H<Subscript>2</Subscript>-optimal tuning algorithms for fixed structure controllers

An H₂-method of optimal tuning is proposed for a fixed order controller. The SISO plant model is considered in state space. The H₂-method of tuning parameter design is based on the minimization of a transient process closeness criterion for appropriate open-loop and closed-loop control systems and their reference models. The controller tuning algorithms use the plant parameter estimations obtained during the plant parameter identification. The analytical expressions are obtained for the square of H₂-norm of a stable dynamic system. The following theorem is proven: the minimum necessary conditions for the functionals of transfer function H₂-norm of open-loop and closed-loop systems are the same as the minimum necessary conditions for the Frobenius norm of the controller parameter tuning polynomial.     

<Emphasis Type="BoldItalic">H</Emphasis><Subscript>2</Subscript>-Control and the Separation Principle for Discrete-Time Markovian Jump Linear Systems

In this paper we consider the H₂-control problem of discrete-time Markovian jump linear systems. We assume that only an output and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed-loop system is mean square stable and minimizes the H₂-norm of the system. As in the case with no jumps, we show that an optimal controller can be obtained from two sets of coupled algebraic Riccati equations, one associated with the optimal control problem when the state variable is available, and the other associated with the optimal filtering problem. This is the principle of separation for discrete-time Markovian jump linear systems. When there is only one mode of operation our results coincide with the traditional separation principle for the H₂-control of discrete-time linear systems. Date received: June 1, 2001. Date revised: October 13, 2003.     

HSR: <Emphasis Type="Italic">L</Emphasis><Subscript>1/2</Subscript>-regularized sparse representation for fast face recognition using hierarchical feature selection

In this paper, we propose a novel method for fast face recognition called L _1/2-regularized sparse representation using hierarchical feature selection. By employing hierarchical feature selection, we can compress the scale and dimension of global dictionary, which directly contributes to the decrease of computational cost in sparse representation that our approach is strongly rooted in. It consists of Gabor wavelets and extreme learning machine auto-encoder (ELM-AE) hierarchically. For Gabor wavelets’ part, local features can be extracted at multiple scales and orientations to form Gabor-feature-based image, which in turn improves the recognition rate. Besides, in the presence of occluded face image, the scale of Gabor-feature-based global dictionary can be compressed accordingly because redundancies exist in Gabor-feature-based occlusion dictionary. For ELM-AE part, the dimension of Gabor-feature-based global dictionary can be compressed because high-dimensional face images can be rapidly represented by low-dimensional feature. By introducing L _1/2 regularization, our approach can produce sparser and more robust representation compared to L ₁-regularized sparse representation-based classification (SRC), which also contributes to the decrease of the computational cost in sparse representation. In comparison with related work such as SRC and Gabor-feature-based SRC, experimental results on a variety of face databases demonstrate the great advantage of our method for computational cost. Moreover, we also achieve approximate or even better recognition rate.     

RWBO（pd, w）： A Novel Backoff Algorithm for IEEE 802.11 DCF

The Probability Distribution of Slot Selection (PDoSS) of IEEE 802.11 DCF is extremely uneven, which makes the packet collision probability very high. In this paper, the authors explore how to make the stations select the slots uniformly, and give an RWBO(pd,w) algorithm for 802.11 DCF to make the PDoSS even and decrease the packet collision probability. A Markov model is given to analyze the PDoSS of RWBO(pa, w). The performance of RWBO(pd, w) is evaluated by simulation in terms of saturation throughput and packet collision probability. The simulation results indicate that RWBO(pa, w) can decrease the packet contention probability to a large extent, and utilize the channel more efficiently as compared to the 802.11 DCF. Moreover, the relation between saturation throughput and walking probability (pd), the relation between saturation throughput and contention windows (w), the relation between packet collision probability and walking probability (pal), and the relation between packet collision probability and contention windows (w) are analyzed. The analysis indicates that RWBO(pd, w) has some remarkable features: its saturation throughout keeps high and packet collision probability keeps very low (under 0.1) in a large range of pd and w, which allow users to configure Pd and w more flexibly.     

Improved Interface Conditions for 2<Emphasis Type="Italic">D</Emphasis> Domain Decomposition with Corners: Numerical Applications

This article deals with a local improvement of domain decomposition methods for 2-dimensional elliptic problems for which either the geometry or the domain decomposition presents conical singularities. After explaining the main results of the theoretical analysis carried out in Chniti et al. (Calcolo 45, 2008), the numerical experiments presented in this article confirm the optimality properties of the new interface conditions.