New Approach to Observer-Based Finite-Time H_(∞)Control of Discrete-Time One-Sided Lipschitz Systems with Uncertainties

This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditions,the authors derive less conservative criterion for the controller design and observer design.A new criterion is proposed to ensure the closed-loop system is finite-time bounded(FTB).The sufficient conditions are established to ensure the closed-loop system is H_(∞)finite-time bounded(H_(∞)FTB)in terms of matrix inequalities.The controller gains and observer gains are given.A numerical example is provided to demonstrate the effectiveness of the proposed results.

Anti-windup-based Dynamic Controller Synthesis for Lipschitz Systems under Actuator Saturation

This paper presents a new method for simultaneous synthesis of dynamic controller and static anti-windup compensator for saturated Lipschitz systems. Thanks to the reformulated Lipschitz property, the Lipschitz systems can be transformed into LPV (linear parameter-varying) systems whose system matrices are affine in a parameter matrix. Based on the modified sector condition dealing with saturation nonlinearity, the design of a nonlinear anti-windup-based controller leads to the solvability of a set of bilinear matrix inequalities (BMI) on the vertices of a bounded convex set which can be solved by the so-called iterative linear matrix inequality (ILMI) algorithm. A numerical example is presented to illustrate the effectiveness of the proposed method. © 2014 Chinese Association of Automation.

Lipschitz条件下高阶可微函数的Ostrowski型不等式

针对满足Lipschitz条件的高阶可微函数,通过建立积分恒等式,利用引入参数求最值的方法,建立了一类高阶可微函数的Ostrowski型不等式,加强了已有的Ostrowski型不等式。

Lipschitz非线性离散系统基于观测器的鲁棒镇定控制设计

本文研究Lipschitz非线性离散时间系统的基于观测器的鲁棒镇定控制问题.首先,针对Lipschitz非线性离散系统,应用微分中值定理和线性参变系统理论,以线性矩阵不等式(LMI)的形式给出基于观测器的鲁棒镇定控制设计的充分条件.随后,将设计结果进一步推广,针对含干扰的Lipschitz非线性离散系统进行H∞性能分析,实现了基于观测器的鲁棒H∞镇定控制,同时给出观测器增益矩阵和控制器增益矩阵的一步求解算法.最后,通过两个数值例子验证了所提方法的有效性.

GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY

A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.

分数次极大算子与Lipschitz函数生成的交换子的紧性

得到分数次极大算子与Lipschitz函数生成的交换子是Lp空间以及Morrey空间上的紧算子,且注意分数次积分算子的处理方法不适用于分数次极大算子.

基于非Lipschitz步长策略的临近分裂可行问题的强收敛性研究

针对Hilbert空间中的临近分裂可行问题,该文提出了一种惯性粘滞类算法.其中主要引入了一种非Lipschitz步长策略,其克服了原步长远离零的缺点.另外,通过弱化临近映射的完全非扩张性,证明了修正后算法的强收敛性.进一步,将所得的结论应用于分裂均衡问题.最后,列举实例充分说明了修正后算法的有效性.

一类二阶迭代函数方程有界光滑解的Lipschitz依赖性

为了研究一类二阶迭代函数方程的C1有界光滑解在C1上确界距离下对已知函数的Lipschitz依赖性,对已知函数的导数施加了Lipschitz条件,并引入新的度量,此度量代表原函数与导函数之间的关系。根据给出Lipschitz依赖性推导过程的相关引理,对其进行了证明,并运用引理计算迭代函数方程光滑解之间的距离,从而得出对已知函数的Lipschitz依赖性。

参数向量Ky Fan不等式与对偶问题解映射Lipschitz连续性最优条件

在赋范线性空间中研究参数向量Ky Fan不等式与对偶问题解映射的Lipschitz连续性。提出了参数向量Ky Fan不等式与对偶问题及其有效解的概念,引入了向量函数伪单调性和强拟凸(凹)性,借助分析方法获得了参数向量Ky Fan不等式与对偶问题解映射的Lipschitz连续性最优条件,并举例加以说明。

非Lipschitz条件下高维McKean-Vlasov随机微分方程解的存在唯一性

研究了一类漂移系数不连续的高维McKean-Vlasov随机微分方程及相应的粒子系统解的存在唯一性.在漂移系数关于空间变量逐段Lipschitz连续的条件下,首先利用Zvonkin变换将方程转换为漂移系数为Lipschitz连续的McKean-Vlasov随机微分方程,变换后的方程存在唯一解.然后由变换函数的性质可得逆函数的存在性和Lipschitz连续性.最后由Ito公式及逆函数的性质可得原来的McKean-Vlasov随机微分方程及相应的粒子系统解的存在唯一性.

光滑神经网络解决一类线性约束的非Lipschitz优化问题

带有线性不等式约束的非光滑非优化问题被广泛应用于稀疏优化,具有重要的研究价值.为了解决这类问题,提出了一种基于光滑化和微分包含理论的神经网络模型.通过理论分析,证明了所提神经网络的状态解全局存在,轨迹能够在有限时间进入可行域并永驻其中,且任何聚点都是目标优化问题的广义稳定点.最后给出数值实验和图像复原实验验证神经网络在理论和应用中的有效性.与现有神经网络相比,它具有以下优势:初始点可以任意选取;避免计算精确罚因子;无需求解复杂的投影算子.

基于Lipschitz常数约束的胶囊网络鲁棒性增强

为了提升胶囊神经网络的对抗鲁棒性,本文提出了基于Lipschitz常数约束的正则化方法,利用对抗训练方法来得到更加鲁棒的胶囊网络,将改进后的模型命名为Lips-CapsNet。相比较其它模型而言,Lips-CapsNet计算简便,不需要对胶囊网络的结构做出任何改变。实验结果显示,模型在MNIST、SVHN等数据集上实现了鲁棒性的提升,尤其是在Fashion-MNIST数据集上,在较强的攻击算法下,对抗样本的预测精度提升可达8%。

单边Lipschitz非线性时滞系统的迭代学习控制

考虑了一类时滞单边Lipschitz非线性系统的迭代学习控制问题。针对该类非线性系统,基于P型学习算法构建了迭代学习控制器。利用单边Lipschitz条件,从理论上证明了在该算法的作用下,系统的输出在整个时间间隔内可实现对期望轨迹的完全跟踪。最后,通过数值仿真验证了算法的有效性。该研究在一定程度上拓展了迭代学习的应用范围,对迭代学习控制理论的进一步推广和完善具有重要意义。

系数满足单边Lipschitz条件的随机微分方程随机周期解的存在唯一性及数值逼近(英文)

本文研究了一类系数满足单边Lipschitz条件的随机微分方程随机周期解的存在唯一性,利用驯化Euler-Maruyama(EM)方法给出了随机周期解的数值逼近,并证明了数值逼近在均方意义下以α∈(0,1/2)阶收敛到精确解.数值算例验证了理论结果.

Global Practical Exponential Stabilization for One-Sided Lipschitz Systems with Time Delay

This paper addresses the practical stabilization problem for a class of one-sided Lipschitz nonlinear time delay systems with external disturbances.In case there is no perturbation,the exponential convergence of the observer was confirmed.When external disturbances appear in the system,a separation principle is established,and the authors show that the closed loop system is exponentially practical stable.By choosing a suitable Lyapunov-Krasovskii functional,the authors derive new sufficient conditions to guarantee the exponential stability of the systems.Finally,a physical model is performed to prove the efficiency and applicability of the suggested approach.

Further Result on the Observer Design for One-Sided Lipschitz Systems

This paper investigates the problem of observer design for a class of control systems.Different from current works,the nonlinear functions in the system only satisfy the property of the one-sided Lipschitz(OSL)condition but not quadratic inner-boundedness(QIB).Moreover,the case where the OSL constant is negative is specially investigated.Firstly,a full-order observer is constructed for the original system.Then,a reduced-order observer is also designed by using the decomposition method.The advantage and effectiveness of the proposed design scheme are shown in a numerical simulation.

Uniform Lipschitz Bound for a Competition Diffusion Advection System with Strong Competition

We prove the uniform Lipschitz bound of solutions for a nonlinear elliptic system modeling the steady state of populations that compete in a heterogeneous environment. This extends known quasi-optimal regularity results and covers the optimal case for this problem. The proof relies upon the blow-up technique and the almost monotonicity formula by Caffarelli, Jerison and Kenig.

Robust H-Filtering for Lipschitz Nonlinear Systems via Multiobjective Optimization

In this paper, a new method of filtering for Lipschitz nonlinear systems is proposed in the form of an LMI optimization problem. The proposed filter has guaranteed decay rate (exponential convergence) and is robust against unknown exogenous disturbance. In addition, thanks to the linearity of the proposed LMIs in the admissible Lipschitz constant, it can be maximized via LMI optimization. This adds an extra important feature to the observer, robustness against nonlinear uncertainty. Explicit bound on the tolerable nonlinear uncertainty is derived. The new LMI formulation also allows optimizations over the disturbance attenuation level ( cost). Then, the admissible Lipschitz constant and the disturbance attenuation level of the filter are simultaneously optimized through LMI multiobjective optimization.

A GENERALIZED LIPSCHITZ SHADOWING PROPERTY FOR FLOWS

In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property if and only if it is structurally stable.

LIPSCHITZ STAR BODIES

In this paper,we study some basic properties on Lipschitz star bodies,such as the equivalence between Lipschitz star bodies and star bodies with respect to a ball,the equivalence between the convergence of Lipschitz star bodies with respect to Hausdorff distance and the convergence of Lipschtz star bodies with respect to radial distance,and the convergence of Steiner symmetrizations of Lipschitz star bodies.