Synchronization control of externally disturbed chaotic spacecraft in pre-assigned settling time

2021 ◽  
pp. 095965182110188
Author(s):  
Israr Ahmad ◽  
Muhammad Shafiq
Keyword(s):  
Finite Time ◽  
Closed Loop ◽  
Settling Time ◽  
Synchronization Error ◽  
Computationally Efficient ◽  
Nonlinear Controller ◽  
Time Duration ◽  
Comparative Performance ◽  
Finite Time Stability ◽  
Robust Nonlinear Controller

This article reports the design of a novel finite-time robust nonlinear controller for the synchronization of two identical chaotic spacecraft. The proposed controller does not cancel nonlinear terms appearing in the chaotic spacecraft dynamics. Avoiding the cancelation of the nonlinear terms of the plant by the controller makes the closed-loop robust stable in the presence of uncertainties in the chaotic spacecraft parameters; this concept blooms base for the design of computationally efficient simple control law. The proposed finite-time robust nonlinear controller (1) synchronizes two nearly identical chaotic spacecraft in finite-time duration, (2) expedites the convergence of errors vector to zero without oscillation, and (3) eradicates the effects of external disturbances. Analysis based on the Lyapunov second theorem proves that the synchronization error converges fast and verifying the closed-loop’s robust global stability. The finite-time stability technique affirms the convergence of the synchronization error to zero in settling time. This research article also studies the effects of the exogenous disturbances and the controller parameter’s slowly smooth variations on the closed-loop performance. The controller parameter variation analysis sets the procedure for tuning the controller parameters. The computer-based simulation results validate the theoretical findings and provide a comparative performance analysis with the other recently proposed synchronization feedback controllers. This article uses Mathematica 12.0 version in the Microsoft 10 environment for all the simulations.

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Wenping Xue ◽  
Kangji Li
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Initial State ◽  
Finite Time Stability ◽  
Time Linear

In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

scholarly journals Finite-Time Stabilization and Destabilization Analysis of Quaternion-Valued Neural Networks with Discrete Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Huiling Duan ◽  
Tao Peng ◽  
Zhengwen Tu ◽  
Jianlong Qiu
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Time Interval ◽  
Nonlinear Controller ◽  
Finite Time Stability ◽  
Stability And Instability ◽  
Discrete Delays ◽  
Finite Time Stabilization ◽  
Matrix Differential ◽  
Vector Matrix

In this paper, the finite-time stabilization and destabilization of a class of quaternion-valued neural networks (QVNNs) with discrete delays are investigated. In order to surmount the difficulty of noncommutativity of quaternion, a new vector matrix differential equation (VMDE) is proposed by employing decomposition method. And then, a nonlinear controller is designed to stabilize the VMDE in a finite-time interval. Furthermore, under that controller, the finite-time stability and instability of the QVNNs are analyzed via Lyapunov function approach, and two criteria are derived, respectively; furthermore, the settling time is also estimated. At last, by two illustrative examples we verify the correctness of the conclusions.

Finite-time feedback control of an input-delay system with nonlinear saturating actuators

2017 ◽  
Vol 40 (10) ◽  
pp. 3059-3067 ◽  
Author(s):  
Xiangze Lin ◽  
Shuaiting Huang ◽  
Shihua Li ◽  
Yun Zou
Keyword(s):  
Feedback Control ◽  
Finite Time ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Delay System ◽  
Input Delay ◽  
Comparison Function ◽  
Finite Time Stability ◽  
Closed Loop Systems ◽  
Saturating Actuators

Finite-time feedback control of input-delay system with nonlinear saturating actuators is addressed in this paper. First, a state feedback controller is designed to make the closed-loop systems finite-time stable. Sufficient conditions which can guarantee finite-time stability of an input-delay system with saturating actuators are given in terms of the comparison function method. For the case where the states cannot be measured, an observer is presented to estimate the unavailable states and the observer-controller compensator strategy is proposed. Finally, an example is employed to illustrate the efficiency of the proposed method. It is not difficult to conclude from the analysis and the simulation results that by virtue of the proposed method the transient characteristics of the closed-loop system can be easily guaranteed to comply with the requirements of the practice.

scholarly journals Disturbance Observer-Based Continuous Finite-Time Sliding Mode Control against Matched and Mismatched Disturbances

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Ngo Phong Nguyen ◽  
Hyondong Oh ◽  
Yoonsoo Kim ◽  
Jun Moon
Keyword(s):  
Finite Time ◽  
Disturbance Observer ◽  
Closed Loop ◽  
Sliding Mode ◽  
Loop System ◽  
Time Varying ◽  
Time Stability ◽  
Closed Loop System ◽  
Finite Time Stability ◽  
Mismatched Disturbances

In this paper, we propose the disturbance observer-based continuous finite-time sliding mode controller (DOBCSMC) for input-affine nonlinear systems in which additive matched and mismatched disturbances exist. The objective is to show the robustness and disturbance attenuation performance of the closed-loop system with the proposed DOBCSMC subjected to general classes of matched and mismatched disturbances. The proposed DOBCSMC consists of three main features: (i) the nonlinear finite-time disturbance observer to obtain a fast and accurate estimation of matched and mismatched disturbances, (ii) the nonlinear sliding surface to ensure high precision in the steady-state phase of the controlled output, and (iii) the continuous supertwisting algorithm to guarantee finite-time convergence of the controlled output and reduce the chattering under the effect of matched and mismatched disturbances. It should be noted that the existing approaches cannot handle time-varying mismatched disturbances and/or cannot guarantee faster finite-time stability of the controlled output. We prove that the closed-loop system with the DOBCSMC guarantees both finite-time reachability to the sliding surface and finite-time stability of the controlled output to the origin. Various simulations are performed to demonstrate the effectiveness of the proposed DOBCSMC. In particular, the simulation results show that the DOBCSMC guarantees faster convergence of the closed-loop system to the origin, higher precision of the controlled output, and better robustness performance against various classes of (time-varying) matched and mismatched disturbances, compared with the existing approaches.

scholarly journals Finite-Time Vibration-Attenuation Controller Design for Structural Systems with Parameter Uncertainties

2014 ◽  
Vol 6 ◽  
pp. 673174 ◽  
Author(s):  
Yuanchun Ding ◽  
Falu Weng ◽  
Ji Ge ◽  
Liming Liang ◽  
Guoliang Yang
Keyword(s):  
Finite Time ◽  
Closed Loop ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Structural Systems ◽  
Time Stability ◽  
Parameter Uncertainties ◽  
Finite Time Stability ◽  
Vibration Attenuation

The problem of finite-time vibration-attenuation controller design for buildings structural systems with parameter uncertainties is the concern of this paper. The objective of designing controllers is to guarantee the finite-time stability of closed-loop systems with a prescribed level of disturbance attenuation. First, based on matrix transformation, the structural system is described as state-space model, which contains parameter uncertainties. Then, based on finite-time stability analysis method, some sufficient conditions for the existence of finite-time vibration-attenuation controllers are obtained. By solving these conditions, the desired controllers can be obtained for the closed-loop system to be finite-time stable with the performance ∥ z∥2 < γ∥ω∥2. It is shown by the simulation results, that compared with some Lyapunov asymptotic stability results, finite-time stability control can obtain better state responses, especially while the system is under nonzero initial states.

Finite-time disturbance observer based-control of flexible spacecraft

2021 ◽  
pp. 107754632110476
Author(s):  
Yasaman Hajnorouzali ◽  
Maryam Malekzadeh ◽  
Mohammad Ataei
Keyword(s):  
Finite Time ◽  
Disturbance Observer ◽  
Closed Loop ◽  
External Disturbance ◽  
Lyapunov Theory ◽  
Flexible Spacecraft ◽  
Mode Shapes ◽  
Sliding Surface ◽  
Finite Time Stability ◽  
The Difference

This paper aims to design an attitude controller for a flexible spacecraft under external disturbance and uncertainty. The spacecraft’s attitude is controlled by a super twisting controller based on a disturbance observer. This paper’s spacecraft system is non-minimum phase since mode-shapes are included in the output; thus, the following four methods are designed to compensate for the constraint: (1) The output redefinition method, where outputs are redefined as a combination of mode-shapes and quaternions. (2) The flexible spacecraft is controlled without measuring the mode-shapes, and only the quaternion parameters are selected as the output. (3) An advanced sliding surface is proposed, in which the mode-shapes are considered in the sliding surface. (4) The difference between flexible and rigid spacecraft dynamics is considered as disturbance, and its effect on the system is compensated. The finite-time stability of the closed-loop system is proved by leveraging the Lyapunov theory. The numerical simulation illustrates the closed-loop system’s effectiveness in terms of robustness compared to the existing controller and the four mentioned methods.

Nested saturation control for overhead crane systems

2011 ◽  
Vol 34 (7) ◽  
pp. 862-875 ◽  
Author(s):  
Rongjie Liu ◽  
Shihua Li ◽  
Shihong Ding
Keyword(s):  
Finite Time ◽  
Closed Loop ◽  
Overhead Crane ◽  
Time Stability ◽  
Closed Loop System ◽  
Triangular Form ◽  
Saturation Control ◽  
Finite Time Stability ◽  
Adding A Power Integrator ◽  
Power Integrator

This paper presents a new control strategy for overhead crane systems. First, by utilizing a coordinate change, the underactuated overhead crane dynamical model can be transformed into an upper-triangular form. Second, a finite-time controller is designed based on the nonlinear nested saturation and adding a power integrator technique. Rigorous proof shows that the controller can guarantee finite-time stability of the closed-loop system. Simulations show the effectiveness of the proposed method.

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