scholarly journals Finite-Time Stabilization for a Class of Nonlinear Differential-Algebraic Systems Subject to Disturbance

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaohui Mo ◽  
Huawei Niu ◽  
Qixun Lan
Keyword(s):  
Finite Time ◽  
External Disturbance ◽  
Design Procedure ◽  
Homogeneous System ◽  
Algebraic Systems ◽  
Control Approach ◽  
Adding A Power Integrator ◽  
Time Control ◽  
Finite Time Stabilization ◽  
Nominal Performance

In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs) subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC) is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC) law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO) is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach.

scholarly journals Finite-Time Stabilization of Stochastic Nonholonomic Systems and Its Application to Mobile Robot

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Fangzheng Gao ◽  
Fushun Yuan
Keyword(s):  
Mobile Robot ◽  
Finite Time ◽  
Controller Design ◽  
Design Procedure ◽  
Nonholonomic Systems ◽  
Finite Time Stability ◽  
Adding A Power Integrator ◽  
Time Control ◽  
Finite Time Stabilization ◽  
System States

This paper investigates the problem of finite-time stabilization for a class of stochastic nonholonomic systems in chained form. By using stochastic finite-time stability theorem and the method of adding a power integrator, a recursive controller design procedure in the stochastic setting is developed. Based on switching strategy to overcome the uncontrollability problem associated withx0(0)=0, global stochastic finite-time regulation of the closed-loop system states is achieved. The proposed scheme can be applied to the finite-time control of nonholonomic mobile robot subject to stochastic disturbances. The simulation results demonstrate the validity of the presented algorithm.

scholarly journals Global Finite-Time Stabilization Problem of Affine Nonlinear Systems with Unknown Functions

2021 ◽  
Author(s):  
Fujin Jia ◽  
Junwei Lu ◽  
Yong-Min Li ◽  
Fangyuan Li
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Control Algorithm ◽  
Lyapunov Analysis ◽  
Stabilization Problem ◽  
Analysis Method ◽  
Control Approach ◽  
Affine Nonlinear Systems ◽  
Simulation Results ◽  
Finite Time Stabilization

In this paper, the global finite-time stabilization (FTS) of nonlinear systems with unknown functions (UFs) is studied. Firstly, in order to deal with UFs, a Lemma is proposed to avoid the Assumptions of UFs. Secondly, based on this Lemma, the control algorithm designed by using backstepping has no partial derivative of virtual controllers, so it avoids the “differential explosion” problem of backstepping. Thirdly, by using Lyapunov analysis method, backstepping and FTS method, a global FTS control algorithm of nonlinear systems with UFs is proposed. Finally, the feasibility of developed control approach is illustrated by the simulation results of a manipulator.

Finite-Time Disturbance Observer Design and Attitude Tracking Control of a Rigid Spacecraft

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Qixun Lan ◽  
Chunjiang Qian ◽  
Shihua Li
Keyword(s):  
Finite Time ◽  
Disturbance Observer ◽  
Observer Design ◽  
Design Approach ◽  
Control Approach ◽  
Time Control ◽  
Time Simulation ◽  
Attitude Tracking ◽  
Rigid Spacecraft ◽  
Attitude Tracking Control

This paper considers the problem of finite-time disturbance observer (FTDO) design and the problem of FTDO based finite-time control for systems subject to nonvanishing disturbances. First of all, based on the homogeneous systems theory and saturation technique, a continuous FTDO design approach is proposed. Then, by using the proposed FTDO design approach, a FTDO is constructed to estimate the disturbances that exist in a rigid spacecraft system. Furthermore, based on a baseline finite-time control law and a feedforward compensation term produced by the FTDO, a composite controller is constructed for the rigid spacecraft system. It is shown that the proposed composite controller will render the rigid spacecraft track the desired attitude trajectory in a finite-time. Simulation results are included to demonstrate the effectiveness of the proposed control approach.

scholarly journals Adaptive Finite-Time Control on SE(3) for Spacecraft Final Proximity Maneuvers with Input Quantization

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Sai Zhang ◽  
Zhen Yang
Keyword(s):  
Finite Time ◽  
Tracking System ◽  
Integrated Control ◽  
External Disturbance ◽  
Uniform Motion ◽  
Input Quantization ◽  
Time Control ◽  
Control Precision ◽  
One Step ◽  
Rendezvous And Docking

In this paper, a bounded finite-time control strategy is developed for the final proximity maneuver of spacecraft rendezvous and docking exposed to external disturbance and input quantization. To realize the integrated control for spacecraft final proximity operation, the coupling kinematics and dynamics of attitude and position are modeled by feat of Lie group SE 3 . With a view to improving the convergence rate and reducing the chattering, an adaptive finite-time controller is proposed for the error tracking system with one-step theoretical proof of stability. Meanwhile, the hysteresis logarithmic quantizer is implemented to effectively reduce the frequency of data transmission and the quantization errors are reduced under the proposed controller. The algorithms outlined above are based on an integrated model expressed by SE 3 and denoted by uniform motion states, which can simplify the design progress and improve control precision. Finally, simulations are provided to exhibit the effectiveness and advantages of the designed strategy.

scholarly journals Distributed Formation Control for Multiple Quadrotor Based on Multi-Agent Theory and Disturbance Observer

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaohua Zhang ◽  
Junli Gao ◽  
Wenfeng Zhang ◽  
Tao Zeng ◽  
Liping Ye
Keyword(s):  
Finite Time ◽  
Formation Control ◽  
Control Method ◽  
Homogeneous System ◽  
Lyapunov Theory ◽  
Uncertain Parameters ◽  
External Disturbances ◽  
Agent Theory ◽  
Time Control ◽  
Multi Agent

This paper presents the disturbance observers-based distributed formation control for multiple quadrotor aircrafts with external disturbances and uncertain parameters using multi-agent theory and finite-time control method. Firstly, the finite-time disturbance observers are proposed to handle the external disturbances on the position-loop. Similarly, when there are both the uncertain parameters and external disturbances on the attitude-loop, the finite-time disturbance observers are designed to estimate the total lump disturbances. By skillfully using homogeneous system theory, Lyapunov theory, and multi-agent theory, the distributed formation control algorithms are developed. Finally, through simulations, the efficiency of the proposed method (including the convergence rate and disturbance rejection) is verified.

scholarly journals Further Result on Finite-Time Stabilization of Stochastic Nonholonomic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Fangzheng Gao ◽  
Fushun Yuan ◽  
Jian Zhang ◽  
Yuqiang Wu
Keyword(s):  
Finite Time ◽  
Design Method ◽  
Nonholonomic Systems ◽  
Feedback Stabilization ◽  
Stochastic Disturbance ◽  
Adding A Power Integrator ◽  
Time Control ◽  
Switching Control Strategy ◽  
Power Integrator ◽  
Theoretical Results

This paper further investigates the problem of finite-time state feedback stabilization for a class of stochastic nonholonomic systems in chained form. Compared with the existing literature, the stochastic nonholonomic systems under investigation have more uncertainties, such as thex0-subsystem contains stochastic disturbance. This renders the existing finite-time control methods highly difficult to the control problem of the systems or even inapplicable. In this paper, by extending adding a power integrator design method to a stochastic system and by skillfully constructingC2Lyapunov function, a novel switching control strategy is proposed, which renders that the states of closed-loop system are almost surely regulated to zero in a finite time. A simulation example is provided to demonstrate the effectiveness of the theoretical results.

scholarly journals Finite-Time Control of Singular Linear Semi-Markov Jump Systems

Algorithms ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 8
Author(s):  
Xiaofu Ji ◽  
Xuehua Liu
Keyword(s):  
Finite Time ◽  
Controller Design ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
One Dimensional ◽  
Time Control ◽  
Jump Systems

The problem of finite-time control for singular linear semi-Markov jump systems (SMJSs) with unknown transition rates is considered in this paper. By designing a new semi-positive definite Lyapunov-like function, state feedback controller design methods are given that allow closed-loop singular linear SMJSs to be regular, impulse-free and stochastically finite-time-stable without external disturbance, and stochastically finite-time bounded with external disturbance. The obtained conditions are expressed by a set of strict matrix inequalities, which can be simplified to a set of linear matrix inequalities by a one dimensional search for a scalar. Two numerical examples are given to illustrate the effectiveness of proposed method.

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