The Experts below are selected from a list of 1908 Experts worldwide ranked by ideXlab platform

Jianxin Xu - One of the best experts on this subject based on the ideXlab platform.

  • composite energy function based iterative learning control for systems with nonparametric uncertainties
    International Journal of Adaptive Control and Signal Processing, 2014
    Co-Authors: Jianxin Xu, Deqing Huang
    Abstract:

    SUMMARY In this work, we propose new iterative learning control (ILC) schemes that deal with nonlinear multi-input multi-output systems under alignment Condition with nonparametric uncertainties. A major contribution of this work is to remove the classical resetting Condition. Another major contribution of this work is to deal with norm-bounded nonlinear uncertainties that satisfy Local Lipschitz Condition, in particular to deal with nonlinear uncertain state-dependent input gain matrix that could be non-square left invertible and Local Lipschitzian. Two types of composite energy function are proposed to facilitate the ILC design and property analysis. Through rigorous analysis, we show that the new ILC schemes proposed warrant the asymptotical tracking convergence of system states. In the end, an illustrative example is provided to demonstrate the efficacy of the proposed ILC scheme. Copyright © 2013 John Wiley & Sons, Ltd.

  • iterative learning control for output constrained systems with both parametric and nonparametric uncertainties
    Automatica, 2013
    Co-Authors: Jianxin Xu
    Abstract:

    In this work, by proposing a Barrier Composite Energy Function (BCEF) method with a novel Barrier Lyapunov Function (BLF), we present a new iterative learning control (ILC) scheme for a class of single-input single-output (SISO) high order nonlinear systems to deal with output-constrained problems under alignment Condition with both parametric and nonparametric system uncertainties. Nonparametric uncertainties such as norm-bounded nonlinear uncertainties satisfying Local Lipschitz Condition can be effectively handled. Backstepping design with the newly proposed BLF is incorporated in analysis to ensure output constraint not violated. Through rigorous analysis, we show that under this new ILC scheme, uniform convergence of state tracking error is guaranteed. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed ILC scheme.

  • state constrained iterative learning control for a class of mimo systems
    IEEE Transactions on Automatic Control, 2013
    Co-Authors: Jianxin Xu
    Abstract:

    In this note, we present a novel iterative learning control (ILC) method for a class of state-constrained multi-input multi-output (MIMO) nonlinear system under state alignment Condition with both parametric and nonparametric uncertainties. Nonparametric uncertainties such as norm-bounded nonlinear uncertainties satisfying Local Lipschitz Condition can be effectively handled. Barrier Composite Energy Function (BCEF) scheme with a novel Barrier Lyapunov Function is proposed to facilitate the analysis of state tracking error convergence while satisfying the state constraints. In the end, an illustrative example is shown to demonstrate the efficacy of the proposed ILC method.

Mao Xuerong - One of the best experts on this subject based on the ideXlab platform.

  • Truncated EM numerical method for generalised Ait-Sahalia-type interest rate model with delay
    'Elsevier BV', 2021
    Co-Authors: Coffie Emmanuel, Mao Xuerong
    Abstract:

    The original Ait-Sahalia model of the spot interest rate proposed by Ait-Sahalia assumes constant volatility. As supported by several empirical studies, volatility is never constant in most financial markets. From application viewpoint, it is important we generalise the Ait-Sahalia model to incorporate volatility as a function of delay in the spot rate. In this paper, we study analytical properties for the true solution of this model and construct several new techniques of the truncated Euler-Maruyama (EM) method to study properties of the numerical solutions under the Local Lipschitz Condition plus Khasminskii-type Condition. Finally, we justify that the truncated EM approximate solution can be used within a Monte Carlo scheme for numerical valuations of some financial instruments such as options and bonds

  • The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise
    'Elsevier BV', 2020
    Co-Authors: Mao Wei, Hu Liangjian, Mao Xuerong
    Abstract:

    The main aim of this paper is to investigate the asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise (HSSwPDLNs). Under the Local Lipschitz Condition and non-linear growth Condition, we investigate the existence and uniqueness of the solution to HSSwPDLNs. By using the Lyapunov functions and M-matrix theory, we establish some sufficient Conditions on the asymptotic stability and polynomial stability for HSSwPDLNs. Finally, two examples are provided to illustrate our results

  • On exponential stability of hybrid neutral stochastic differential delay equations with different structures
    2020
    Co-Authors: Wu A., Mao Wei, Mao Xuerong, You Surong, Hu Liangjian
    Abstract:

    This article discusses the problem of exponential stability for a class of hybrid neutral stochastic differential delay equations with highly nonlinear coeffcients and different structures in different switching modes. In such systems, the coeffcients will satisfy the Local Lipschitz Condition and suitable Khasminskii-types Conditions. The set of switching states will be divided into two subsets. In different subsets, the coeffcients will be dominated by polynomials with different degrees. By virtue of M-matrices and suitable Lyapunov functions dependent on coeffcient structures and switching modes, some results including the existence-and-uniqueness, boundedness and exponential stability of the solution are proposed and prove

  • Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching
    2019
    Co-Authors: Mao Wei, Hu Liangjian, Mao Xuerong
    Abstract:

    This paper focuses on the general decay stability of nonlinear neutral stochastic pantograph equations with Markovian switching (NSPEwMSs). Under the Local Lipschitz Condition and non-linear growth Condition, the existence and almost sure stability with general decay of the solution for NSPEwMSs are investigated. By means of M-matrix theory, some sufficient Conditions on the general decay stability are also established for NSPEwMSs

  • Basic theory and stability analysis for neutral stochastic functional differential equations with pure jumps
    'Springer Science and Business Media LLC', 2019
    Co-Authors: Li Mengling, Deng Feiqi, Mao Xuerong
    Abstract:

    This paper investigates the existence and uniqueness of solutions to neutral stochastic functional differential equations with pure jumps (NSFDEwPJs). The boundedness and almost sure exponential stability are also considered. In general, the classical existence and uniqueness theorem of solutions can be obtained under a Local Lipschitz Condition and linear growth Condition. However, there are many equations that do not obey the linear growth Condition. Therefore, our first aim is to establish new theorems where the linear growth Condition is no longer required whereas the upper bound for the diffusion operator will play a leading role. Moreover, the pth moment boundedness and almost sure exponential stability are also obtained under some loose Conditions. Finally, we present two examples to illustrate the effectiveness of our results

Minghui Song - One of the best experts on this subject based on the ideXlab platform.

Hu Liangjian - One of the best experts on this subject based on the ideXlab platform.

  • On exponential stability of hybrid neutral stochastic differential delay equations with different structures
    2020
    Co-Authors: Wu A., Mao Wei, Mao Xuerong, You Surong, Hu Liangjian
    Abstract:

    This article discusses the problem of exponential stability for a class of hybrid neutral stochastic differential delay equations with highly nonlinear coeffcients and different structures in different switching modes. In such systems, the coeffcients will satisfy the Local Lipschitz Condition and suitable Khasminskii-types Conditions. The set of switching states will be divided into two subsets. In different subsets, the coeffcients will be dominated by polynomials with different degrees. By virtue of M-matrices and suitable Lyapunov functions dependent on coeffcient structures and switching modes, some results including the existence-and-uniqueness, boundedness and exponential stability of the solution are proposed and prove

  • The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise
    'Elsevier BV', 2020
    Co-Authors: Mao Wei, Hu Liangjian, Mao Xuerong
    Abstract:

    The main aim of this paper is to investigate the asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise (HSSwPDLNs). Under the Local Lipschitz Condition and non-linear growth Condition, we investigate the existence and uniqueness of the solution to HSSwPDLNs. By using the Lyapunov functions and M-matrix theory, we establish some sufficient Conditions on the asymptotic stability and polynomial stability for HSSwPDLNs. Finally, two examples are provided to illustrate our results

  • Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching
    2019
    Co-Authors: Mao Wei, Hu Liangjian, Mao Xuerong
    Abstract:

    This paper focuses on the general decay stability of nonlinear neutral stochastic pantograph equations with Markovian switching (NSPEwMSs). Under the Local Lipschitz Condition and non-linear growth Condition, the existence and almost sure stability with general decay of the solution for NSPEwMSs are investigated. By means of M-matrix theory, some sufficient Conditions on the general decay stability are also established for NSPEwMSs

  • Convergence rate and stability of the truncated Euler-Maruyama method for stochastic differential equations
    'Elsevier BV', 2018
    Co-Authors: Hu Liangjian, Li Xiaoyue, Mao Xuerong
    Abstract:

    Recently, Mao [13] developed a new explicit method, called the truncated Euler- Maruyama (EM) method, for the nonlinear SDE and established the strong convergence theory under the Local Lipschitz Condition plus the Khasminskii-type Condition. In his another follow-up paper [14], he discussed the rates of Lq -convergence of the truncated EM method for q ≥ 2 and showed that the order of Lq-convergence can be arbitrarily close to q/2 under some additional Conditions. However, there are some restrictions on the truncation functions and these restrictions sometimes might force the step size to be so small that the truncated EM method would be inapplicable. The key aim of this paper is to establish the convergence rate without these restrictions. The other aim is to study the stability of the truncated EM method. The advantages of our new results will be highlighted by the comparisons with the results in [13, 14] as well as others on the tamed EM and implicit methods

Xuerong Mao - One of the best experts on this subject based on the ideXlab platform.

  • neutral stochastic functional differential equations with levy jumps under the Local Lipschitz Condition
    Advances in Difference Equations, 2017
    Co-Authors: Wei Mao, Xuerong Mao
    Abstract:

    In this paper, a general neutral stochastic functional differential equations with infinite delay and Levy jumps (NSFDEwLJs) is studied. We investigate the existence and uniqueness of solutions to NSFDEwLJs at the phase space $C_{g}$ under the Local Caratheodory type Conditions. Meanwhile, we also give the exponential estimates and almost surely asymptotic estimates of solutions to NSFDEwLJs.

  • convergence rates of the truncated euler maruyama method for stochastic differential equations
    Journal of Computational and Applied Mathematics, 2016
    Co-Authors: Xuerong Mao
    Abstract:

    Influenced by Higham et?al. (2002), several numerical methods have been developed to study the strong convergence of the numerical solutions to stochastic differential equations (SDEs) under the Local Lipschitz Condition. These numerical methods include the tamed Euler-Maruyama (EM) method, the tamed Milstein method, the stopped EM, the backward EM, the backward forward EM, etc. Recently, we developed a new explicit method in Mao (2015), called the truncated EM method, for the nonlinear SDE d x ( t ) = f ( x ( t ) ) d t + g ( x ( t ) ) d B ( t ) and established the strong convergence theory under the Local Lipschitz Condition plus the Khasminskii-type Condition x T f ( x ) + p - 1 2 | g ( x ) | 2 ? K ( 1 + | x | 2 ) . However, due to the page limit there, we did not study the convergence rates for the method, which is the aim of this paper. We will, under some additional Conditions, discuss the rates of L q -convergence of the truncated EM method for 2 ? q < p and show that the order of L q -convergence can be arbitrarily close to q / 2 .

  • the truncated euler maruyama method for stochastic differential equations
    Journal of Computational and Applied Mathematics, 2015
    Co-Authors: Xuerong Mao
    Abstract:

    Influenced by Higham et?al. (2003), several numerical methods have been developed to study the strong convergence of the numerical solutions to stochastic differential equations (SDEs) under the Local Lipschitz Condition. These numerical methods include the tamed Euler-Maruyama (EM) method, the tamed Milstein method, the stopped EM, the backward EM, the backward forward EM, etc. In this paper we will develop a new explicit method, called the truncated EM method, for the nonlinear SDE d x ( t ) = f ( x ( t ) ) d t + g ( x ( t ) ) d B ( t ) and establish the strong convergence theory under the Local Lipschitz Condition plus the Khasminskii-type Condition x T f ( x ) + p - 1 2 ? g ( x ) ? 2 ? K ( 1 + ? x ? 2 ) . The type of convergence specifically addressed in this paper is strong- L q convergence for 2 ? q < p , and p is a parameter in the Khasminskii-type Condition.