scholarly journals A Novel Approach to Fixed-Time Stabilization for a Class of Uncertain Second-Order Nonlinear Systems

2020 ◽  
Vol 10 (1) ◽  
pp. 424
Author(s):  
Chih-Chiang Chen ◽  
Guan-Shiun Chen
Keyword(s):  
Nonlinear Systems ◽  
Controller Design ◽  
Fixed Time ◽  
Second Order ◽  
Closed Loop System ◽  
New Approach ◽  
Attitude Stabilization ◽  
Adding A Power Integrator ◽  
Novel Approach ◽  
Power Integrator

This paper is concerned with the problem of fixed-time stabilization for a class of uncertain second-order nonlinear systems. By delicately introducing extra manipulations in the feedback domination and revamping the technique of adding a power integrator, a new approach is developed, by which a state feedback controller, together with a suitable Lyapunov function, which is critical for verifying fixed-time convergence, can be explicitly organized to render the closed-loop system fixed-time stable. The major novelty of this paper is attributed to a subtle strategy that offers a distinct perspective in controller design as well as stability analysis in the problem of fixed-time stabilization for nonlinear systems. Finally, the proposed approach is applied to the attitude stabilization of a spacecraft to demonstrate its merits and effectiveness.

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.

Fixed-time trajectory tracking control for multiple nonholonomic mobile robots

2020 ◽  
pp. 014233122096641
Author(s):  
Meiying Ou ◽  
Haibin Sun ◽  
Zhenxing Zhang ◽  
Lingchun Li
Keyword(s):  
Mobile Robots ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Initial Conditions ◽  
Fixed Time ◽  
Nonholonomic Mobile Robots ◽  
Trajectory Tracking Control ◽  
Adding A Power Integrator ◽  
Time Control ◽  
Power Integrator

This paper investigates the fixed-time trajectory tracking control for a group of nonholonomic mobile robots, where the desired trajectory is generated by a virtual leader, the leader’s information is available to only a subset of the followers, and the followers are assumed to have only local interaction. According to fixed-time control theory and adding a power integrator technique, distributed fixed-time tracking controllers are developed for each robot such that all states of each robot can reach the desired value in a fixed time. Moreover, the settling time is independent of the system initial conditions and only determined by the controller parameters. Simulation results illustrate and verify the effectiveness of the proposed schemes.

scholarly journals Nonsingular Global Fixed-Time Stabilization for Nonlinear Systems

Complexity ◽  
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.

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 Marine Autopilots’ Multipurpose Control Laws Synthesis for Actuators Time Delay

2020 ◽  
Vol 8 (7) ◽  
pp. 477 ◽  
Author(s):  
Evgeny I. Veremey ◽  
Sergei V. Pogozhev ◽  
Margarita V. Sotnikova
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Closed Loop ◽  
Controller Design ◽  
Dynamic Features ◽  
Closed Loop System ◽  
Control Laws ◽  
New Approach ◽  
Feedback Synthesis ◽  
Autopilot Systems

One analytical design problem involves constructing control laws for marine autopilot systems. Despite numerous known solutions, this problem can still be further developed by taking into account the actual conditions of the control system operation. An important issue for discussion is the feedback synthesis for marine ships with time delays in their rudders’ actuators. In this work, a new approach is proposed for providing all the desirable dynamic features of a closed-loop system with autopilot while taking into account the presence of a time delay. This approach is based on the predictive compensation of time delays via the specific transformation of an initially given reference controller with a special multipurpose structure. The applicability and effectiveness of the proposed method is further illustrated by a practical example of a controller design.

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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