and fuzzy rules, and discuss the characteristics of the controller. We use MATLAB as a simulation language. Simulation tests are conducted with different parameters, and the results are given in the paper. We introduce a ship control test bed. The controller is installed on the ship control test bed, and sea trials are conducted in the open sea. The sea trial results are also shown in the paper.

RBFNN-based nonsingular fast terminal sliding mode control for robotic manipulators including actuator dynamics

This paper presents a stable neural network control, scheme for manipulators. Cerebellar model articulation (CMAC) or radial basis function (RBF) neural networks are used. The main contribution of this paper is the stability proof of neural network controllers for manipulators. This distinguishes the paper from other work. The results of this paper also have a closer relation to conventional adaptive control. This means that the neural network controller can either work alone if there is no a priori knowledge or work together with conventional adaptive control. Any a priori knowledge can also easily be used to train the neural networks off-line and, therefore, improve the online performance.

This article proposed a novel control approach for trajectory tracking of robotic airships. First, the nonlinear dynamics model of a robotic airship is derived and formulated. Second, a sliding mode controller is designed to track the commanded trajectory for its robustness against parametric variations and external disturbances. To address the chattering problem results from the sliding mode controller, a radial basis function neural network is adopted to construct the neural network self-gain-scheduling sliding mode controller in which the control gains are scheduled synchronously with the sliding surface via radial basis function neural network according to the learning algorithm, with switching sliding surface and its differential as radial basis function neural network inputs and control gains as radial basis function neural network outputs. In addition, the stability and convergence of the closed-loop controller are proven using the Lyapunov stability theorem. Finally, the effectiveness and robustness of the proposed controller are demonstrated via numerical simulations. Contrasting simulation results indicate that the neural network self-gain-scheduling sliding mode controller attenuates the chattering effectively and has better performance against the sliding mode controller.