scholarly journals Appointed-Time Integral Barrier Lyapunov Function-Based Trajectory Tracking Control for a Hovercraft with Performance Constraints

2020 ◽  
Vol 10 (20) ◽  
pp. 7381
Author(s):  
Mingyu Fu ◽  
Tan Zhang ◽  
Fuguang Ding ◽  
Duansong Wang
Keyword(s):  
Lyapunov Function ◽  
Trajectory Tracking ◽  
Function Technique ◽  
Tracking Errors ◽  
Constraint Function ◽  
Performance Constraints ◽  
Barrier Lyapunov Function ◽  
Time Performance ◽  
Time Integral ◽  
Performance Constraint

This paper develops a totally new appointed-time integral barrier Lyapunov function-based trajectory tracking algorithm for a hovercraft in the presence of multiple performance constraints and model uncertainties. Firstly, an appointed-time performance constraint function is skillfully designed, which proposes to pre-specify the a priori transient and steady performances on the system tracking errors. Secondly, a new integral barrier Lyapunov function is constructed, which combines with the appointed-time performance constraint function to guarantee that the performance constraints on the system tracking errors are never violated. On this basis, an adaptive trajectory tracking controller is derived using the appointed-time integral barrier Lyapunov function technique in the combination of neural networks. According to Lyapunov’s stability theory, it can be shown that the proposed controller is capable of ensuring transient and steady performances on the output tracking errors. In particular, the position and speed tracking can be fulfilled in a user-appointed time without requiring complex control parameters selection. Finally, results from a comparative simulation study verify the efficacy and advantage of the proposed control approach.

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

2021 ◽  
Author(s):  
Hossein Ahmadian ◽  
Mehdi Arefi ◽  
Alireza Khayatian ◽  
Allahyar Montazeri
Keyword(s):  
Adaptive Control ◽  
Lyapunov Function ◽  
Trajectory Tracking ◽  
Tracking Error ◽  
Control Technique ◽  
Remotely Operated Vehicle ◽  
Pass Filter ◽  
Low Pass Filter ◽  
L1 Adaptive Control ◽  
Barrier Lyapunov Function

Abstract 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.

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

2021 ◽  
Author(s):  
Xiaolin Wang ◽  
Jihui Xu ◽  
Maolong Lv ◽  
Lei Zhang ◽  
Zilong Zhao
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Control Design ◽  
Fixed Time ◽  
High Order ◽  
Time Varying ◽  
Actuator Faults ◽  
State Variables ◽  
Tracking Errors ◽  
Barrier Lyapunov Function

Abstract 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.

Adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics

2021 ◽  
pp. 014233122098563
Author(s):  
Fei Shen ◽  
Xinjun Wang ◽  
Xinghui Yin
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Dead Zone ◽  
Small Neighborhood ◽  
Unmodeled Dynamics ◽  
Stochastic Nonlinear Systems ◽  
Dynamic Surface ◽  
Barrier Lyapunov Function ◽  
Full State

This paper investigates the problem of adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics. To stabilize such a system, a dynamic signal is introduced to dominate unmodeled dynamics and an assistant signal is constructed to compensate for the effect of the dead zone. Dynamic surface control is used to solve the “complexity explosion” problem in traditional backstepping design. Two cases of symmetric and asymmetric Barrier Lyapunov functions are discussed respectively in this paper. The proposed Barrier Lyapunov function based on backstepping method can ensure that the output tracking error converges in the small neighborhood of the origin. This control scheme can ensure that semi-globally uniformly ultimately boundedness of all signals in the closed-loop system. Two simulation cases are proposed to verify the effectiveness of the theoretical method.

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