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

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
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.

scholarly journals Finite-TimeH∞Control for Time-Delayed Stochastic Systems with Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenhua Gao ◽  
Feiqi Deng ◽  
Ruiqiu Zhang ◽  
Wenhui Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Time Stability ◽  
Finite Time Stability ◽  
Weighting Matrix ◽  
Simulation Results ◽  
Dependent State

This paper studies the problem of finite-timeH∞control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-timeH∞control is obtained. Simulation results illustrate the effectiveness of the proposed method.

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

2019 ◽  
Vol 15 (2) ◽  
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.

Output Feedback Attitude Tracking for Spacecraft Under Control Saturation and Disturbance

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Qinglei Hu ◽  
Boyan Jiang ◽  
Youmin Zhang
Keyword(s):  
Output Feedback ◽  
Finite Time ◽  
External Disturbance ◽  
Input Saturation ◽  
Control Input ◽  
Time Stability ◽  
Finite Time Stability ◽  
Output Feedback Controller ◽  
Attitude Tracking ◽  
Control Saturation

This paper proposes a class of velocity-free attitude stable controller using a novel finite-time observer for spacecraft attitude tracking, which explicitly takes into account control input saturation to assure fast and accurate response and to achieve effective compensation to the effect of external disturbance as well. First, a novel semiglobal finite-time convergent observer is proposed to estimate the angular velocity in a finite-time under external disturbance. Then, a simple global output feedback controller is proposed by adoption of the designed finite-time observer. Rigorous proofs show that the proposed observer can achieve the finite-time stability and the controller rigorously enforces actuator magnitude constraints. Numerical simulations illustrate the spacecraft performance obtained using the proposed controller.

FINITE-TIME SYNCHRONIZATION OF DYNAMICAL NETWORKS COUPLED WITH COMPLEX-VARIABLE CHAOTIC SYSTEMS

2013 ◽  
Vol 24 (09) ◽  
pp. 1350058 ◽  
Author(s):  
ZHAOYAN WU ◽  
QINGLING YE ◽  
DANFENG LIU
Keyword(s):  
Complex Variable ◽  
Finite Time ◽  
Function Method ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Dynamical Networks ◽  
Finite Time Stability ◽  
Lyapunov Function Method

In this paper, finite-time synchronization of dynamical networks coupled with complex-variable chaotic systems is investigated. According to Lyapunov function method and finite-time stability theory, both the dynamical networks without and with coupling delay are considered through designing proper finite-time controllers. Several sufficient conditions for finite-time synchronization are derived and verified to be effective by some numerical examples.

scholarly journals Fuzzy Finite-Time Stability of Chaotic Systems with Time-Varying Delay and Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Dong Li ◽  
Jinde Cao
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Time Varying ◽  
Time Stability ◽  
Parameter Uncertainties ◽  
New Model ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
S Model ◽  
Varying Delay

This paper discusses the finite-time stability of chaotic systems with time-varying delay and parameter uncertainties. A new model based on Takagi-Sugeno (T-S) model is proposed for representing chaotic systems. By the new model, finite-time stability of chaotic systems can be converted into stabilization of fuzzy T-S systems with parameter uncertainties. A sufficient condition is given in terms of matrix inequalities, which guarantees the finite-time stability for fuzzy systems can be achieved. Numerical simulations on the chaotic systems are presented to demonstrate the effectiveness of the theoretical results.

scholarly journals Finite-Time Stability and Stabilization of Switched Linear Time-Varying Systems with Time-Varying Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Lulu Feng ◽  
Ping Zhao
Keyword(s):  
Finite Time ◽  
Linear Time ◽  
Average Dwell Time ◽  
Control Input ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Time Varying Systems ◽  
Varying Delay

This paper deals with the finite-time stability (FTS) of switched linear time-varying (SLTV) systems with time-varying delay. Firstly, based on Lyapunov–Krasovskii functional technique and average dwell time (ADT) approach, a sufficient criterion on FTS for SLTV systems with time-varying delay is obtained. For the SLTV system with delay and control input, based on the criterion, a state feedback controller is designed such that the closed-loop system is finite-time stable (FTS). Finally, an example is employed to illustrate the validity of our results.

Robust Finite-Time Stabilization of Fractional-Order Chaotic Systems based on Fractional Lyapunov Stability Theory

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa
Keyword(s):  
Fractional Order ◽  
Lyapunov Stability ◽  
Finite Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Convergence Time ◽  
Control Approach ◽  
Finite Time Stability

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.

scholarly journals Stabilization with Prescribed Instant for High-Order Integrator Systems

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

<p>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).</p><p>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.</p><p> </p><p>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.<br></p><p></p>

Finite-Time Chaos Control of Lorenz Chaotic System Based on the Passive Control Teachnique

2013 ◽  
Vol 397-400 ◽  
pp. 1345-1350
Author(s):  
Feng Liu
Keyword(s):  
Chaotic System ◽  
Finite Time ◽  
Chaos Control ◽  
Passive Control ◽  
Control Method ◽  
Control Technique ◽  
Time Stability ◽  
Finite Time Stability ◽  
Lorenz Chaotic System ◽  
Robust To Noise

Finite-time chaos control of Lorenz chaotic system applying the passive control method is investigated in this paper. Based on the finite-time stability theory and the passive control technique, the passive controller are proposed to realize finite-time chaos control of Lorenz chaotic system. The controller is robust to noise. Both theoretical and numerical simulations show the effectiveness of the proposed method.

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