Adaptive control method for chaotic power systems based on finite-time stability theory and passivity-based control approach

This paper concerns the problem of stabilization of uncertain fractional-order chaotic systems in finite time. On the basis of fractional Lyapunov stability theory, a robust finite-time fractional controller is introduced to control chaos of fractional-order chaotic systems in the presence of system uncertainties. The finite-time stability of the closed-loop system is analytically proved. An estimation of the convergence time is also given. Some numerical simulations are provided to illustrate the usefulness and applicability of the proposed robust finite-time control approach. It is worth noting that the proposed fractional control method is applicable for stabilizing a broad range of uncertain fractional-order nonlinear systems in a given finite time.

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Finite Time Stability of Finance Systems with or without Market Confidence Using Less Control Input

Mathematical Problems in Engineering ◽

10.1155/2018/7149801 ◽

2018 ◽

Vol 2018 ◽

pp. 1-15 ◽

Cited By ~ 1

Author(s):

Chao Ma ◽

Yujuan Tian ◽

Zhongfeng Qu

Keyword(s):

Finite Time ◽

Chaotic Systems ◽

Control Method ◽

Control Input ◽

Three Dimension ◽

Time Stability ◽

Finance System ◽

Finite Time Stability ◽

Single Controller ◽

Simulation Results

In this paper, we make an exploration of a technique to control a class of finance chaotic systems. This technique allows one to achieve the finite time stability of the finance system more effectively with less control input energy. First, the finite time stability of three dimension finance system without market confidence is analyzed by using a single controller. Then, two controllers are designed to stabilize the four-dimension finance system with market confidence. Moreover, the finite time stability of the three-dimension and four-dimension finance system with unknown parameter is also studied. Finally, simulation results are presented to show the chaotic behaviour of the finance systems, verify the effectiveness of the proposed control method, and illustrate its advantages compared with other methods.

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Partial Finite-Time Stabilization of Perturbed Nonlinear Systems Based on the Novel Concept of Nonsingular Terminal Sliding Mode Method

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4045632 ◽

2019 ◽

Vol 15 (2) ◽

Cited By ~ 1

Author(s):

Hamid Razmjooei ◽

Mohammad Hossein Shafiei

Keyword(s):

Finite Time ◽

Control Method ◽

Sliding Mode ◽

Nonlinear Dynamical System ◽

The Novel ◽

Time Stability ◽

Terminal Sliding Mode ◽

Finite Time Stability ◽

Nonsingular Terminal Sliding Mode ◽

Novel Concept

Abstract In this article, a new technique to design a robust controller to achieve finite-time partial stabilization for a class of nonlinear perturbed systems is proposed. Indeed the system is partially stabilized in a finite time, based on the novel concept of the nonsingular terminal sliding mode (TSM) control method. In the first step, the nonlinear dynamical system is divided into two subsystems based on their required stability properties of the system's states (where finite-time stability is only desired for the first subsystem). Then, using a partial diffeomorphism map to transform the first subsystem into the normal form, the control law is designed. Indeed, by introducing this new concept of the TSM method, robust finite-time stability of only a part of the system's state is guaranteed. Subsequently, simulation results demonstrate the effectiveness of the proposed method, and the results are compared with the existing methods.

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Combined Input–Output Finite-time Stability with H∞ Static Output-feedback Control Approach for Active Suspension

IETE Journal of Research ◽

10.1080/03772063.2021.1973587 ◽

2021 ◽

pp. 1-11

Author(s):

Arivazhagan Anandan ◽

Arunachalam Kandavel

Keyword(s):

Output Feedback ◽

Finite Time ◽

Output Feedback Control ◽

Static Output Feedback ◽

Input Output ◽

Time Stability ◽

Control Approach ◽

Finite Time Stability ◽

Static Output Feedback Control ◽

Static Output

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Finite-Time Synchronization of Singular Hybrid Coupled Networks

Journal of Applied Mathematics ◽

10.1155/2013/378376 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Cong Zheng ◽

Jinde Cao

Keyword(s):

Finite Time ◽

Stability Theory ◽

State Feedback ◽

Time Synchronization ◽

Singular Systems ◽

Sufficient Conditions ◽

Feedback Controller ◽

Time Stability ◽

Finite Time Stability ◽

Coupled Networks

This paper investigates finite-time synchronization of the singular hybrid coupled networks. The singular systems studied in this paper are assumed to be regular and impulse-free. Some sufficient conditions are derived to ensure finite-time synchronization of the singular hybrid coupled networks under a state feedback controller by using finite-time stability theory. A numerical example is finally exploited to show the effectiveness of the obtained results.

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Stabilization with Prescribed Instant for High-Order Integrator Systems

10.36227/techrxiv.14938044 ◽

2021 ◽

Author(s):

Jiyuan Kuang ◽

Jianxing Liu ◽

Yabin Gao ◽

Chih-Chiang Chen ◽

Xiaoju Zhang ◽

...

Keyword(s):

Finite Time ◽

Control Method ◽

Fixed Time ◽

Time Instant ◽

Convergence Time ◽

Human Beings ◽

Time Stability ◽

Finite Time Stability ◽

System States ◽

The Impact

This paper is a research related to finite-time stability. Different from traditional fixed-time, predefined-time, and prescribed time stability that more or less have some conservativeness, we manage to stabilize system states onto the equilibrium at an arbitrarily selected time instant irrespective of initial system states and parameters. In another word, the conservativeness of convergence time in our proposed control method is proved to be zero. Moreover, the control is bounded and also gradually goes to zero at the selected instant. It is obviously an improvement compared with the existing finite-time stabilization (FNTS), such as fixed-time stabilization (FTS), predefined-time stabilization (PDTS), and prescribed-time stabilization (PSTS).The FNTS property is of great interest for scenarios where real-time constraints need to be satisfied, e.g., in missile guidance, the impact time control guidance laws require stabilization in a desired time. Our proposed PSIS can deal with the FNTS problems. For other tasks with more accurate requirement on time, the FTS, the PDTS, and the PSTS are insufficient. For instant, two robot arms playing the piano. Music has its’ rhythm, each note is expected to appear at a specific time instant, or the music will sounds terrible. There are many other tasks that are easy for human beings but difficult for robots, e.g.. dancing and sports. The author think it is because human have rhythm feeling, while robots have not. Hence, it is important to develop such control methodologies.

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Sliding Mode Cooperative Control for Multirobot Systems: A Finite-Time Approach

Mathematical Problems in Engineering ◽

10.1155/2013/450201 ◽

2013 ◽

Vol 2013 ◽

pp. 1-16 ◽

Cited By ~ 5

Author(s):

Masood Ghasemi ◽

Sergey G. Nersesov

Keyword(s):

Steady State ◽

Multiagent Systems ◽

Finite Time ◽

Cooperative Control ◽

Sliding Mode ◽

Laplacian Matrix ◽

Graph Laplacian ◽

Time Stability ◽

Control Approach ◽

Finite Time Stability

Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finite-time stability to apply it to the problem of coordinated motion in multiagent systems. We consider a group of agents described by Euler-Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. We further extend these results to multiagent systems involving underactuated dynamical agents such as mobile wheeled robots. For this case, we show that while the position variables can be coordinated in finite time, the orientation variables converge to the steady states asymptotically. Finally, we validate our results experimentally using a wheeled mobile robot platform.

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Finite-Time Stability Analysis and Control for a Class of Stochastic Singular Biological Economic Systems Based on T-S Fuzzy Model

Abstract and Applied Analysis ◽

10.1155/2013/946491 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 8

Author(s):

Shuangyun Xing ◽

Qingling Zhang ◽

Yi Zhang

Keyword(s):

Finite Time ◽

Fuzzy Systems ◽

Sufficient Conditions ◽

Fuzzy Model ◽

Economic Systems ◽

Time Stability ◽

Control Approach ◽

Finite Time Stability ◽

Stability And Control ◽

And Control

This paper studies the problem of finite-time stability and control for a class of stochastic singular biological economic systems. It shows that such systems exhibit the distinct dynamic behavior when the economic profit is a variable rather than a constant. Firstly, the stochastic singular biological economic systems are established as fuzzy models based on T-S fuzzy control approach. These models are described by stochastic singular T-S fuzzy systems. Then, novel sufficient conditions of finite-time stability are obtained for the stochastic singular biological economic systems, and the state feedback controller is designed so that the population (state of the systems) can be driven to the bounded range by the management of the open resource. Finally, by using Matlab software, numerical examples are given to illustrate the effectiveness of the obtained results.

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Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

Chinese Physics B ◽

10.1088/1674-1056/18/4/019 ◽

2009 ◽

Vol 18 (4) ◽

pp. 1399-1403 ◽

Cited By ~ 20

Author(s):

Wei Du-Qu ◽

Zhang Bo

Keyword(s):

Permanent Magnet ◽

Finite Time ◽

Stability Theory ◽

Permanent Magnet Synchronous Motor ◽

Synchronous Motor ◽

Time Stability ◽

Controlling Chaos ◽

Finite Time Stability

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FINITE-TIME CHAOS SYNCHRONIZATION OF A NEW HYPERCHAOTIC LORENZ SYSTEM

International Journal of Modern Physics B ◽

10.1142/s0217979213500331 ◽

2013 ◽

Vol 27 (09) ◽

pp. 1350033 ◽

Cited By ~ 8

Author(s):

XINGYUAN WANG ◽

XULONG GAO ◽

LULU WANG

Keyword(s):

Theoretical Analysis ◽

Finite Time ◽

Stability Theory ◽

Chaos Synchronization ◽

Lorenz System ◽

Time Stability ◽

Robust Controller ◽

Finite Time Stability ◽

Error System ◽

Hyperchaotic Lorenz System

This paper deals with the finite-time chaos synchronization of a new hyperchaotic Lorenz system. Based on the finite-time stability theory, a simple and robust controller is proposed to realize finite-time chaos synchronization for the hyperchaotic Lorenz system. Theoretical analysis proved that the scheme can ensure the error system globally finite-time stable. Numerical simulations are provided to show the effectiveness of the proposed schemes.

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