Finite-Time Prescribed Performance Trajectory Tracking Control for Underactuated Autonomous Underwater Vehicles Based on a Tan-Type Barrier Lyapunov Function

Abstract

This paper proposed a finite-time prescribed performance control scheme for underactuated autonomous underwater vehicles (AUVs) based on adaptive neural networks and a tan-type barrier Lyapunov function. Even in the presence of output constraints and environmental disturbances, the AUV can also precisely track the desired trajectory in a finite time. By introducing a tan-type barrier Lyapunov Function (TBLF), the singularity problem in process design is solved and all output errors are guaranteed to satisfy the prescribed performance specifications. Dynamic surface control (DSC) and the minimal learning parameter (MLP) are employed to greatly simplify the complexity of the algorithm and enhance the robustness of the control system, respectively. Lyapunov stability analysis proves that the proposed controller guarantees all signals in the closed-loop system to be uniformly ultimately bounded (UUB), and that the tracking errors converge to a small neighborhood near the origin in a finite time. Finally, the simulation results demonstrate the effectiveness and feasibility of the proposed controller.

Observer-Based Adaptive Prescribed- Time H ∞ Coordinated Control for Multiple Robot Manipulators With Prescribed Performance and Input Quantization

“…Remark 7: The first-order filter in [37] speeds up convergence, but the convergence rate is related to the gain coefficients. In [38], the command filter achieved system convergence in a fixed time, but it could not approach the unknown upper bound of the virtual control input derivatives.…”

“…where 0 < r < 1, T c > 0. Theorem 3: For a particular case of multi-RM systems (4) and (7), the system control rates are as shown in (7) and (37), and conditions p 0 > ∂ 2 1 2 are satisfied to realize the cooperative control problem taking into account the model nonlinear items and external disturbances to ensure that the whole multi-RM system is stabilized at a prescribed time.…”

Global Prescribed Performance-Based Fault-Tolerant Control for Trajectory Tracking of the ACV With Uncertainty

“…Remark 7. An integral form of the barrier Lyapunov function is used in [22] and [16] , while a logarithmic form is used in [14] . These functions are too cumbersome in their derivation, and a novel (with a simple structure and effective) barrier Lyapunov function is chosen in this paper to limit the state errors.…”

“…The focus then has to be on ensuring robustness of the tracking control system for ACV under strong uncertainty. Non-linear disturbance observer (NDO) [16] [18] is also a better selection that was utilized to suppress uncertainty compared to the more computationally intensive neural network estimation methods. A terminal sliding mode controller in [19] with PPF based on the sliding mode disturbance observer (SMDO) of the extended state observer (ESO) is applied to the tracking system of the underwater vehicle.…”

Command-Filter-Based Region-Tracking Control for Autonomous Underwater Vehicles with Measurement Noise

“…In recent years, with the development of performance constraint control theory, methods that can actively constrain transient and steady-state performance have been proposed, such as the obstacle Lyapunov function method [14][15][16], the funnel constraint method [17][18][19], and the prescribed performance function method [20][21][22][23][24][25][26][27]. Among them, the prescribed performance function method is used in AUV control because of its flexibility in setting constraints such as convergence rate, overshoot, and steady-state error range.…”