Stabilization with Prescribed Instant for High-Order Integrator Systems

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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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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Finite-Time Stabilization of Large-Scale Impulsive Dynamical Systems

Stability and Control of Large-Scale Dynamical Systems ◽

10.23943/princeton/9780691153469.003.0012 ◽

2011 ◽

Author(s):

Wassim M. Haddad ◽

Sergey G. Nersesov

Keyword(s):

Dynamical Systems ◽

Finite Time ◽

Large Scale ◽

Sufficient Conditions ◽

Time Stability ◽

Finite Time Stability ◽

Lipschitz Continuous ◽

Time Dynamics ◽

Stabilizing Controllers ◽

System States

This chapter describes sufficient conditions for finite-time stability of nonlinear impulsive dynamical systems. For impulsive dynamical systems, it may be possible to reset the system states to an equilibrium state, in which case finite-time convergence of the system trajectories can be achieved without the requirement of non-Lipschitzian dynamics. Furthermore, due to system resettings, impulsive dynamical systems may exhibit non-uniqueness of solutions in reverse time even when the continuous-time dynamics are Lipschitz continuous. The chapter presents stability results using vector Lyapunov functions wherein finite-time stability of the impulsive system is guaranteed via finite-time stability of a hybrid vector comparison system. These results are used to develop hybrid finite-time stabilizing controllers for impulsive dynamical systems. Decentralized finite-time stabilizers for large-scale impulsive dynamical systems are also constructed. Finally, it gives a numerical example to illustrate the utility of the proposed framework.

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

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2018.05.005 ◽

2018 ◽

Vol 112 ◽

pp. 159-167 ◽

Cited By ~ 10

Author(s):

Cong Wang ◽

Hongli Zhang ◽

Wenhui Fan ◽

Ping Ma

Keyword(s):

Adaptive Control ◽

Power Systems ◽

Finite Time ◽

Stability Theory ◽

Control Method ◽

Time Stability ◽

Control Approach ◽

Finite Time Stability ◽

Passivity Based Control

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

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4005323 ◽

2012 ◽

Vol 7 (2) ◽

Cited By ~ 41

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.

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Continuous-Time Optimization of Time-Varying Cost Functions via Finite-Time Stability with Pre-Defined Convergence Time

2020 American Control Conference (ACC) ◽

10.23919/acc45564.2020.9147809 ◽

2020 ◽

Author(s):

Orlando Romero ◽

Mouhacine Benosman

Keyword(s):

Continuous Time ◽

Finite Time ◽

Convergence Time ◽

Cost Functions ◽

Time Varying ◽

Time Stability ◽

Finite Time Stability ◽

Time Optimization

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.397-400.1345 ◽

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.385-386.945 ◽

2013 ◽

Vol 385-386 ◽

pp. 945-950 ◽

Cited By ~ 1

Author(s):

Yi Feng Wei

Keyword(s):

Chaotic System ◽

Finite Time ◽

Chaos Synchronization ◽

Passive Control ◽

Control Method ◽

Control Technique ◽

Time Stability ◽

Finite Time Stability ◽

Lorenz Chaotic System ◽

Robust To Noise

Finite-time chaos synchronization 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 synchronization of Lorenz chaotic system. The controller is simple and robust to noise. Both theoretical and numerical simulations show the effectiveness of the proposed method.

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