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 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.

scholarly journals Global Finite-Time Stabilization for a Class of Uncertain High-Order Nonlinear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jian Wang ◽  
Jing Xie ◽  
Fangzheng Gao
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Feedback ◽  
High Order ◽  
Finite Time Stability ◽  
Adding A Power Integrator ◽  
System A ◽  
Continuous State ◽  
Finite Time Stabilization ◽  
Power Integrator

This paper addresses the problem of global finite-time stabilization by state feedback for a class of high-order nonlinear systems under weaker condition. By using the methods of adding a power integrator, a continuous state feedback controller is successfully constructed to guarantee the global finite-time stability of the resulting closed-loop system. A simulation example is provided to illustrate the effectiveness of the proposed approach.

scholarly journals Nonsmooth Adaptive Control Design for a Large Class of Uncertain High-Order Stochastic Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Jian Zhang ◽  
Yungang Liu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Original System ◽  
High Order ◽  
Stochastic Nonlinear Systems ◽  
Zero Dynamics ◽  
Control Lyapunov Function ◽  
Adding A Power Integrator ◽  
Partial State ◽  
System States

This paper investigates the problem of the global stabilization via partial-state feedback and adaptive technique for a class of high-order stochastic nonlinear systems with more uncertainties/unknowns and stochastic zero dynamics. First of all, two stochastic stability concepts are slightly extended to allow the systems with more than one solution. To solve the problem, a lot of substantial technical difficulties should be overcome since the presence of severe uncertainties/unknowns, unmeasurable zero dynamics, and stochastic noise. By introducing the suitable adaptive updated law for an unknown design parameter and appropriate control Lyapunov function, and by using the method of adding a power integrator, an adaptive continuous (nonsmooth) partial-state feedback controller without overparameterization is successfully designed, which guarantees that the closed-loop states are bounded and the original system states eventually converge to zero, both with probability one. A simulation example is provided to illustrate the effectiveness of the proposed approach.

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.

Continuous Feedback Control Design for a Class of Singular High-Order Nonlinear Systems

2013 ◽  
Vol 325-326 ◽  
pp. 1157-1161
Author(s):  
Cheng Sun ◽  
He Xu Sun ◽  
Xin Wei Diao
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
High Order ◽  
Systematic Design ◽  
Feedback Controllers ◽  
Stabilizing Controllers ◽  
Adding A Power Integrator ◽  
Continuous State ◽  
Continuous Feedback ◽  
Power Integrator

nherently nonlinear systems may not be stabilized, even locally by any smooth feedback but continuously stabilizable. This paper studies the design of continuous state feedback controllers for a class of singular high order non-linear systems. A systematic design method which combines backstepping theory with the idea of adding a power integrator is presented for globally stabilizing controllers of this class of systems.

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