A nonlinear functional approach to LFT model validation

Model validation provides a useful means of assessing the ability of a model to account for a specific experimental observation, and has application to modeling, identification and fault detection. In this paper, we consider a new approach to the model validation problem by deploying quadratic functionals, and more generally nonlinear functionals, to specify noise and dynamical perturbation sets. Specifically, we consider a general linear fractional transformation framework for the model structure, and use constraints involving nonlinear functional inequalities to specify model non-linearities and unknown perturbations, and characteristics of noise and disturbance signals. Sufficient conditions for invalidation of such models are provided in terms of semidefinite programming problems.     

Risk-sensitivity conditions for stochastic uncertain model validation

The paper presents sufficient and necessary conditions that verify the relevance of an assumed linear stochastic system model for problems in which probabilistic characteristics of the plant are not known exactly. The approach is to establish the existence of an admissible probability space on which the output of the candidate stochastic system model is consistent (in a stochastic sense) with the noisy output of the plant.     

Probabilistic model validation for uncertain nonlinear systems

This paper presents a probabilistic model validation methodology for nonlinear systems in time-domain. The proposed formulation is simple, intuitive, and accounts both deterministic and stochastic nonlinear systems with parametric and nonparametric uncertainties. Instead of hard invalidation methods available in the literature, a relaxed notion of validation in probability is introduced. To guarantee provably correct inference, algorithm for constructing probabilistically robust validation certificate is given along with computational complexities. Several examples are worked out to illustrate its use.     

Stabilization of uncertain linear systems: an LFT approach

This paper develops machinery for control of uncertain linear systems described in terms of linear fractional transformations (LFTs) on transform variables and uncertainty blocks with primary focus on stabilization and controller parameterization. This machinery directly generalizes familiar state-space techniques. The notation of Q-stability is defined as a natural type of robust stability, and output feedback stabilizability is characterized in terms of Q-stabilizability and Q-detectability which in turn are related to full information and full control problems. Computation is in terms of convex linear matrix inequalities (LMIs), the controllers have a separation structure, and the parameterization of all stabilizing controllers is characterized as an LFT on a stable, free parameter     

Robust stability of uncertain singular time-delay systems via LFT approach

The robust stability problem of continuous-time singular systems with multiple state delays and bounded parametric uncertainties is considered. Both commensurate and non-commensurate delays are investigated. On the basis of the linear fractional transformations (LFTs) framework and μ-analysis, a systematic approach is derived to convert the robustness problem to a robust nonsingularity problem. Some explicit conditions are proposed to guarantee the uncertain singular time-delay system being regular, impulse-free and stable independent of delay. Two illustrative examples are given to show the feasibility of the proposed technique.     

Robust and switched feedforward control of uncertain LFT systems

This paper presents a new robust switched feedforward control scheme for a class of uncertain systems described in a standard linear fractional transformation form. First, the analysis conditions for switching stability are derived by using a piecewise Lyapunov function incorporated with the min‐switching control technique. Based on the analysis results, the synthesis conditions are then formulated as a special type of bilinear matrix inequalities, which can be solved by means of linear matrix inequalities and line search. Both robust and feedforward control problems are considered. The proposed robust switched control scheme outperforms existing robust feedforward control approaches for uncertain systems based on single quadratic Lyapunov function, and leads to less conservative control design. Numerical examples will be used to illustrate the effectiveness and advantages of the proposed results. Copyright © 2015 John Wiley & Sons, Ltd.     

On the consistency between an LFT described model set and frequencydomain data

The main objective of this technical note is to derive a simple necessary and sufficient condition for a linear fractional transformation (LFT) perturbed model set being consistent with frequency domain plant input-output data. Only discrete-time models and unstructured modeling errors are dealt with. Compared with the available results in which the eigenvalues of a matrix are involved, this condition is related only to the Euclidean norms of two vectors. Moreover, these vectors linearly depend on measurement errors. Some of its applications to model set validation have been briefly discussed. Based on this condition, an almost analytic solution has been established for model set validation under a deterministic framework when the measurement errors are energy bounded. Numerical simulations show that this consistency condition can lead to a significant computation cost reduction     

Evaluating probabilistic models with uncertain model parameters

Probabilistic models are commonly used to evaluate quality attributes, such as reliability, availability, safety and performance of software-intensive systems. The accuracy of the evaluation results depends on a number of system properties which have to be estimated, such as environmental factors or system usage. Researchers have tackled this problem by including uncertainties in the probabilistic models and solving them analytically or with simulations. The input parameters are commonly assumed to be normally distributed. Accordingly, reporting the mean and variances of the resulting attributes is usually considered sufficient. However, many of the uncertain factors do not follow normal distributions, and analytical methods to derive objective uncertainties become impractical with increasing complexity of the probabilistic models. In this work, we introduce a simulation-based approach which uses Discrete Time Markov Chains and probabilistic model checking to accommodate a diverse set of parameter range distributions. The number of simulation runs automatically regulates to the desired significance level and reports the desired percentiles of the values which ultimately characterises a specific quality attribute of the system. We include a case study which illustrates the flexibility of this approach using the evaluation of several probabilistic properties.     

Robust H/sub 2/ and H/sub /spl infin// filters for uncertain LFT systems

In this note, robust H/sub 2/ and H/sub /spl infin// filter design problems are considered. The uncertainties, unstructured or structured, are norm bounded and represented by linear fractional transformation (LFT). The main result is that after upper-bounding the objectives, the problems of minimizing the upper bounds are converted to finite dimensional convex optimization problems involving linear matrix inequalities (LMIs). These are extensions of well-known results for systems with polytopic uncertainty. It is shown that for the unstructured, norm bounded uncertainty case, the upper bounds are directly minimized (without further overbounding), yielding less conservative results than previously available. An elementary numerical example is given to illustrate the results.     

Nonclassical dynamics with time- and intensity-dependent coupling

Nonclassical light and collapse-revival dynamics are consequences of dynamical quantum interference in transient photon-atom interaction. We study the time evolution of atom and photons in a high quality cavity for time-dependent atom-field coupling, with different initial field states and initial atomic states. The inversion for initial superposed atomic state seems to be independent of initial classical fields but can be stimulated by the Schrodinger cat field. Interesting effects of the transient coupling are found through analysis of the collapse-revival in population inversion and the features in the Wigner function. Oscillatory coupling coefficient can prolong the occurrence of collapse, in analogy to the Zeno effect. The intensity atom-field coupling duration is an important parameter for controlling atomic inversion and producing frozen nonclassical light in the cavity after the atom-field coupling ceases.     

Aircraft turbofan engine linear model with uncertain eigenvalues

This paper presents an aircraft turbofan engine model identification in time domain. The identification makes use of a multivariable linear model of turbofan engine dynamics having uncertain eigenvalues. The uncertainty describes the difference between nonlinear and linear models. The bounds for real and imaginary parts of uncertain matrix eigenvalues are determined using nonlinear programming. The results of identification application using a detailed nonlinear model of an aircraft turbofan engine are presented.     

On the reproduction of closed-loop experimental data by an LFT perturbed model set

This paper investigates the consistency between frequency domain closed-loop experimental data and a model set with linear fractional unstructured uncertainties. When the number of unstable poles of the transfer function matrices (TFM) in the model set are identical, a necessary and sufficient condition is derived for the reproduction of experimental data. This condition is expressed as the non-positiveness of a quadratic form of the external disturbances and measurement errors, together with a linear constraint. In this derivation, it is not required that all the TFMs in the model set are internally stabilizable by the controller. The condition is also not necessary for the closed-loop system consisting of the nominal model and the controller to be internally stable. It is believed that this condition is theoretically and computationally attractive in model set validation, no matter whether a deterministic or stochastic framework is adopted.     

资金需求不确定的银行卡网络鲁棒运作模型

研究了银行卡网络在实时高效运营的条件下,各成员银行的资金运作问题.在分析国内银联网络资金需求情况的基础上,运用随机模拟方法生成不确定需求情景,建立了以网络系统成本最小为目标的鲁棒模型.数值仿真结果表明,模型的解相对保守,能有效地保证银行卡网络运作的鲁棒性.     

LFT modelling and identification of anaerobic digestion

In this paper, a reduced order model of anaerobic digestion is first proposed, with the main goal to develop an efficient tool for process monitoring and control. Then, in order to perform parameter estimation, the model has been rewritten in a linear fractional transformation (LFT) formulation, using a symbolic tool originally developed for linear models and modified for the processing of nonlinear models. Two different test cases have been considered. In a first case, the data used for parameter identification have been generated by simulating the well known and more complex ADM1 model, considering waste activated sludge as substrate. In a second case, experimental data were collected on a laboratory scale equipment, operated in a semi-batch experiment, performing the anaerobic digestion of ultra-filtered cheese-whey.     

基于不确定模型误差系统的变分贝叶斯STCKF

强跟踪容积卡尔曼滤波器在对含有模型误差和时变噪声的非线性系统进行滤波时, 容易出现性能降低甚至发散. 鉴于此, 提出一种基于变分贝叶斯的强跟踪容积卡尔曼滤波算法. 该算法运用虚拟噪声法补偿模型误差, 假设虚拟噪声均值非零, 且满足高斯分布, 虚拟噪声方差服从逆gamma分布, 在强跟踪容积卡尔曼滤波器估计状态的同时, 采用变分贝叶斯推理估计虚拟噪声参数. 仿真结果表明, 所提出算法对含模型误差与时变噪声的非线性系统具有较好的估计精度, 相比于自适应算法具有更强的鲁棒性.     

具有噪声信息与状态模型不确定系统的IMM自适应滤波

卡尔曼滤波器广泛用于解决线性高斯系统的状态估计问题.然而,在实际应用中过程噪声和系统模型参数先验信息未知,且量测受到异常值干扰,给准确估计系统状态带来极大困难.针对具有噪声信息和状态模型不确定的动态系统,提出一种广义交互式多模型自适应滤波算法.该算法设计多个模型并行的方式对系统不确定进行处理,对于每个模型,建立Skew-T分布非对称重尾噪声表示模型,为了解决过程噪声与系统协方差相互耦合难以求解的问题,利用逆威沙特分布对系统预测协方差矩阵进行描述,并通过变分贝叶斯推理递归计算系统状态的后验分布.仿真结果和实验验证表明,在噪声信息和状态模型不确定条件下,所提出算法具有较高的估计精度.