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.

scholarly journals Low-Complexity Adaptive Saturated Control of a Class of Nonlinear Systems with Its Application

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Gang Zhang ◽  
Deqiang Cheng ◽  
Qiqi Kou
Keyword(s):  
Nonlinear Systems ◽  
Dead Zone ◽  
External Disturbance ◽  
Original System ◽  
Low Complexity ◽  
Control Law ◽  
Zone Model ◽  
Time Varying ◽  
Saturated Control ◽  
Output Constraint

This paper investigates a low-complexity saturated control law for a class of nonlinear systems with consideration of the time-varying output constraint, control constraint, and external disturbance. First, a dead-zone model is employed to transform the control saturation nonlinearity into a linear one with respect to the real input signal. Then, the original system with time-varying output constraint is transformed into a constraint-free one, based on which a novel adaptive saturated control law is devised along the filtered error manifold. By employing minimum learning parameter technique and virtual error concept, only two adaptive parameters are needed to update online, which reduces the computational burdens dramatically. Finally, the applications to Duffing-Holmes chaotic system are organized to validate the effectiveness of the proposed control law.

Compensation of Time-Varying Input and State Delays for Nonlinear Systems

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Nikolaos Bekiaris-Liberis ◽  
Miroslav Krstic
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Time Varying ◽  
Feedback Systems ◽  
Feedback Controllers ◽  
Stabilizing Controller ◽  
Numerical Examples ◽  
Infinite Dimensional ◽  
State Delays ◽  
Main Challenge

We consider general nonlinear systems with time-varying input and state delays for which we design predictor-based feedback controllers. Based on a time-varying infinite-dimensional backstepping transformation that we introduce, our controller achieves global asymptotic stability in the presence of a time-varying input delay, which is proved with the aid of a strict Lyapunov function that we construct. Then, we “backstep” one time-varying integrator and we design a globally stabilizing controller for nonlinear strict-feedback systems with time-varying delays on the virtual inputs. The main challenge in this case is the construction of the backstepping transformations since the predictors for different states use different prediction windows. Our designs are illustrated by three numerical examples, including unicycle stabilization.

scholarly journals Asymptotic Stabilization by State Feedback for a Class of Stochastic Nonlinear Systems with Time-Varying Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui Wang ◽  
Wuquan Li ◽  
Xiuhong Wang
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Original System ◽  
Feedback Stabilization ◽  
Stochastic Nonlinear Systems ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Control Coefficients

This paper investigates the problem of state-feedback stabilization for a class of upper-triangular stochastic nonlinear systems with time-varying control coefficients. By introducing effective coordinates, the original system is transformed into an equivalent one with tunable gain. After that, by using the low gain homogeneous domination technique and choosing the low gain parameter skillfully, the closed-loop system can be proved to be globally asymptotically stable in probability. The efficiency of the state-feedback controller is demonstrated by a simulation example.

scholarly journals Global Stability of Positive Discrete-time Time-varying Nonlinear Feedback Systems

2021 ◽  
Vol 3 (1) ◽  
pp. 17-20
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Global Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Positive Time

The global stability of positive  discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.

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 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.

scholarly journals Non-Recursive Adaptive Control Design Methodology for Nonlinear Systems With Mismatched Time-Varying Disturbances

2021 ◽  
Author(s):  
Xin Dong ◽  
Zhang Chuanlin ◽  
Chenggang Cui
Keyword(s):  
Adaptive Control ◽  
Stability Analysis ◽  
Nonlinear Systems ◽  
Sliding Mode ◽  
Design Procedure ◽  
Control Design ◽  
Original System ◽  
Time Varying ◽  
Transient Time ◽  
Control Scheme

Abstract This paper proposes a non-recursive adaptive control scheme for a class of lower-triangular nonlinear systems with mismatched time-varying disturbances. As a result, an exact tracking control scheme is constructed straightforwardly from the system in a novel non-recursive synthesis manner. Firstly, with the help of higher-order sliding mode observer (HOSMO), the original system is delicately transformed into an equivalent stabilizable system. Then, a non-recursive stabilizer with a simple update mechanism for the dynamic gain can be derived. Subsequently, a rigorous stability analysis shows the theoretical justification of the proposed design framework. New characteristics of the proposed algorithm are mainly twofold: 1) The proposed adaption mechanism could substantially adjust the transient-time performance with the presence of different levels of disturbances. 2) The composite control design procedure is essentially detached with stability analysis, which could largely facilitate practical implementations.

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