Adaptive fixed-time control for nonlinear systems against time-varying actuator faults

Abstract The adaptive fixed-time control problem for nonlinear systems with time-varying actuator faults is investigated in this paper. A novel adaptive fixed-time controller is designed via combining the Lyapunov stability theory with the backstepping method. It can be adapted to both system uncertainties and unknown actuator faults. Compared with the existing fault-tolerant control schemes subject to actuator faults, the adaptive fixed-time neural networks control scheme can make sure that the tracking error is convergent in a small neighborhood of the origin within a fixed-time interval, and it does not depend on the original states of the system and actuator faults. In light of the control scheme proposed in this paper, the fixed-time stability of the closed-loop system can be guaranteed by theoretical analysis, and a numerical example is provided to verify the effectiveness of obtained theoretical results.

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

10.21203/rs.3.rs-1056917/v1 ◽

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.

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Finite-Time Tracking Control for Nonstrict-Feedback State-Delayed Nonlinear Systems with Full-State Constraints and Unmodeled Dynamics

Complexity ◽

10.1155/2020/8887925 ◽

2020 ◽

Vol 2020 ◽

pp. 1-18

Author(s):

Yangang Yao ◽

Jieqing Tan ◽

Jian Wu

Keyword(s):

Nonlinear Systems ◽

Finite Time ◽

Tracking Control ◽

State Constraints ◽

Unmodeled Dynamics ◽

Time Varying ◽

Cubic Form ◽

Time Control ◽

Full State ◽

Full State Constraints

The problem of finite-time tracking control is discussed for a class of uncertain nonstrict-feedback time-varying state delay nonlinear systems with full-state constraints and unmodeled dynamics. Different from traditional finite-control methods, a C 1 smooth finite-time adaptive control framework is introduced by employing a smooth switch between the fractional and cubic form state feedback, so that the desired fast finite-time control performance can be guaranteed. By constructing appropriate Lyapunov-Krasovskii functionals, the uncertain terms produced by time-varying state delays are compensated for and unmodeled dynamics is coped with by introducing a dynamical signal. In order to avoid the inherent problem of “complexity of explosion” in the backstepping-design process, the DSC technology with a novel nonlinear filter is introduced to simplify the structure of the controller. Furthermore, the results show that all the internal error signals are driven to converge into small regions in a finite time, and the full-state constraints are not violated. Simulation results verify the effectiveness of the proposed method.

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Finite-Time Control for Nonlinear Systems with Time-Varying Delay and Exogenous Disturbance

Symmetry ◽

10.3390/sym12030447 ◽

2020 ◽

Vol 12 (3) ◽

pp. 447 ◽

Cited By ~ 2

Author(s):

Yanli Ruan ◽

Tianmin Huang

Keyword(s):

Time Delay ◽

Nonlinear Systems ◽

Finite Time ◽

Delay System ◽

Time Varying ◽

Time Delay System ◽

Time Varying Delay ◽

Time Control ◽

Exogenous Disturbance ◽

Varying Delay

This paper is concerned with the problem of finite-time control for nonlinear systems with time-varying delay and exogenous disturbance, which can be represented by a Takagi–Sugeno (T-S) fuzzy model. First, by constructing a novel augmented Lyapunov–Krasovskii functional involving several symmetric positive definite matrices, a new delay-dependent finite-time boundedness criterion is established for the considered T-S fuzzy time-delay system by employing an improved reciprocally convex combination inequality. Then, a memory state feedback controller is designed to guarantee the finite-time boundness of the closed-loop T-S fuzzy time-delay system, which is in the framework of linear matrix inequalities (LMIs). Finally, the effectiveness and merits of the proposed results are shown by a numerical example.

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Global adaptive finite-time control for uncertain nonlinear systems with actuator faults and unknown control directions

Nonlinear Dynamics ◽

10.1007/s11071-019-05146-8 ◽

2019 ◽

Vol 97 (4) ◽

pp. 2533-2545 ◽

Cited By ~ 2

Author(s):

Jiali Ma ◽

Ju H. Park ◽

Shengyuan Xu

Keyword(s):

Nonlinear Systems ◽

Finite Time ◽

Uncertain Nonlinear Systems ◽

Actuator Faults ◽

Unknown Control Directions ◽

Time Control ◽

Unknown Control

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Approximate guaranteed cost fault-tolerant control of unknown nonlinear systems with time-varying actuator faults

Nonlinear Dynamics ◽

10.1007/s11071-015-2324-6 ◽

2015 ◽

Vol 83 (1-2) ◽

pp. 269-282 ◽

Cited By ~ 13

Author(s):

Chun-Hua Xie ◽

Guang-Hong Yang

Keyword(s):

Nonlinear Systems ◽

Fault Tolerant ◽

Fault Tolerant Control ◽

Time Varying ◽

Actuator Faults ◽

Guaranteed Cost

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Nonsingular Global Fixed-Time Stabilization for Nonlinear Systems

Complexity ◽

10.1155/2021/9933472 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Wei Hu ◽

Zhangyong Zhou ◽

Junjun Tang

Keyword(s):

Nonlinear Systems ◽

Control Method ◽

Original System ◽

Fixed Time ◽

Time Varying ◽

Feedback Systems ◽

Convergence Problem ◽

Adding A Power Integrator ◽

Coordinate Mapping ◽

Novel Concept

Since existing results about fixed-time stabilization are only applied to strict feedback systems, this paper investigates the nonsingular fixed-time stabilization of more general high-order nonlinear systems. Based on a novel concept named coordinate mapping of time domain, a control method is first proposed to transform the nonsingular fixed-time convergence problem into the finite-time convergence problem of a transformed time-varying system. By extending the existing, adding a power integrator technique into the considered time-varying system, a periodic controller is constructed to stabilize the original system in fixed time. The results of simulations verify the effectiveness of the proposed method.

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