Barrier Lyapunov function-based robot control with an augmented neural network approximator

Purpose Considering the complexity of dynamic and friction modeling, this paper aims to develop an adaptive trajectory tracking control scheme for robot manipulators in a universal unmodeled method, avoiding complicated modeling processes. Design/methodology/approach An augmented neural network (NN) constituted of radial basis function neural networks (RBFNNs) and additional sigmoid-jump activation function (SJF) neurons is introduced to approximate complicated dynamics of the system: the RBFNNs estimate the continuous dynamic term and SJF neurons handle the discontinuous friction torques. Moreover, the control algorithm is designed based on Barrier Lyapunov Function (BLF) to constrain output error. Findings Lyapunov stability analysis demonstrates the exponential stability of the closed-loop system and guarantees the tracking errors within predefined boundaries. The introduction of SJFs alleviates the limitation of RBFNNs on discontinuous function approximation. Owing to the fast learning speed of RBFNNs and jump response of SJFs, this modified NN approximator can reconstruct the system model accurately at a low compute cost, and thereby better tracking performance can be obtained. Experiments conducted on a manipulator verify the improvement and superiority of the proposed scheme in tracking performance and uncertainty compensation compared to a standard NN control scheme. Originality/value An enhanced NN approximator constituted of RBFNN and additional SJF neurons is presented which can compensate the continuous dynamic and discontinuous friction simultaneously. This control algorithm has potential usages in high-performance robots with unknown dynamic and variable friction. Furthermore, it is the first time to combine the augmented NN approximator with BLF. After more exact model compensation, a smaller tracking error is realized and a more stringent constraint of output error can be implemented. The proposed control scheme is applicable to some constraint occasion like an exoskeleton and surgical robot.

Barrier Lyapunov Function-Based Fixed-Time FTC for High-Order Nonlinear Systems with Predefined Tracking Accuracy

This article proposes a fixed-time adaptive fault-tolerant control methodology for a larger class of high-order nonlinear systems subject to full-state constraints and actuator faults. In contrast with the stateof-the-art results, the distinguishing feature of our control design consists in proposing a novel high-order tantype barrier Lyapunov function (BLF) which ensures state variables to be some asymmetric time-varying compact sets under tan-type constraints and expands the application range of tan-type BLF (i.e., from low-order to high-order, from symmetric time-invariant to asymmetric time-varying). Apart from this, the proposed control design ensures the tracking errors converge to specified residual sets within fixed-time and makes the size of the convergence regions of tracking errors adjustable a priori by means of a new BLF-based tuning function and a projection operator. A variable-separable lemma is delicately embedded into the control design to extract the control terms in a linear-like fashion which not only overcomes the difficulty that virtual control signals appear in a non-affine manner, but also solves the problem of actuator faults. Comparative simulations results finally validate the e ectiveness of the proposed scheme.

Robust Prescribed Performance Control of Uncertain Vehicle Lateral System under State Constraints

In the study of the zero-error tracking control problem for vehicle lateral control systems under full-state constraints and nonparametric uncertainties, the zero-error tracking control problem is presented in this paper. A neural adaptive tracking control scheme is proposed by combining the error transformation of the vehicle lateral control system with the barrier Lyapunov function, which realizes that the tracking error of the vehicle lateral control converges to a prescribed compact set at a controllable or specified convergence rate in a specified finite time. The scheme has the following significant characteristics: 1) Based on the Nussbaum gain, the preset new energy finite-time control algorithm, the tracking error of the vehicle lateral control system with non-parametric uncertainty and external disturbance decreases to zero with t → ∞. In addition, it also has the control ability to cope with the presence or even unknown moment of inertia of the system. 2) Barrier Lyapunov function (BLF) ensures the bounded input of the neural network during the whole system envelope, and ensures the stable learning and approximation of the neural network. Furthermore, the bounded stability of the closed-loop system is proved by Lyapunov analysis. Finally, the effectiveness and superiority of the proposed control method are verified by simulation.

Robust Tracking Control of the Euler–Lagrange System Based on Barrier Lyapunov Function and Self-Structuring Neural Networks

This article studies the robust tracking control problems of Euler–Lagrange (EL) systems with uncertainties. To enhance the robustness of the control systems, an asymmetric tan-type barrier Lyapunov function (ATBLF) is used to dynamic constraint position tracking errors. To deal with the problems of the system uncertainties, the self-structuring neural network (SSNN) is developed to estimate the unknown dynamics model and avoid the calculation burden. The robust compensator is designed to estimate and compensate neural network (NN) approximation errors and unknown disturbances. In addition, a relative threshold event-triggered strategy is introduced, which greatly saves communication resources. Under the proposed robust control scheme, tracking behavior can be implemented with disturbance and unknown dynamics of the EL systems. All signals in the closed-loop system are proved to be bounded by stability analysis, and the tracking error can converge to the neighborhood near the origin. The numerical simulation results show the effectiveness and the validity of the proposed robust control scheme.

A fast L1 adaptive constrained back-stepping controller using barrier Lyapunov function for anuncertain submersible vehicle

In this paper, a new L1 adaptive back-stepping controller based on the barrier Lyapunov function (BLF) is proposed to respect the position and velocity constraints usually imposed in designing Euler-Lagrange systems. The purpose of this investigation is to improve different aspects of a conventional L1 adaptive control. More specifically, the modified controller has a lower complexity by removing the low-pass filter from the design procedure. The performance of the controller is also enhanced by having a faster convergence speed and increased robustness against nonlinear uncertainties and disturbances arising in practical applications. The proposed scheme is evaluated on two different Euler-Lagrange systems, i.e. a 6-DOF remotely operated vehicle (ROV) and a single-link manipulator. The results for the new back-stepping design are assessed in both scenarios in terms of settling time, percentage of overshoot, and trajectory tracking error. The results confirm that both tracking and state estimation errors for position and velocity outputs outperform the standard L1 adaptive control technique. The results also demonstrate the high performance of the proposed approach in removing the matched nonlinear time-varying disturbances and dynamic uncertainties and a good trajectory tracking despite the uncertainty on the input gain of the system.