H2/ l1 混合优化问题的凸二次规划解法

采用上逼近算法求解H1/l1混合优化问题,首先将其转化为有限维的凸二次规划问题,并利用Lemke互补转轴算法求解;然后逐次进行逼近,计算请示例表明所得结果是正确的。     

H2 and H∞ robust filtering for convexbounded uncertain systems

Investigates robust filtering design problems in H₂ and H_∞ spaces for continuous-time systems subjected to parameter uncertainty belonging to a convex bounded-polyhedral domain. It is shown that, by a suitable change of variables, both designs can be converted into convex programming problems written in terms of linear matrix inequalities. The results generalize the ones available in the literature to date in several directions. First, all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured. Then, assuming the order of the uncertain system is known, the optimal guaranteed performance H₂ and H_∞ filters are proven to be of the same order as the order of the system. A numerical example illustrate the theoretical results     

不确定离散时间系统的H2/ H∞最优保性能控制

针对具有两个不同被调输出的一类不确定离散时间系统,研究其H2/H∞状态反馈保性能控制问题,基于线性矩阵不等式处理方法。推导出存在H2/H∞保性能控制律的充分必要条件,并用一个线性矩阵不等式的可行解给出了所有保性能控制律的参数化表示,进而通过建立和求解一个凸优化问题,给出了H2/H∞最优保性能控制律设计方法,最后通过一个例子说明了所提出方法的有效性。     

主动悬架H2/ 广义H2输出反馈控制

本文提出了一种主动悬架控制的H₂ /广义H₂ 输出反馈控制方法. 依照国际标准ISO2631.3选择垂直和俯仰加速度的频率加权. 根据路面干扰谱特征, 选用H₂ 范数作为乘坐舒适性的指标, 广义H₂ 范数描述轮胎接地性等时域约束要求. 在多目标控制框架下, 将输出反馈控制器的设计转化为求解LMI优化问题. 基于半车模型, 给出了输出反馈主动悬架系统的频域分析和时域仿真.     

Approximation methods of scalar mixed H2/l1problems for discrete-time systems

The scalar mixed H₂/l₁ problem for discrete-time systems is considered. The continuity property of the optimal value with respect to changes in the l₁ constraint is studied. An upper approximation method and a lower approximation method of the optimal value are given. Suboptimal values and superoptimal values of the problem can be obtained by solving a sequence of finite dimensional quadratic programming problems     

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     

Dissipative H2/H∞ controller synthesis

In certain applications, such as the colocated control of flexible structures, the plant is known to be positive real. Hence, closed-loop stability is unconditionally guaranteed as long as the controller is also positive real. One approach to designing positive real controllers is the LQG-based positive real synthesis technique of Lozano-Leal and Joshi. The contribution of this paper is the extension of this positive real synthesis technique to include an H_∞-norm constraint on closed-loop performance     

MIMO离散时间系统混合l1/H2控制

研究了MIMO(多输入多输出)离散时间系统的混合l₁/H₂优化问题,该问题可描述为最优化一个传递函数矩阵的l₁范数同时保证另一个传递函数矩阵的H₂范数满足预定的指标.研究了最优目标函数值关于H₂范数指标的连续性.证明了MIMO系统混合l₁/H₂控制问题最优解的存在性.由于基于标定-Q(scaled-Q)方法求解MIMO混合l₁/H₂问题,避免了进行零点插值运算的困难.通过求解有限维非线性规划问题可得到最优目标值的收敛的上下界.     

基于遗传算法的混合降阶H 2 öH ∞控制器

讨论了混合降阶H2/H∞控制器的设计问题,提出了应用遗传算法设计混合降阶H2/H∞控制器的一种方法.通过遗传算法对次优H∞降阶控制器进行H2性能优化,设计出鲁棒性既强又满足系统性能要求的混合降阶H2/H∞控制器.它分别在H∞降阶和H2性能优化中两次应用遗传算法,遗传算法采用实数编码形式,其算子分别选用排序选择和最佳个体保存相结合的选择算子、实值中间重组的交叉算子及实值变异的变异算子.利用国产某型飞机对该方法进行仿真,其结果表明得到的混合降阶H2/H∞控制器具有良好的H∞性能和H2性能.     

Electrostatic sprayed SnO2 and Cu-doped SnO2 films for H2S detection

This paper presents the ability of electrostatic sprayed tin oxide (SnO₂) and tin oxide doped with copper oxide (1, 2, and 4 at.% Cu) films to detect different pollutant gases, i.e., H₂S, SO₂, and NO₂. The influence of a copper oxide dopant on the SnO₂ morphology is studied using scanning electron microscopy (SEM) technique, which reveals a small decrease in the porosity and particle size when the amount of dopant is increased. The sensing properties of the SnO₂ films are greatly improved by doping, i.e., the Cu-doped SnO₂ films have large response to low concentration (10 ppm) of H₂S at low operating temperature (100 °C). Furthermore, no cross-sensitivity to 1 ppm NO₂ and 20 ppm SO₂ is observed. Among the studied films, the 1 at.% Cu-doped SnO₂ layer is the most sensitive in the detection of all the studied gases.     

H2 near-optimal model reduction

This note considers the problem of finding a stable reduced-order model for a given stable model so that its H₂ model reduction cost differs by less than a prescribed error from the optimal cost, which may or may not be achievable. It is shown that this new version of the long-standing H₂ optimal model reduction problem can be reduced to a well-posed smooth constrained minimization problem whose global solution is guaranteed to exist. In addition, a globally convergent algorithm in the form of an ordinary differential equation is derived     

H2 norm checking for systems with parameteruncertainties

This paper studies the problem of H₂ norm checking for a MIMO system with parameter uncertainties. Under the assumptions that the coefficients of the numerator polynomial of the system's transfer function are multi-affine functions of the uncertain parameter that varies in a convex polytope, and that the coefficients of the denominator polynomial of the system's transfer function are affine functions of the uncertain parameter which varies in a convex polytope, a vertex checking result is obtained     

广义线性系统的H2性能分析

利用广义Lyapunov方程,研究广义连续线性系统的稳定性,给出了一个充要条件.基于该Lyapunov方程,给出了计算广义连续线性系统的H2范数的状态空间方法.     

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     

H2 sensing characteristics of highly textured Pd-doped SnO2 thin films

The effects of the crystallographic orientation on the H₂ gas sensing properties were investigated in highly oriented polycrystalline Pd-doped SnO₂ films, which were obtained using rf magnetron sputtering of a Pd (0.5 wt%)-SnO₂ target on various substrates (a-, m-, r-, and c-cut sapphire and quartz). All the films had a similar thickness (110 nm), root-mean-square (rms) roughness (1.3 nm), surface area, and chemical status (O, Sn, and Pd). However, the orientation of the films was strongly affected by the orientation of the substrates. The (1 0 1), (0 0 2), and (1 0 1) oriented films were grown on (a-cut), (m-cut), and (r-cut) Al₂O₃ substrates, respectively, and rather randomly oriented films were deposited on (0 0 0 1) (c-cut) Al₂O₃ and quartz substrates. In addition, the oriented Pd-doped SnO₂ films were highly textured and had in-plane orientation relationships with the substrates similar to the epitaxial films. The (1 0 1) Pd-doped SnO₂ films on and Al₂O₃ showed a considerably higher H₂ sensitivity, and their gas response decreased with increasing sensing temperature (400–550 °C). The films deposited on and (0 0 0 1) Al₂O₃ showed the maximum sensitivity at 500 °C. The comparison of the H₂ gas response between undoped and Pd-doped SnO₂ films revealed that the Pd-doping shifted the optimum sensing temperature to a lower value instead of improving the gas sensitivity.     

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     

H2 guaranteed cost control for singularly perturbeduncertain systems

The H₂ guaranteed cost control problem for a singularly perturbed norm-bounded uncertain system is addressed using the quadratic stabilizability framework. After defining the corresponding slow and fast uncertain subsystems, the set of quadratic stabilizing composite controls is characterized. Two Riccati equations have to be solved, one for the slow subsystem and the other for the fast subsystem. Choosing appropriately the weighting matrices, it is shown how to pick up in the set of quadratic stabilizing composite controls, a control minimizing an upper bound on the H₂ norm of a certain transfer matrix. The case of the guaranteed cost control problem for the reduced system is also investigated     

Model quality evaluation in H2 identification

Model quality evaluation in set-membership identification is investigated, In the recent literature, two main approaches have been used to investigate this problem, based on the concepts of n-width and of radius of information. In this paper it is shown that the n-width is related to the asymptotic value of the conditional radius of information of the identification problem with noise free measurements. Upper and lower bounds of the conditional radius of information are derived for the H₂ identification of exponentially stable systems using approximating n-dimensional models linear in the parameters in the presence of power bounded measurement errors. The derived bounds are shown to be convergent to the radius for a large number of data and model dimensions. Moreover, a formula for computing the worst case identification error for any linear algorithm is given. In particular, it is shown that the identification error of the least square algorithm may be increasing with respect to the model dimension (“peaking effect”), An almost-optimal linear algorithm is presented, that is not affected by this peaking effect, and indeed is asymptotically optimal     

On a New Method for H2 -Based Decomposition

This note proposes a simple linear matrix inequality (LMI) system for the design of static precompensators to reduce the interactions of a multivariable system. The approach is based on minimizing the H₂ norm of a modified system and the LMIs are derived from the well known technique of pseudodiagonalisation. The approach is applied to two complex real-life benchmark problems with high levels of interaction. It is shown that its performance is significantly better than previously proposed LMI optimization techniques for designing static precompensators     

FR-operator approach to the H2 analysis and synthesis ofsampled-data systems

Recently, a frequency-domain operator called frequency response (FR) operator was defined and shown to represent the transfer characteristics of a stable sampled-data system. Using this novel frequency-domain notion and introducing its extended notion called hybrid FR-operator, we define an H₂-norm for sampled-data systems in this paper. Then, sampled-data H₂ control problems are formulated and solved, whereby the usefulness of these frequency-domain notions is demonstrated both in the analysis and synthesis aspects of sampled-data systems. For the case of sampled-data systems with hybrid (i.e., both continuous-time and discrete-time) input and output signals, the H₂-norm defined by a hybrid FR-operator turns out to be slightly different from that defined in previous studies. The source of the discrepancy is also identified