Proximity point algorithm for low-rank matrix recovery from sparse noise corrupted data

The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.     

FAST OPTIMIZATION METHOD OF REENTRY TRAJECTORY CONSIDERING AERODYNAMIC PARAMETER PERTURBATION

针对传统再入轨迹优化方法收敛速度慢、对初值敏感程度高等的局限性,提出了一种基于序列凸优化的再入轨迹快速求解方法.该方法以倾侧角的变化率作为控制量,改进了现有凸化策略,考虑到抑制数值优化过程中由于数值离散方式带来的锯齿化现象,采用 B 样条曲线离散控制量,同时为避免算法在初始猜想值附近出现伪不可行的问题,增加额外虚拟控制量,通过一种"回溯直线"搜索的方法,提高算法的稳定性、快速性和寻优结果的光滑性.为研究飞行器再入过程中的气动参数扰动问题,采用采样点少、易于实现,计算效率高的广义混沌多项式理论研究方法,建立了基于广义混沌多项式和凸优化相结合的再入轨迹鲁棒优化模型,该模型在优化过程中考虑气动参数扰动对寻优结果的影响作用,避免了传统轨迹与制导律的复杂迭代设计环节,可有效降低优化轨迹对气动参数扰动的敏感程度,在气动参数不确定条件的干扰下,依然可以保证飞行器顺利安全的完成飞行任务.最后,以美国某可重复使用飞行器的再入任务为例,验证了基于序列凸优化的再入轨迹优化方法的快速性以及鲁棒优化模型对气动参数扰动的抗干扰性能力,表明了该方法具有一定的工程应用性.     

考虑气动参数扰动的再入轨迹快速优化方法

针对传统再入轨迹优化方法收敛速度慢、对初值敏感程度高等的局限性,提出了一种基于序列凸优化的再入轨迹快速求解方法.该方法以倾侧角的变化率作为控制量,改进了现有凸化策略,考虑到抑制数值优化过程中由于数值离散方式带来的锯齿化现象,采用 B 样条曲线离散控制量,同时为避免算法在初始猜想值附近出现伪不可行的问题,增加额外虚拟控制量,通过一种"回溯直线"搜索的方法,提高算法的稳定性、快速性和寻优结果的光滑性.为研究飞行器再入过程中的气动参数扰动问题,采用采样点少、易于实现,计算效率高的广义混沌多项式理论研究方法,建立了基于广义混沌多项式和凸优化相结合的再入轨迹鲁棒优化模型,该模型在优化过程中考虑气动参数扰动对寻优结果的影响作用,避免了传统轨迹与制导律的复杂迭代设计环节,可有效降低优化轨迹对气动参数扰动的敏感程度,在气动参数不确定条件的干扰下,依然可以保证飞行器顺利安全的完成飞行任务.最后,以美国某可重复使用飞行器的再入任务为例,验证了基于序列凸优化的再入轨迹优化方法的快速性以及鲁棒优化模型对气动参数扰动的抗干扰性能力,表明了该方法具有一定的工程应用性.      

Generalized passivity-based chaos synchronization

In this paper, a new passivity-based synchronization method for a general class of chaotic systems is proposed. Based on the Lyapunov theory and the linear matrix inequality （LMI） approach, the passivity-based controller is presented to make the synchronization error system not only passive but also asymptotically stable. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation studies for the Genesio-Tesi chaotic system and the Qi chaotic system are presented to demonstrate the effectiveness of the proposed scheme.     

MINIMAL POLYNOMIAL MATRIX AND LINEAR MULTIVARIABLE SYSTEM(Ⅱ)

part(Ⅰ) of this work is on the theory of minimal polynomial matrix and Part(Ⅱ)is onthe applications of this theory to linear multivarible systeme.In I of this part,using the theory to Part(Ⅰ),some results about input part of a linearmultivarble system are discussed in detail and in Ⅱ,using duality properties,the conceptsabout row n.p.m.and row generating system,etc.are given. and some results about outputpart of linear multivariable system are discussed, too.In Ⅲ,we discuss the approach whichcan give the polynomial model with less dimension from the state-space model and in Ⅳ wediscuss tha inverse of the problem to give the state-space model from the polynomial model.Some interesting examples are given to explain the theory and the approach.     

Distributed proportional plus second-order spatial derivative control for distributed parameter systems subject to spatiotemporal uncertainties

In this paper, a robust distributed control design based on proportional plus second-order spatial derivative (P-sD $^2$ ) is proposed for exponential stabilization and minimization of spatial variation of a class of distributed parameter systems (DPSs) with spatiotemporal uncertainties, whose model is represented by parabolic partial differential equations with spatially varying coefficients. Based on the Lyapunov’s direct method, a robust distributed P-sD $^2$ controller is developed to not only exponentially stabilize the DPS for all admissible spatiotemporal uncertainties but also minimize the spatial variation of the process. The outcome of the robust distributed P-sD $^2$ control problem is formulated as a spatial differential bilinear matrix inequality (SDBMI) problem. A local optimization algorithm that the SDBMI is treated as a double spatial differential linear matrix inequality (SDLMI) is presented to solve this SDBMI problem. Furthermore, the SDLMI optimization problem can be approximately solved via the finite difference method and the existing convex optimization techniques. Finally, the proposed design method is successfully applied to feedback control problem of the FitzHugh–Nagumo equation.     

Construction of polynomial matrix using block coefficient matrix representation auto-regressive moving average model for actively controlled structures

The polynomial matrix using the block coefficient matrix representation auto-regressive moving average (referred to as the PM-ARMA) model is constructed in this paper for actively controlled multi-degree-of-freedom (MDOF) structures with time-delay through equivalently transforming the preliminary state space realization into the new state space realization. The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average (ARMA) model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators. (The sensors and actuators are required to maintain the identical number.) under any dimensional stationary stochastic excitation. The project supported by the National Natural Science Foundation of China (50278054)     

用对角质量矩阵时有限单元特征值问题的准确度

本文讨论的对角化质量矩阵是在动能积分的公式中将积分点取在有限单元的结点上而得到的,本文给出了用这种矩阵时,固有频率、固有振型和对应的应力的对角化误差与动能积分的代数精确度、插值位移场的多项式的阶次、应变能中导数的最高阶数的关系,利用这些关系和多个算例讨论了对角化质量矩阵的应用性问题。     

The synchronization between two discrete-time chaotic systems using active robust model predictive control

In this paper, we consider the synchronization of two discrete-time chaotic systems. A novel active robust model predictive strategy is proposed to guarantee the synchronization of two discrete-time systems in the presence of model uncertainty. The proposed approach reduces the synchronization to a convex optimization involving linear matrix inequalities. The numerical simulations illustrate the effectiveness of the proposed method.     

Robust H∞ filtering for discrete-time impulsive systems with uncertainty

This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a discrete-time impulsive systems. Then,a sufficient condition of asymptotical stability and H∞ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to show effectiveness of the obtained result.     

航天器有限时间饱和姿态跟踪控制

针对刚体航天器系统,对存在模型不确定性、外界干扰力矩和控制器饱和等条件下的姿态跟踪控制问题进行了研究。首先,考虑未知模型不确定性和外界干扰,且总干扰上界为未知常数,结合快速非奇异终端滑模、快速终端滑模趋近律以及辅助系统构造了基本的鲁棒有限时间饱和控制器,并通过辅助系统直接补偿了控制器饱和;其次,针对系统总干扰具有多项式上界的情形,进一步结合自适应控制算法,对其上界函数中的未知参数进行在线估计,并设计了自适应有限时间饱和控制器。同时,基于Lyapunov稳定性理论证明了所提出控制算法的有限时间收敛特性。最后,通过数值仿真验证所提出控制算法的控制效果,在两种控制器作用下姿态的跟踪精度分别为5×10-5和1×10-5,证明了所提出控制算法的有效性。     

结构非概率鲁棒可靠性准则

通过反例指出Ben-Haim的鲁棒可靠性准则是错误的同时．利用集合数学理论中的凸集合间的偏序关系，给出了新的非概率凸模型理论的鲁棒可靠性准则。并用数值算例说明了所提出的结构非概率凸模型鲁棒可靠性理论的正确性和实用性。     

模型不确定压电柔性结构的多目标振动控制

以压电柔性结构为对象,考虑其被控模态参数的不确定性和因剔除残余模态所引起的动态不确定性,建立了结构的不确定线性分式模型;根据不确定模型设计了一个对结构进行振动控制的动态输出反馈控制器,使闭环系统满足鲁棒稳定、扰动抑制、极点配置约束及控制输入约束等性能要求;并利用线性矩阵不等式,将具有多个性能要求的振动控制问题转化为具有线性矩阵不等式约束和线性目标函数的凸优化问题。最后以简支压电柔性梁为例,设计了一个融合多性能指标的动态输出反馈非同位控制器,并给出了仿真结果。     

Experimental simulation of matrix cracking and debonding in a model brittle matrix composite

A model composite material system was designed to simulate typical damage mechanisms in unidirectional fiber reinforced brittle matrix composites. Experiments were performed at low to high quasistatic, macroscopic loading rates . At all loading rates reversal of the transverse strain was observed and was correlated to matrix cracking and debonding. The optical method of coherent gradient sensing (CGS) was used to obtain qualitative information regarding the stress fields and to observe the progression of damage. It was found that the sequence of damage formation (damage path) depended on the macroscopic loading rate. At lower loading rates periodic matrix cracks developed; minimal debonding of the reinforcement-matrix interface occurred only much later in the experiment. At higher loading rates extensive debonding followed propagation of the initial matrix crack, and periodic cracking was not observed. Several features of the material response of the model material system were also observed in a previously studied unidirectional ceramic matrix composite.     

Instrumental variables approach to identification of a class of MIMO Wiener systems

A new approach to identification of multi-input multi-output (MIMO) Wiener systems using the instrumental variables method is presented. It is assumed that static nonlinear elements are invertible and their inverse characteristics can be expressed or approximated by polynomials of known orders. It is also assumed that the linear part of the Wiener system can be represented by a matrix polynomial form. Based on these assumptions, the Wiener system is transformed introducing a new parameterization and its parameters are estimated using a linear-in-parameters model. To solve the problem of non-consistency of least squares parameter estimates, an instrumental variables method is employed. A numerical example is included to show the effectiveness and the practical feasibility of the presented approach.     

Analytical development of disturbed matrix eigenvalue problem applied to mixed convection stability analysis in Darcy media

This work consists in evaluating algebraically and numerically the influence of a disturbance on the spectral values of a diagonalizable matrix. Thus, two approaches will be possible; to use the theorem of disturbances of a matrix depending on a parameter, due to Lidskii and primarily based on the structure of Jordan of the no disturbed matrix. The second approach consists in factorizing the matrix system, and then carrying out a numerical calculation of the roots of the disturbances matrix characteristic polynomial. This problem can be a standard model in the equations of the continuous media mechanics. During this work, we chose to use the second approach and in order to illustrate the application, we choose the Rayleigh–Bénard problem in Darcy media, disturbed by a filtering through flow. The matrix form of the problem is calculated starting from a linear stability analysis by a finite elements method. We show that it is possible to break up the general phenomenon into other elementary ones described respectively by a disturbed matrix and a disturbance. A good agreement between the two methods was seen. To cite this article: H.B. Hamed, R. Bennacer, C. R. Mecanique 336 (2008).     

A compressed-sensing approach for closed-loop optimal control of nonlinear systems

We present a method that seeks to combine the properties of optimal control with the robust character of closed-loop control. The method relies on the availability of a reduced model of the system to be controlled, in order to express the control problem in a low-dimensional space where the system-state-dependent optimal control law is subsequently approximated in a preprocessing stage. A polynomial expansion is used for the approximation, enabling fast update of the optimal control law each time a new observation of the system state is made available. It results in a real-time compatible, efficient (optimal-like), and robust control strategy. A compressed-sensing approach is proposed to efficiently construct the approximate control law, exploiting the compressible character of the optimal control law in the retained approximation basis. The method is demonstrated for the control of the flow around a cylinder and is shown to perform as well as the much more costly receding-horizon optimal control approach, where the exact optimal control problem is actually recomputed, even in the presence of large aleatoric perturbations. Potential and remaining issues toward application to larger dimensional reduced systems are also discussed, and some directions for improvement are suggested.     

基于凸集模型结构稳健性优化设计

不确定性因素大量存在于实际工程中,采用凸集变量描述结构不确定性参数,进一步将凸集模型划分为超椭球模型和区间模型。由试验点数量确定选用两类模型的标准,从本质上指明了两类模型的区别。分别对两类模型中不确定变量进行标准化,通过对比分析,阐述了基于超椭球模型和区间模型优化方法和求解过程的共同点与区别。借用超椭球模型分析思路,对优化过程中的变量进行分类,为突出稳健性优化设计特点,考虑约束条件从特殊到一般,重点描述基于区间模型稳健性优化的基本思想方法。采用目标性能分析方法,强调指定可靠性指标的唯一性,给出了稳健性优化的具体算法、求解步骤和迭代收敛准则。对实际算例进行了分析与求解,与已有结果比较,验证了本文方法的正确性和有效性。     

The Problem of Generalized D-Stability in Unbounded LMI Regions and Its Computational Aspects

Journal of Dynamics and Differential Equations - We generalize the concepts of D-stability and additive D-stability of matrices. For this, we consider a family of unbounded regions defined in terms...