Performance of an Adaptive Controller for the Neuromuscular Blockade Based on Inversion of a Wiener Model

An adaptive controller based on a minimally parameterized parsimonious Wiener model for the effect of the muscle relaxant rocuronium in the neuromuscular blockade is presented. The controller structure combines inversion of the recursively identified static nonlinearity of the Wiener model with a positive compartmental control law for the linearized system. The overall strategy exploits the fact that the model has only two parameters, which are estimated by an extended Kalman filter. Due to the fact that the positive control law for total mass conservation of compartmental systems is only proven to be convergent for time‐invariant systems, the identification of the parameter in the linear block of the minimally parameterized parsimonious Wiener model is stopped when the controller is turned on. The controller was implemented in the platform Galeno and tested in simulation and in thirteen real cases of patients under general anesthesia. The good reference tracking results and robustness to noise show the reliability of the proposed strategy.     

Bifurcation analysis of PID-controlled neuromuscular blockade in closed-loop anesthesia

The problem of PID-controlled neuromuscular blockade (NMB) in closed-loop anesthesia is considered. Contrary to the usual practice of designing PID-controllers for nonlinear systems on the basis of a linearized model and online tests, bifurcation analysis is utilized in this paper for that purpose. Two nonlinear Wiener models for the NMB are considered: a conventional pharmacokinetic/pharmacodynamic (PK/PD) model and a parsimonious model suitable for online parameter estimation. The models under a PID feedback are analyzed in order to discern the safe intervals of the controller parameters that are not subject to complex dynamical phenomena. The parsimony of the mathematical model is instrumental in minimizing the number of bifurcation parameters. The analyses show that the closed-loop systems undergo Andronov–Hopf bifurcation at a point in the model parameter space giving rise to nonlinear oscillations. For steeper, but still feasible slopes of the nonlinear function parameterizing the static nonlinearity of the Wiener models, deterministic chaos can arise in the closed loop for lower concentrations of the anesthetic drug. A model-based PID-controller tuning procedure is suggested that guarantees a certain settling time and robustness margin of the resulting loop with respect to the bifurcation. The tuning procedure is illustrated on mathematical models identified from patient data and the corresponding PID controllers.     

Minimality and identifiability of discrete‐time switched autoregressive exogenous systems

This article studies the problem of minimality and identifiability for switched autoregressive exogenous (SARX) systems. We propose formal definitions of the concepts of identifiability and minimality for SARX models. Based on these formalizations, we derive conditions for minimality and identifiability of SARX systems. In particular, we show that polynomially parameterized SARX systems are generically identifiable.     

A comparative study of three advanced controllers for the regulation of hypnosis

The anesthetic state is a dynamic combination of hypnosis, analgesia and neuromuscular blockade that is maintained by infusing a cocktail of drugs. This work focuses on controlling the hypnosis during a surgical procedure by automatic regulation of isoflurane and employs Bispectral Index (BIS) as the primary controlled variable. A seventh-order nonlinear pharmacokinetic–pharmacodynamic representation has been used for the hypnosis dynamics of patients. This study uses a model predictive control structure for the regulation of BIS. Performance of this controller has been tested for a range of patients and compared with two previously employed control strategies (cascade internal model controller and cascade controller with modeling error compensation). Performance of the three controllers has also been studied for a step change in BIS, measured disturbances and noise in the measured variables. Numerical simulations show that the model predictive controller performed better than the other two controllers.     

Identification and Identifiability of Unknown Parameters in Multibody Dynamic Systems

Assessing design changes in mechanical systems from simulationresults requires both accurate dynamic models and accurate values forparameters in the models. Model parameters are often unavailable ordifficult to measure. This study details an identification procedure fordetermining optimal values for unknown or estimated model parametersfrom experimental test data. The resulting optimization problem issolved by Levenberg–Marquardt methods. Partial derivative matricesneeded for the optimization are computed through sensitivity analysis.The sensitivity equations to be solved are generated analytically.Unfortunately, not all parameters can be uniquely determined using anidentification procedure. An issue of parameter identifiability remains.Since a global identifiability test is impractical for even the simplestmodels, a local identifiability test is developed. Two examples areprovided. The first example highlights the test for parameteridentifiability, while the second shows the usefulness of parameteridentification by determining vehicle suspension parameters fromexperimentally measured data.     

Identifiability of homogeneous systems using the state isomorphism approach

New results are presented concerning the state isomorphism approach to global identifiability analysis of parameterized classes of nonlinear state space systems with specified initial states. In particular we study the class of homogeneous systems, for which, under certain conditions, the local state isomorphism for a pair of indistinguishable parameter vectors is shown to be homogeneous of degree one. For homogeneous polynomial systems, conditions are given under which the local state isomorphism becomes linear. Here, the issue of whether or not the observability rank condition holds at the origin is shown to be of key importance. The scope of the results, which extend to the multivariable case, is discussed and illustrated by a number of worked examples. This demonstrates how the developed theory can be put to use to investigate the global identifiability properties of parameterized model classes.     

基于 Kinect 的拉普拉斯网格形变三维人脸建模

为了快速创建真实感较强的三维人脸模型,提出了基于 Kinect 的拉普拉斯网格形 变建模方法。利用 Kinect 获取彩色和深度图像信息,对深度图像进行双边滤波处理,对彩色图 像进行低层级顶点定位;构建标准三维人脸模型,并为该人脸模型中的顶点建立低、中、高 3 个级别的层级结构,通过低、中层级中顶点的位置关系创建 Sibson 局部坐标约束;利用该约束 构建彩色图像中间层级顶点,并结合深度信息对标准三维人脸模型进行拉普拉斯网格变形,获 得真实感较强的三维人脸模型。实验结果表明,该算法在建模的真实感上得到了提高,与对比 算法相比,在建模时间上得到很大的优化。     

Generalised Hammerstein–Wiener system estimation and a benchmark application

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The parameter estimation of this model is investigated using a standard prediction error criterion coupled with a robust gradient based search algorithm. This approach is profiled using a Wiener–Hammerstein Benchmark example, which illustrates it to be effective and, via Monte-Carlo simulation, relatively robust against capture in local minima.     

Assessing local structural identifiability for environmental models

The local structural identifiability problem is investigated for the general case and demonstrated for a well-known microbial degradation model that includes 13 unknown parameters and 3 additional states. We address the identifiability question using a novel algorithm that can be used for large models with many parameters to be identified. A key ingredient in the analysis is the application of a singular value decomposition of the normalized parametric output sensitivity matrix that is obtained through a simple model integration. The SVD results are further analysed and verified in a complementary symbolic computation. It is especially the swiftness and accuracy of the suggested method that we consider to be a substantial advantage in comparison to existing methods for a structural identifiability analysis. The method also opens, in a natural way, the analysis of (parametric) uncertainty in general, and this is demonstrated in more detail in the results section.     

Factors affecting the identifiability of compartmental models

The identifiability of compartmental models is analysed through a series of examples which have been used to describe physiological or pharmacokinetic processes. Emphasis is placed on aspects of experimental identifiability which have hitherto received little attention in identifiability analysis. It is shown that where a single-input, single-output experiment results in non-identifiability or local identifiability, it is often possible to improve the situation by measuring more responses or simultaneously perturbing more inputs. Identifiability is then shown usually to depend on whether the observation gains are known and on the shape of the inputs, when more than one is applied. The relative merits of the Laplace transform and normal mode methods of analysing identifiability are discussed and illustrated with a substantial example. The identifiability analysis of a nonlinear compartmental model, with state-dependent rate coefficients, is presented. It is shown that inclusion of a neglected (nonlinear) relationship can make a previously non-identifiable model uniquely identifiable.     

维纳模型的最小二乘支持向量机辨识

针对传统维纳模型辨识方法存在算法复杂、精度低的问题,通过对最小二乘支持向量机建模原理和维纳模型结构特点的分析,提出一种基于最小二乘支持向量机的维纳模型辨识新方法.该方法充分利用了维纳模型中具有线性环节这一先验知识,实现了线性和非线性环节参数的同时辨识.对于多变量维纳模型,该方法同样适用.给出并证明了该方法存在唯一解的约束条件 - 参数部分列满秩.仿真实验表明了该方法的有效性,与标准最小二乘支持向量机辨识方法相比,该方法具有更高的精度.     

Fuzzy local linearization and local basis function expansion innonlinear system modeling

Fuzzy local linearization is compared with local basis function expansion for modeling unknown nonlinear processes. First-order Takagi-Sugeno fuzzy model and the analysis of variance (ANOVA) decomposition are combined for the fuzzy local linearization of nonlinear systems, in which B-splines are used as membership functions of the fuzzy sets for input space partition. A modified algorithm for adaptive spline modeling of observation data (MASMOD) is developed for determining the number of necessary B-splines and their knot positions to achieve parsimonious models. This paper illustrates that fuzzy local linearization models have several advantages over local basis function expansion based models in nonlinear system modeling.     

Curvature estimation in oriented patterns using curvilinear modelsapplied to gradient vector fields

Curved oriented patterns are dominated by high frequencies and exhibit zero gradients on ridges and valleys. Existing curvature estimators fail here. The characterization of curved oriented patterns based on translation invariance lacks an estimation of local curvature and yields a biased curvature-dependent confidence measure. Using parameterized curvilinear models we measure the amount of local gradient energy along the model gradient as a function of model curvature. Minimizing the residual energy yields a closed-form solution for the local curvature estimate and the corresponding confidence measure. We show that simple curvilinear models are applicable in the analysis of a wide variety of curved oriented patterns     

A probabilistic approach to multivariable robust filtering andopen-loop control

A new approach to robust filtering, prediction, and smoothing of discrete-time signal vectors is presented. Linear time-invariant filters are designed to be insensitive to spectral uncertainty in signal models. The goal is to obtain a simple design method, leading to filters which are not overly conservative. Modeling errors are described by sets of models, parameterized by random variables with known covariances. These covariances could either be estimated from data or be used as robustness “tuning knobs.” A robust design is obtained by minimizing the ℋ₂-norm or, equivalently, the mean square estimation error, averaged with respect to the assumed model errors. A polynomial solution, based on an averaged spectral factorization and a unilateral Diophantine equation, is derived. The robust estimator is referred to as a cautious Wiener filter. It turns out to be only slightly more complicated to design than an ordinary Wiener filter. The methodology can be applied to any open-loop filtering or control problem. In particular, we illustrate this for the design of robust multivariable feedforward regulators, decoupling and model matching filters     

Nonlinear robust constrained control of partially uncontrollable and open-loop unstable systems

In this paper we consider a bilinear matrix inequality (BMI) based method, which provides an ellipsoidal estimate of the region of attraction, for nonlinear constrained robust stabilization. Robustness against model uncertainty is handled. The method is based on an uncertain multi-model representation of the plant parameterized by affine local models and their respective supports in the state-space, and an associated piecewise affine state-feedback structure. We show that the method is applicable to uncertain constrained systems that are partially uncontrollable and open-loop unstable.     

A priori identifiability: An overview on definitions and approaches

For a system, a priori identifiability is a theoretical property depending only on the model and guarantees that its parameters can be uniquely determined from observations. This paper provides a survey of the various and numerous definitions of a priori identifiability given in the literature, for both deterministic continuous and discrete-time models. A classification is done by distinguishing analytical and algebraic definitions as well as local and global ones. Moreover, this paper provides an overview on the distinct methods to test the parameter identifiability. They are classified into the so-called output equality approaches, local state isomorphism approaches and differential algebra approaches. A few examples are detailed to illustrate the methods and complete this survey.     

Equivalence and identifiability analysis of uncontrolled nonlinear dynamical systems

The problem of parameter identifiability has been considered from different points of view in the case of nonlinear dynamical systems. For analytic systems the standard approach for uncontrolled systems is the Taylor series approach (Pohjanpalo, Math. Biosciences 41 (1978) 21), or the approaches based on differential algebra for polynomial and rational systems. The similarity transformation approach, based on the local state isomorphism theorem, gives a sufficient and necessary condition for global identifiability of nonlinear controlled systems. But it leads only to a necessary condition for identifiability in the case of some uncontrolled systems. Our contribution consists in using the equivalence of systems, based on the straightening out theorem, to analyse the identifiability of uncontrolled systems. From this theory, we state the necessary or sufficient identifiability conditions, some of them depending on the state variable dimension.     

Numerical and visual evaluation of hydrological and environmental models using the Monte Carlo analysis toolbox

The detailed evaluation of mathematical models and the consideration of uncertainty in the modeling of hydrological and environmental systems are of increasing importance, and are sometimes even demanded by decision makers. At the same time, the growing complexity of models to represent real-world systems makes it more and more difficult to understand model behavior, sensitivities and uncertainties. The Monte Carlo Analysis Toolbox (MCAT) is a Matlab library of visual and numerical analysis tools for the evaluation of hydrological and environmental models. Input to the MCAT is the result of a Monte Carlo or population evolution based sampling of the parameter space of the model structure under investigation. The MCAT can be used off-line, i.e. it does not have to be connected to the evaluated model, and can thus be used for any model for which an appropriate sampling can be performed. The MCAT contains tools for the evaluation of performance, identifiability, sensitivity, predictive uncertainty and also allows for the testing of hypotheses with respect to the model structure used. In addition to research applications, the MCAT can be used as a teaching tool in courses that include the use of mathematical models.     

A parameter estimation and identifiability analysis methodology applied to a street canyon air pollution model

Mathematical models are increasingly used in environmental science thus increasing the importance of uncertainty and sensitivity analyses. In the present study, an iterative parameter estimation and identifiability analysis methodology is applied to an atmospheric model – the Operational Street Pollution Model (OSPM^®). To assess the predictive validity of the model, the data is split into an estimation and a prediction data set using two data splitting approaches and data preparation techniques (clustering and outlier detection) are analysed. The sensitivity analysis, being part of the identifiability analysis, showed that some model parameters were significantly more sensitive than others. The application of the determined optimal parameter values was shown to successfully equilibrate the model biases among the individual streets and species. It was as well shown that the frequentist approach applied for the uncertainty calculations underestimated the parameter uncertainties. The model parameter uncertainty was qualitatively assessed to be significant, and reduction strategies were identified.