多输入多输出变量带误差模型的最坏情况频域辨识

本文将单输入单输出(SISO)变量带误差(EIV)模型的频域最坏情况辨识方法推广应用于多输入多输出 (MIMO)情况. 类似于SISO情况, 多输入多输出变量带误差(MIMO EIV)模型的辨识模型集合由估计的系统名义模型及 其最坏情况误差界描述. 所估计的系统名义模型表征为正规右图符号, 其最坏情况误差界具有可能的更少保守性, 可利 用EIV 模型的先验信息和后验信息由v-gap度量量化得到. 因此, 这种模型集合非常适合于后期利用Vinnicombe提出 的H1回路成形法设计鲁棒控制器. 最后, 利用一数值仿真实例验证所提出辨识方法的有效性.     

Stability and weighted sensitivity analysis of robust controller for heat exchanger

This study presents a parametric system identification approach to estimate the dynamics of a chemical plant from experimental data and develops a robust PID controller for the plant. Parametric system identification of the heat exchanger system has been carried out using experimental data and prediction error method. The estimated model of the heat exchanger system is a time-delay model and a robust PID controller for the time-delayed model has been designed considering weighted sensitivity criteria. The mathematical background of parametric system identification, stability analysis, and ${{\rm H}_\infty }$ weighted sensitivity analysis have been provided in this paper. A graphical plot has been provided to determine the stability region in the $( {{K_{\rm p}},{K_{\rm i}}} )$, $( {{K_{\rm p}},{K_{\rm d}}} )$ and $( {{K_{\rm i}},{K_{\rm d}}} )$ plane. The stability region is a locus dependent on parameters of the controller and frequency, in the parameter plane.     

Event-triggered state estimation for T-S fuzzy affine systems based on piecewise Lyapunov-Krasovskii functionals

This paper investigates the problem of event-triggered ${\rm H}_\infty$ state estimation for Takagi-Sugeno (T-S) fuzzy affine systems. The objective is to design an event-triggered scheme and an observer such that the resulting estimation error system is asymptotically stable with a prescribed ${\rm H}_{\infty}$ performance and at the same time unnecessary output measurement transmission can be reduced. First, an event-triggered scheme is proposed to determine whether the sampled measurements should be transmitted or not. The output measurements, which trigger the condition, are supposed to suffer a network-induced time-varying and bounded delay before arriving at the observer. Then, by adopting the input delay method, the estimation error system can be reformulated as a piecewise delay system. Based on the piecewise Lyapunov-Krasovskii functional and the Finsler''s lemma, the event-triggered ${\rm H}_{\infty}$ observer design method is developed. Moreover, an algorithm is proposed to co-design the observer gains and the event-triggering parameters to guarantee that the estimation error system is asymptotically stable with a given disturbance attenuation level and the signal transmission rate is reduced as much as possible. Simulation studies are given to show the effectiveness of the proposed method.     

Robust control for electric vehicle powertrains

This paper considers the application of robust control methods ($\mu$- and ${\rm H}_{\infty}$-synthesis) to the speed and acceleration control problem encountered in electric vehicle powertrains. To this end, we consider a two degree of freedom control structure with a reference model. The underlying powertrain model is derived and combined into the corresponding interconnected system required for $\mu$- and ${\rm H}_{\infty}$-synthesis. The closed-loop performance of the resulting controllers are compared in a detailed simulation analysis that includes nonlinear effects. It is observed that the $\mu$-controller offers performance advantages in particular for the acceleration control problem, but at the price of a high-order controller.     

Distributed \begin{document}$H_{2}/H_\infty$\end{document} Filter Design for Discrete-Time Switched Systems

This paper addresses an infinite horizon distributed H2/H∞ filtering for discrete-time systems under conditions of bounded power and white stochastic signals. The filter algorithm is designed by computing a pair of gains namely the estimator and the coupling. Herein, we implement a filter to estimate unknown parameters such that the closed-loop multi-sensor accomplishes the desired performances of the proposed H2 and H∞ schemes over a finite horizon. A switched strategy is implemented to switch between the states once the operation conditions have changed due to disturbances. It is shown that the stability of the overall filtering-error system with H2/H∞ performance can be established if a piecewise-quadratic Lyapunov function is properly constructed. A simulation example is given to show the effectiveness of the proposed approach.     

Some Relations between Approximation Problems and PCPs over the Real Numbers

In [10] it was recently shown that that is the existence of transparent long proofs for was established. The latter denotes the class of real number decision problems verifiable in polynomial time as introduced by Blum et al. [6]. The present paper is devoted to the question what impact a potential full real number theorem would have on approximation issues in the BSS model of computation. We study two natural optimization problems in the BSS model. The first, denoted by MAX-QPS, is related to polynomial systems; the other, MAX-q-CAP, deals with algebraic circuits. Our main results combine the PCP framework over with approximation issues for these two problems. We also give a negative approximation result for a variant of the MAX-QPS problem.     

基于量子计算的粗糙集核属性求解算法

粗糙集的核属性求解问题在经典计算中是一个NP问题.现有的方法中最优的时间复杂度也需要${\rm O}$$ \left(|C||U|\right)$($U$为论域、$C$为属性列数).由于量子计算的并行性特点, 本文致力于采用量子计算的方法来求解粗糙集的核属性, 拟提出了一种基于量子计算的粗糙集核属性求解算法.经过仿真实验, 在任何情况下, 该算法都能以1的总概率得到目标分量; 且通过理论分析证明了算法的时间复杂度不会高于${\rm O}$$\left(|\frac{{\rm{ \mathsf{ π}}}}{2\arcsin\sqrt {\frac{M}{C}}}+1||U|\right)$.     

Quantum Error Correction of Time-correlated Errors

The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of quantum systems; an error corrected during the previous cycle may reoccur later due to physical processes specific for each physical implementation of the qubits. In this paper, we study quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm we propose allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code when the two logical qubits and are entangled states of 2 ⁿ basis states in .      

A note on reverse scheduling with maximum lateness objective

The inverse and reverse counterparts of the single-machine scheduling problem $1||L_{\max }$ are studied in [2], in which the complexity classification is provided for various combinations of adjustable parameters (due dates and processing times) and for five different types of norm: $\ell _{1},\ell _{2},\ell _{\infty },\ell _{H}^{\Sigma } $ , and $\ell _{H}^{\max }$ . It appears that the $O(n^{2})$ -time algorithm for the reverse problem with adjustable due dates contains a flaw. In this note, we present the structural properties of the reverse model, establishing a link with the forward scheduling problem with due dates and deadlines. For the four norms $\ell _{1},\ell _{\infty },\ell _{H}^{\Sigma }$ , and $ \ell _{H}^{\max }$ , the complexity results are derived based on the properties of the corresponding forward problems, while the case of the norm $\ell _{2}$ is treated separately. As a by-product, we resolve an open question on the complexity of problem $1||\sum \alpha _{j}T_{j}^{2}$ .     

H∞ position transfer and regulation for floating offshore wind turbines

This paper proposes ${\rm H}_\infty$ controller design for platform position transfer and regulation of floating offshore wind turbines. The platform movability of floating wind turbines can be utilized in mitigating the wake effect in the wind farm, thereby maximizing the wind farm''s total power capture and efficiency. The controller is designed so that aerodynamic force is adjusted to meet the three objectives simultaneously, that is, 1) to generate the desired electrical power level, 2) to achieve the desired platform position, and 3) to suppress the platform oscillation. To acquire sufficient aerodynamic force to move the heavy platform, the pitch-to-stall blade pitching strategy is taken instead of the commonly-used pitch-to-feather strategy. The desired power level is attained by the standard constant-power strategy for the generator torque, while ${\rm H}_\infty$ state-feedback control of blade pitch and nacelle yaw angles is adopted for the position regulation and platform oscillation suppression. Weighting constants for the ${\rm H}_\infty$ controller design are adjusted to take the trade-off between the position regulation accuracy and the platform motion reduction. To demonstrate the efficiency of the proposed controller, a virtual 5-MW semi-submersible wind turbine is considered. Simulation results show that the designed ${\rm H}_\infty$ controller successfully accomplishes the platform position transfer and regulation as well as the platform oscillation reduction against wind and wave disturbances, and that it outperforms a previously-proposed linear quadratic controller with an integrator.     

Attractive energy contribution to nanoconfined fluids behavior: the normal pressure tensor

The aim of our research is to demonstrate the role of attractive intermolecular potential energy on normal pressure tensor of confined molecular fluids inside nanoslit pores of two structureless purely repulsive parallel walls in xy plane at z = 0 and z = H, in equilibrium with a bulk homogeneous fluid at the same temperature and at a uniform density. To achieve this we have derived the perturbation theory version of the normal pressure tensor of confined inhomogeneous fluids in nanoslit pores:

Optimally Adaptive Integration of Univariate Lipschitz Functions

We consider the problem of approximately integrating a Lipschitz function f (with a known Lipschitz constant) over an interval. The goal is to achieve an additive error of at most ε using as few samples of f as possible. We use the adaptive framework: on all problem instances an adaptive algorithm should perform almost as well as the best possible algorithm tuned for the particular problem instance. We distinguish between and , the performances of the best possible deterministic and randomized algorithms, respectively. We give a deterministic algorithm that uses samples and show that an asymptotically better algorithm is impossible. However, any deterministic algorithm requires samples on some problem instance. By combining a deterministic adaptive algorithm and Monte Carlo sampling with variance reduction, we give an algorithm that uses at most samples. We also show that any algorithm requires samples in expectation on some problem instance (f,ε), which proves that our algorithm is optimal.     

On the Power of Unambiguity in Alternating Machines

Unambiguity in alternating Turing machines has received considerable attention in the context of analyzing globally unique games by Aida et al. [ACRW] and in the design of efficient protocols involving globally unique games by Crasmaru et al. [CGRS]. This paper explores the power of unambiguity in alternating Turing machines in the following settings: 1. We show that unambiguity-based hierarchies-AUPH, UPH, and UPH-are infinite in some relativized world. For each , we construct another relativized world where the unambiguity-based hierarchies collapse so that they have exactly k distinct levels and their k-th levels coincide with PSPACE. These results shed light on the relativized power of the unambiguity-based hierarchies, and parallel the results known for the case of the polynomial hierarchy. 2. For every , we define the bounded-level unambiguous alternating solution class UAS(k) as the class of all sets L for which there exists a polynomial-time alternating Turing machine N, which need not be unambiguous on every input, with at most k alternations such that if and only if x is accepted unambiguously by N. We construct a relativized world where, for all and . 3. Finally, we show that robustly k-level unambiguous alternating polynomial-time Turing machines, i.e., polynomial-time alternating Turing machines that for every oracle have k alternating levels and are unambiguous, accept languages that are computable in , for every oracle A. This generalizes a result of Hartmanis and Hemachandra [HH].     

L 2-optimal identification of MIMO errors-in-variables models from the v-gap geometrical interpretation

An L ₂-optimal identification method is extended to cope with MIMO errors-in-variables (EIV) model estimation based on a geometrical interpretation for the v-gap metric. The L ₂-optimal approximate models are composed of system and noise models and characterised by a normalised right graph symbol (NRGS) and its complementary inner factor (CIF), respectively. This metric can be evaluated as the supreme of sine values of the maximal principal angles between NRGS frequency responses of two concerned models. In order to make full use of the angular cosine formula for complex vectors to reduce computational loads, a CIF of the NRGS of the perturbed model is introduced and thus, the system parameter optimisation can be efficiently solved by sequential quadratic programming methods. With the estimated system model, the associated noise model can be built by right multiplication of an inner matrix. Finally, a simulation example demonstrates the effectiveness of the proposed identification method.     

Approximation Algorithms for Quickest Spanning Tree Problems

Let $G=(V,E)$ be an undirected multigraph with a special vertex ${\it root} \in V$, and where each edge $e \in E$ is endowed with a length $l(e) \geq 0$ and a capacity $c(e) > 0$. For a path $P$ that connects $u$ and $v$, the {\it transmission time} of $P$ is defined as $t(P)=\mbox{\large$\Sigma$}_{e \in P} l(e) + \max_{e \in P}\!{(1 / c(e))}$. For a spanning tree $T$, let $P_{u,v}^T$ be the unique $u$--$v$ path in $T$. The {\sc quickest radius spanning tree problem} is to find a spanning tree $T$ of $G$ such that $\max _{v \in V} t(P^T_{root,v})$ is minimized. In this paper we present a 2-approximation algorithm for this problem, and show that unless $P =NP$, there is no approximation algorithm with a performance guarantee of $2 - \epsilon$ for any $\epsilon >0$. The {\sc quickest diameter spanning tree problem} is to find a spanning tree $T$ of $G$ such that $\max_{u,v \in V} t(P^T_{u,v})$ is minimized. We present a ${3 \over 2}$-approximation to this problem, and prove that unless $P=NP$ there is no approximation algorithm with a performance guarantee of ${3 \over 2}-\epsilon$ for any $\epsilon >0$.     

Approximation Algorithms for Quickest Spanning Tree Problems

Let $G=(V,E)$ be an undirected multigraph with a special vertex ${\it root} \in V$, and where each edge $e \in E$ is endowed with a length $l(e) \geq 0$ and a capacity $c(e) > 0$. For a path $P$ that connects $u$ and $v$, the {\it transmission time} of $P$ is defined as $t(P)=\mbox{\large$\Sigma$}_{e \in P} l(e) + \max_{e \in P}\!{(1 / c(e))}$. For a spanning tree $T$, let $P_{u,v}^T$ be the unique $u$--$v$ path in $T$. The {\sc quickest radius spanning tree problem} is to find a spanning tree $T$ of $G$ such that $\max _{v \in V} t(P^T_{root,v})$ is minimized. In this paper we present a 2-approximation algorithm for this problem, and show that unless $P =NP$, there is no approximation algorithm with a performance guarantee of $2 - \epsilon$ for any $\epsilon >0$. The {\sc quickest diameter spanning tree problem} is to find a spanning tree $T$ of $G$ such that $\max_{u,v \in V} t(P^T_{u,v})$ is minimized. We present a ${3 \over 2}$-approximation to this problem, and prove that unless $P=NP$ there is no approximation algorithm with a performance guarantee of ${3 \over 2}-\epsilon$ for any $\epsilon >0$.     

The Random Members of a Π 1 0 ${\Pi }_{1}^{0}$ Class

Theory of Computing Systems - We examine several notions of randomness for elements in a given ${\Pi }_{1}^{0}$ class $\mathcal {P}$ . Such an effectively closed subset $\mathcal {P}$ of 2 ω...     

New types of fuzzy ideals of near-rings

In this paper, we consider the $(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$ -fuzzy and $(\overline{\in}_{\gamma},\overline{\in}_{\gamma} \vee \; \overline{\hbox{q}}_{\delta})$ -fuzzy subnear-rings (ideals) of a near-ring. Some new characterizations are also given. In particular, we introduce the concepts of (strong) prime $(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$ -fuzzy ideals of near-rings and discuss the relationship between strong prime $(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$ -fuzzy ideals and prime $(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$ -fuzzy ideals of near-rings.     

Michell cantilevers constructed within trapezoidal domains—Part II: virtual displacement fields

The present second part of the paper deals with the virtual displacement fields associated with the optimality conditions , where σ _T and σ _C represent the allowable values of the tensile and compressive stress, respectively. The displacement fields vanish along a straight segment of a line support and are constructed within an infinite domain bounded by two half-lines. The displacement fields are provided by the integral formulae involving the Lamé fields found in part I of this paper. All the results are expressed in terms of Lommel-like functions. These results make it possible to determine the volumes of the optimal cantilevers designs within the feasible domain considered. Computation of the volumes along with analyses of concrete cantilevers will be the subject of part IV of the present paper.