Absolute stability of sampled-data systems with a sector nonlinearity

This paper studies the absolute stability problem of sampled-data systems with a sector nonlinearity. Using the FR-operator technique, a frequency-domain criterion with a Nyquist-like plot is derived. It can be regarded as a sampled-data version of the circle criterion. It is shown that the “absolute-stability gain margin” can be read directly from the plot.     

Relating H2 and H∞-norm bounds forsampled-data systems

We relate the H_∞ and H₂ norms for multi-input/multi-output sampled-data feedback control systems, where a continuous-time plant is controlled by a digital compensator with hold and sampler. Upper bounds on both H₂ and H_∞ norms are obtained based on fundamental relations derived by two different approaches, namely the hybrid state-space approach and the fast sampling and lifting approach     

Multiobjective H2/H∞ control

For a linear time-invariant system with several disturbance inputs and controlled outputs, we show how to minimize the nominal H₂-norm performance in one channel while keeping bounds on the H₂-norm or H_∞-norm performance (implying robust stability) in the other channels. This multiobjective H₂ /H_∞-problem in an infinite dimensional space is reduced to sequences of finite dimensional convex optimization problems. We show how to compute the optimal value and how to numerically detect the existence of a rational optimal controller. If it exists, we reveal how the novel trick of optimizing the trace norm of the Youla parameter over certain convex constraints allows one to design a nearly optimal controller whose Youla parameter is of the same order as the optimal one     

ℋ2-optimal design of multirate sampled-data systems

Treating causality constraints, this paper studies optimal synthesis of multirate sampled-data systems with an ℋ₂ performance criteria. An explicit solution is obtained by input-output space extensions (lifting) and frequency-domain techniques     

Optimal Stochastic SD Control With Preview

The problem of H₂-optimal sampled-data (SD) preview control is considered. It is assumed that a stochastic reference signal corrupted with additive colored noise acts upon the system so that future values of this input are known within a preview window tau . A rigorous frequency-domain solution of the problem is given for SISO SD systems on the basis of the parametric transfer function concept. Numerator and denominator degrees of the optimal controller are calculated explicitly on the basis of initial data. The dependence of the optimal cost function on tau is investigated and the limiting value as tau rarr infin is found. Moreover, it is shown that this limit depends on the relation between tau and the sampling period.     

Output feedback control of Markov jump linear systems incontinuous-time

This paper addresses the dynamic output feedback control problem of continuous-time Markovian jump linear systems. The fundamental point in the analysis is an LMI characterization, comprising all dynamical compensators that stabilize the closed-loop system in the mean square sense. The H₂ and H_∞-norm control problems are studied, and the H₂ and H_∞ filtering problems are solved as a by product     

H2-optimal sampled-data control

The H₂-optimal control of continuous-time linear time-invariant systems by sampled-data controllers is discussed. Two different solutions, state space and operator theoretic, are given. In both cases, the H₂ sampled-data problem is shown to be equivalent to a certain discrete-time H₂ problem. Other topics discussed include input-output stability of sampled-data systems, performance recovery in digital implementation of analog controllers, and sampled-data control of systems with the possibility of multiple-time delays     

Robust H∞ control for linear systems withnorm-bounded time-varying uncertainty

Robust H_∞ control design for linear systems with uncertainty in both the state and input matrices is treated. A state feedback control design which stabilizes the plant and guarantees an H_∞-norm bound constraint on disturbance attenuation for all admissible uncertainties is presented. The robust H_∞ control problem is solved via the notion of quadratic stabilization with an H_∞ -norm bound. Necessary and sufficient conditions for quadratic stabilization with an H_∞-norm bound are derived. The results can be regarded as extensions of existing results on H_∞ control and robust stabilization of uncertain linear systems     

H2 and H∞ control forinfinite-dimensional systems with jumps

We consider a semigroup model with jumps in the state that covers distributed parameter systems with impulse control or sampled-data distributed parameter systems with control realized through zero-order or first-order hold. We then introduce the H₂ and H_∞ problems for this system and give the solutions in terms of the solutions of Riccati equations with jumps     

Mixed l1/H∞ control of MIMO systems viaconvex optimization

We present a methodology for designing mixed l₁/H_∞ controllers for MIMO systems. These controllers allow for minimizing the worst case peak output due to persistent disturbances, while at the same time satisfying an H_∞-norm constraint upon a given closed loop transfer function. Therefore, they are of particular interest for applications dealing with multiple performance specifications given in terms of the worst case peak values, both in the time and frequency domains. The main results of the paper show that: 1) contrary to the H₂/H_∞ case, the l₁/H_∞ problem admits a solution in l₁; and 2) rational suboptimal controllers can be obtained by solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and a four-block H_∞ problem. Moreover, this sequence of controllers converges in the l₁ topology to an optimum     

Robust Latent Factor Analysis for Precise Representation of High-Dimensional and Sparse Data

High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.     

Optimal H2/l1 control via duality theory

In this paper we consider the problem of minimizing the H₂ -norm of the closed-loop map while maintaining its l₁-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed-loop maps. Utilizing duality theory, it is shown that the optimal solution is unique, and, in the nontrivial case where the l₁ constraint is active, the optimal solution has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the l₁-constraint are established     

Decentralized Resilient H∞ Load Frequency Control for Cyber-Physical Power Systems Under DoS Attacks

This paper designs a decentralized resilient H_∞ load frequency control (LFC) scheme for multi-area cyber-physical power systems (CPPSs). Under the network-based control framework, the sampled measurements are transmitted through the communication networks, which may be attacked by energy-limited denial-of-service (DoS) attacks with a characterization of the maximum count of continuous data losses (resilience index). Each area is controlled in a decentralized mode, and the impacts on one area from other areas via their interconnections are regarded as the additional load disturbance of this area. Then, the closed-loop LFC system of each area under DoS attacks is modeled as an aperiodic sampled-data control system with external disturbances. Under this modeling, a decentralized resilient H_∞ scheme is presented to design the state-feedback controllers with guaranteed H_∞ performance and resilience index based on a novel transmission interval-dependent loop functional method. When given the controllers, the proposed scheme can obtain a less conservative H_∞ performance and resilience index that the LFC system can tolerate. The effectiveness of the proposed LFC scheme is evaluated on a one-area CPPS and two three-area CPPSs under DoS attacks.      

Computing the L2-induced norm of a compression operator

A new computationally viable approach is derived for computing the induced norm of a state space compression operator; that is an integral operator defined on the finite length space L₂[0,h]. Determining this norm is a crucial component in the control analysis of both delay systems and sampled-data systems. The technique developed may have application to a wider variety of integral operators.     

基于自适应双lp-l2范数的单幅模糊图像超分辨率盲重建

为了提高低分辨率模糊图像的质量,提出了一种基于自适应双l_p-l₂范数的超分辨率盲重建方法。该方法分为模糊核估计子过程和超分辨率非盲重建子过程。在模糊核估计子过程中,使用双l_p-l₂范数先验同时约束锐化图像和模糊核的估计,并使用图像梯度的阈值分割,实现锐化图像l_p-l₂范数约束的自适应组合;在超分辨率非盲重建子过程中,结合估计到的模糊核,使用基于非局部中心化稀疏表示的超分辨率方法重建出最终的高分辨率图像。仿真实验中,与基于双l₀-l₂范数的方法相比,该算法重建结果的平均峰值信噪比（PSNR）提高了0.16 dB,平均结构相似度（SSIM）提高了0.0045,平均差方和比降低了0.13。实验结果表明,所提方法能估计出较准确的模糊核,最终的重建图像中,振铃得到有效抑制,图像质量较好。     

H∞-norm approximation of systems by constantmatrices and related results

In this work the H_∞-norm approximation of a given stable proper rational transfer function by a constant matrix is considered. A new improved bound on H_∞-norm of a given stable transfer function is derived. Optimal approximation for relaxation systems is given     

Further results on the L1 analysis of sampled-data systems via kernel approximation approach

This paper gives two methods for the L₁ analysis of sampled-data systems, by which we mean computing the L_∞-induced norm of sampled-data systems. This is achieved by developing what we call the kernel approximation approach in the setting of sampled-data systems. We first consider the lifting treatment of sampled-data systems and give an operator theoretic representation of their input/output relation. We further apply the fast-lifting technique by which the sampling interval [0, h) is divided into M subintervals with an equal width, and provide methods for computing the L_∞-induced norm. In contrast to a similar approach developed earlier called the input approximation approach, we use an idea of kernel approximation, in which the kernel function of an input operator and the hold function of an output operator are approximated by piecewise constant or piecewise linear functions. Furthermore, it is shown that the approximation errors in the piecewise constant approximation or piecewise linear approximation scheme converge to 0 at the rate of 1/M or 1/M², respectively. In comparison with the existing input approximation approach, in which the input function (rather than the kernel function) of the input operator is approximated by piecewise constant or piecewise linear functions, we show that the kernel approximation approach gives improved computation results. More precisely, even though the convergence rates in the kernel approximation approach remain qualitatively the same as those in the input approximation approach, the newly developed former approach could lead to quantitatively improved approximation errors than the latter approach particularly when the piecewise linear approximation scheme is taken. Finally, a numerical example is given to demonstrate the effectiveness of the kernel approximation approach with this scheme.     

Hankel norm of sampled-data systems

Generalizes the concept of Hankel norm for purely continuous-time systems to sampled-data systems. The Hankel norm of a sampled-data system is defined by taking into account intersample behaviors. The formula of the Hankel norm of a sampled-data system is given by a hybrid state-space model approach. The authors show that the Hankel norm is equal to that of an equivalent discrete-time system. Two simple examples including sampled-data controller reduction are demonstrated