Global fixed-time stabilization for a class of uncertain high-order nonlinear systems with dead-zone input nonlinearity

2018 ◽  
Vol 41 (7) ◽  
pp. 1888-1895
Author(s):  
Fangzheng Gao ◽  
Yanling Shang ◽  
Yuqiang Wu ◽  
Yanhong Liu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Dead Zone ◽  
Fixed Time ◽  
High Order ◽  
Closed Loop System ◽  
Sign Function ◽  
Input Nonlinearity ◽  
Power Integrator

This paper considers the problem of global fixed-time stabilization for a class of uncertain high-order nonlinear systems. One distinct characteristic of this work is that the system under consideration possesses the dead-zone input nonlinearity. By delicately combining the sign function with a power integrator technique, a state feedback controller is designed such that the states of the resulting closed-loop system converge to the origin within a fixed time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

scholarly journals A New Approach to Adaptive Stabilization of Stochastic High-Order Nonholonomic Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Guangju Li ◽  
Kemei Zhang
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Nonholonomic Systems ◽  
High Order ◽  
Function Technique ◽  
Adaptive Stabilization ◽  
Closed Loop System ◽  
Sign Function ◽  
New Approach ◽  
Asymptotic Stability In Probability

This paper studies the problem of adaptive stabilization for a class of stochastic high-order nonholonomic systems. Under the weaker assumptions, by constructing the appropriate Lyapunov function and combining sign function technique, an adaptive state feedback controller is designed to guarantee global asymptotic stability in probability of the closed-loop system. The effectiveness of the controller is demonstrated by a mechanical system.

scholarly journals Global Stabilization of High-Order Time-Delay Nonlinear Systems under a Weaker Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Nengwei Zhang ◽  
Enbin Zhang ◽  
Fangzheng Gao
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Design Procedure ◽  
High Order ◽  
Global Stabilization ◽  
Closed Loop System ◽  
System A ◽  
Continuous State ◽  
High Order Time

Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

scholarly journals The Adaptive Neural Control for a Class of High-Order Uncertain Stochastic Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Xiaoyan Qin
Keyword(s):  
Nonlinear Systems ◽  
Neural Control ◽  
Closed Loop ◽  
Control Method ◽  
High Order ◽  
Stochastic Nonlinear Systems ◽  
Closed Loop System ◽  
Adaptive Neural Control ◽  
Control Scheme ◽  
Approximation Capability

This paper studies the problem of the adaptive neural control for a class of high-order uncertain stochastic nonlinear systems. By using some techniques such as the backstepping recursive technique, Young’s inequality, and approximation capability, a novel adaptive neural control scheme is constructed. The proposed control method can guarantee that the signals of the closed-loop system are bounded in probability, and only one parameter needs to be updated online. One example is given to show the effectiveness of the proposed control method.

scholarly journals Adaptive Finite-Time Stabilization of High-Order Nonlinear Systems with Dynamic and Parametric Uncertainties

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Meng-Meng Jiang ◽  
Xue-Jun Xie
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Finite Time ◽  
State Feedback ◽  
High Order ◽  
Parametric Uncertainties ◽  
Nonlinear Functions ◽  
Sign Function ◽  
Dynamic Uncertainty ◽  
Finite Time Stabilization

Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS) is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.

A State-scaling Design for Prescribed-time Stabilization of High-order Nonlinear Systems with Input Quantization

2021 ◽  
Author(s):  
Wenhui Zhang ◽  
Fangzheng Gao ◽  
Jiacai Huang ◽  
Yuqiang Wu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
High Order ◽  
Equivalent Transformation ◽  
Input Quantization ◽  
Adding A Power Integrator ◽  
Performance Requirements ◽  
System States ◽  
Power Integrator ◽  
New Framework

Abstract This article considers global stabilization problem for a kind of uncertain high-order nonlinear systems (HONSs). Two distinct characteristics of this study are that the considered system possesses the input-quantized actuator, and the prescribed time convergence of the system states is wanted. To address these, a novel state-scaling transformation (SST) is firstly introduced to convert the aboriginal prescribed-time stabilization (PTS) to the asymptotic stabilization of the transformed one. Then, under the new framework of equivalent transformation, a quantized state feedback controller that achieves of the performance requirements is developed with the aid of the technique of adding a power integrator (API). Finally, simulation results of a liquid-level system are provided to confirm the efficacy of the proposed approach.

scholarly journals State-Feedback Stabilization for Stochastic High-Order Nonlinear Systems with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Fangzheng Gao ◽  
Zheng Yuan ◽  
Fushun Yuan
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Design Procedure ◽  
High Order ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Nonlinear Growth ◽  
Adding A Power Integrator ◽  
Power Integrator ◽  
Weaker Conditions

This paper investigates the problem of state-feedback stabilization for a class of stochastic high-order nonlinear systems with time-varying delays. Under the weaker conditions on the power order and the nonlinear growth, by using the method of adding a power integrator, a state-feedback controller is successfully designed, and the global asymptotic stability in the probability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov-Krasovskii functional. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

scholarly journals Adaptive Neural Tracking Control for Discrete-Time Switched Nonlinear Systems with Dead Zone Inputs

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Jidong Wang ◽  
Lengxue Zhu ◽  
Xiaoping Si
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Tracking Control ◽  
Closed Loop ◽  
Dead Zone ◽  
Switched Nonlinear Systems ◽  
Closed Loop System ◽  
Neural Controllers ◽  
Arbitrary Switching

In this paper, the adaptive neural controllers of subsystems are proposed for a class of discrete-time switched nonlinear systems with dead zone inputs under arbitrary switching signals. Due to the complicated framework of the discrete-time switched nonlinear systems and the existence of the dead zone, it brings about difficulties for controlling such a class of systems. In addition, the radial basis function neural networks are employed to approximate the unknown terms of each subsystem. Switched update laws are designed while the parameter estimation is invariable until its corresponding subsystem is active. Then, the closed-loop system is stable and all the signals are bounded. Finally, to illustrate the effectiveness of the proposed method, an example is employed.

Further results on adaptive state feedback stabilization for a class of stochastic feedforward nonlinear systems with time delays

2018 ◽  
Vol 41 (1) ◽  
pp. 127-134 ◽  
Author(s):  
Xiaoyan Qin ◽  
Huifang Min
Keyword(s):  
Nonlinear Systems ◽  
Time Delays ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Transformation Technique ◽  
Globally Asymptotically Stable ◽  
Feedforward Nonlinear Systems

This paper further discusses the state feedback stabilization for stochastic high-order feedforward nonlinear systems with input time delay. By constructing the appropriate Lyapunov–Krasovskii functional, and using the variable transformation technique and the homogeneous domination idea, a state feedback controller is designed to ensure that the closed-loop system will be globally asymptotically stable in probability. Finally, an example is given to verify the effectiveness of the obtained analytical results.

scholarly journals State-feedback stabilization for stochastic high-order nonlinear systems with a ratio of odd integers power

2010 ◽  
Vol 15 (1) ◽  
pp. 39-53 ◽  
Author(s):  
L. Liu ◽  
N. Duan
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
High Order ◽  
Feedback Stabilization ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Optimal Stabilization ◽  
Adding A Power Integrator ◽  
Power Integrator ◽  
Smooth State

This paper investigates the problem of globally asymptotically stable in probability by state-feedback for a class of stochastic high-order nonlinear systems with a ratio of odd integers power. By extending the adding a power integrator technique and choosing an appropriate Lyapunov function, a linear smooth state-feedback controller is explicitly constructed to render the system globally asymptotically stable in probability. Furthermore, we address the problem of state-feedback inverse optimal stabilization in probability. A simulation example is provided to show the effectiveness of the proposed approach.

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