A reduced regularization strategy for economic NMPC

Nonlinear Model Predictive Control (NMPC) enables the incorporation of detailed dynamic process models for nonlinear, multivariable control with constraints. This optimization-based framework also leads to on-line dynamic optimization with performance-based and so-called economic objectives. Nevertheless, economic NMPC (eNMPC) still requires careful formulation of the nonlinear programming (NLP) subproblem to guarantee stability. In this study, we derive a novel reduced regularization eNMPC approach with stability guarantees. Compared with full state regularization, the proposed strategy is less conservative and easier to implement. The resulting eNMPC framework is firstly demonstrated on a nonlinear continuous stirred-tank reactor (CSTR) example and a large-scale double distillation system example. Then the proposed strategy is applied to a challenging nonlinear CO₂ capture model, where bubbling fluidized bed models comprise a solid-sorbent post-combustion carbon capture system. Our results indicate the benefits of this improved eNMPC approach over tracking to the setpoint, and better stability over eNMPC without regularization.     

Deformable registration using patch-wise shape matching

We present a novel approach for non-rigid registration of partially overlapping surfaces acquired from a deforming object. To allow for large and general deformations our method employs a nonlinear physics-inspired deformation model, which has been designed with a particular focus on robustness and performance. We discretize the surface into a set of overlapping patches, for each of which an optimal rigid motion is found and interpolated faithfully using dual quaternion blending. Using this discretization we can formulate the two components of our objective function—a fitting and a regularization term—as a combined global shape matching problem, which can be solved through a very robust numerical approach. Interleaving the optimization with successive patch refinement results in an efficient hierarchical coarse-to-fine optimization. Compared to other approaches our as-rigid-as-possible deformation model is faster, causes less distortion, and gives more accurate fitting results.     

基于可视化计算的图形建模及参数寻优环境的设计与实现

研究了复杂非线性系统参数优化环境的可视化建模技术及软件实现问题．应用先进的仿真技术,采用面向对象和结构化设计方法,通过通用软件实现了复杂系统参数自动寻优环境的高度可视化的一体化;与基于常规高级和谐设计语言的参数寻优方法相比,该方法不仅不用传统程序代码对算法编程,而且可方便地对系统进行多参数自动迭代寻优试验及进行智能化分析．     

非线性离散动态系统优化与参数估计集成的多模型方法

在非线性系统分时段线性化多模型基础上,给出了非线性离散动态系统优化与参数估 计集成的多模型方法,并论证了算法的最优性和收敛性.在存在模型-实际差异的情况下,从分 时段线性化多模型出发通过迭代运算可得到实际非线性离散动态系统的真实最优解.仿真结果 表明了算法的有效性和实用性.     

Adaptive eigenspace for multi-parameter inverse scattering problems

A nonlinear optimization method is proposed for inverse scattering problems in the frequency domain, when the unknown medium is characterized by one or several spatially varying parameters. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type method combined with frequency stepping. Instead of a grid-based discrete representation, each parameter is projected to a separate finite-dimensional subspace, which is iteratively adapted during the optimization. Each subspace is spanned by the first few eigenfunctions of a linearized regularization penalty functional chosen a priori. The (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Numerical results illustrate the accuracy and efficiency of the resulting adaptive eigenspace regularization for single and multi-parameter problems, including the well-known Marmousi model from geosciences.     

Least squares support vector machines with tuning based on chaotic differential evolution approach applied to the identification of a thermal process

In the past decade, support vector machines (SVMs) have gained the attention of many researchers. SVMs are non-parametric supervised learning schemes that rely on statistical learning theory which enables learning machines to generalize well to unseen data. SVMs refer to kernel-based methods that have been introduced as a robust approach to classification and regression problems, lately has handled nonlinear identification problems, the so called support vector regression. In SVMs designs for nonlinear identification, a nonlinear model is represented by an expansion in terms of nonlinear mappings of the model input. The nonlinear mappings define a feature space, which may have infinite dimension. In this context, a relevant identification approach is the least squares support vector machines (LS-SVMs). Compared to the other identification method, LS-SVMs possess prominent advantages: its generalization performance (i.e. error rates on test sets) either matches or is significantly better than that of the competing methods, and more importantly, the performance does not depend on the dimensionality of the input data. Consider a constrained optimization problem of quadratic programing with a regularized cost function, the training process of LS-SVM involves the selection of kernel parameters and the regularization parameter of the objective function. A good choice of these parameters is crucial for the performance of the estimator. In this paper, the LS-SVMs design proposed is the combination of LS-SVM and a new chaotic differential evolution optimization approach based on Ikeda map (CDEK). The CDEK is adopted in tuning of regularization parameter and the radial basis function bandwith. Simulations using LS-SVMs on NARX (Nonlinear AutoRegressive with eXogenous inputs) for the identification of a thermal process show the effectiveness and practicality of the proposed CDEK algorithm when compared with the classical DE approach.     

Multi-loop nonlinear internal model controller design under nonlinear dynamic PLS framework using ARX-neural network model

In this paper, a novel multi-loop nonlinear internal model control (IMC) strategy for multiple-input multiple-output (MIMO) systems is presented under the partial least squares (PLS) framework, which automatically decomposes the system into several univariate subsystems in the latent space. To formulate a nonlinear dynamic PLS framework, we propose an ARX-neural network (ARX-NN) cascaded structure, and incorporate it into PLS inner model. A gradient-based optimization approach is then provided to identify the parameter sets of the ARX-NN PLS model so that the plant-model mismatch is minimized. Furthermore, with perfect model, we show that the response of the closed loop system can be reduced to a simple linear IMC filter with the original system delay. The simulation results of a methylcyclohexane (MCH) distillation column from Aspen Dynamic Module, demonstrate the effectiveness of our approach in terms of disturbance rejection and tracking performance.     

A parameter optimization method for radial basis function type models

This paper considers the nonlinear systems modeling problem for control. A structured nonlinear parameter optimization method (SNPOM) adapted to radial basis function (RBF) networks and an RBF network-style coefficients autoregressive model with exogenous variable model parameter estimation is presented. This is an off-line nonlinear model parameter optimization method, depending partly on the Levenberg-Marquardt method for nonlinear parameter optimization and partly on the least-squares method using singular value decomposition for linear parameter estimation. When compared with some other algorithms, the SNPOM accelerates the computational convergence of the parameter optimization search process of RBF-type models. The usefulness of this approach is illustrated by means of several examples.     

A bias-corrected estimator for nonlinear systems with output-error type model structures

Parametric identification of linear time-invariant (LTI) systems with output-error (OE) type of noise model structures has a well-established theoretical framework. Different algorithms, like instrumental-variables based approaches or prediction error methods (PEMs), have been proposed in the literature to compute a consistent parameter estimate for linear OE systems. Although the prediction error method provides a consistent parameter estimate also for nonlinear output-error (NOE) systems, it requires to compute the solution of a nonconvex optimization problem. Therefore, an accurate initialization of the numerical optimization algorithms is required, otherwise they may get stuck in a local minimum and, as a consequence, the computed estimate of the system might not be accurate. In this paper, we propose an approach to obtain, in a computationally efficient fashion, a consistent parameter estimate for output-error systems with polynomial nonlinearities. The performance of the method is demonstrated through a simulation example.     

具有未知非线性死区的自适应模糊控制

基于滑模控制原理，利用模糊系统的逼近能力，提出一种自适应模糊控制方法．该方法提出一种简化非线性死区输入模型，取消了非线性死区输入模型的倾斜度相等以及死区边界对称的条件，还取消了非线性死区输入模型各种参数已知的条件．该方法通过引入逼近误差的自适应补偿项来消除建模误差和参数估计误差的影响．理论分析证明了闭环系统是半全局一致终结有界，跟踪误差收敛到零．仿真结果表明了该方案的有效性．     

Linear control of nonlinear systems based on nonlinearity measures

In reality, virtually every process is a nonlinear system. Nevertheless, linear controller design methods have proved to be adequate in many applications. In practice, the linear controller design is usually done disregarding a possible nonlinear plant/linear model mismatch. In this work we introduce a general framework for the development of linear controllers for nonlinear systems based on nonlinearity measures. Nonlinearity measures are tools to assess the extent of a system’s inherent nonlinearity instead of just recognizing a system as being linear or nonlinear. Recent work shows that nonlinearity measures characterize the magnitude of the modeling error when an optimal linear model is used for the nonlinear system. The best linear model can then be used to design a linear controller that robustly stabilizes the linear system in presence of the nonlinear modeling error. A crucial point is that both, the best linear model and the modeling error, are determined for a specified region of operation, thus significantly increasing the class of applicable nonlinear systems. Examples demonstrate the (necessity and) effectiveness of the proposed approach.     

Application of evolutionary programming to adaptive regularization in image restoration

Image restoration is a difficult problem due to the ill-conditioned nature of the associated inverse filtering operation, which requires regularization techniques. The choice of the corresponding regularization parameter is thus an important issue since an incorrect choice would either lead to noisy appearances in the smooth regions or excessive blurring of the textured regions. In addition, this choice has to be made adaptively across, different image regions to ensure the best subjective quality for the restored image. We employ evolutionary programming (EP) to solve this adaptive regularization problem by generating a population of potential regularization strategies, and allowing them to compete under a new error measure which characterizes a large class of images in terms of their local correlational properties. The nonavailability of explicit gradient information for this measure motivates the adoption of EP techniques for its optimization, which allows efficient search at multiple error surface points. The adoption of EP also allows the broadening of the range of possible cost functions for image processing so that we can choose the most relevant function rather than the most tractable one for a particular image processing application.     

Constrained nonlinear multivariable control of a fluid catalytic cracking process

In this paper, a nonlinear constrained optimization strategy is proposed and applied to the reactor-regenerator section of a fluid catalytic cracking (FCC) unit. A nonlinear dynamic model of the fluid catalytic cracking process was used for the dynamic analysis of the plant and nonlinear multivariable control system. The model realistically simulates the riser-reactor and the one stage regenerator by assembling the mass and energy balances on the system of reactions. The model results were tested in a real-time application and the results were used to provide the initial values for the nonlinear control system design. A dynamic parameter update algorithm was used to reduce the effect of large modelling errors by regularly updating the model parameters. The constrained nonlinear optimization algorithm and strategies were tested in real-time on the fluid catalytic cracking reactor-regenerator. The results compared favourably to those from a linear multivariable controller.     

An iterative algorithm for myocardial activation time imaging

An iterative algorithm based on a general regularization scheme for nonlinear ill-posed problems in Hilbert scales (method A) is applied to the magnetocardiographic inverse problem imaging the surface myocardial activation time map. This approach is compared to an algorithm using an optimization routine for nonlinear ill-posed problems based on Tikhonov's approach of second order (method B). Method A showed good computational performance and the scheme for determining the proper regularization parameter lambda was found to be easier than in case of method B. The formulation is applied to magnetocardiographic recordings from a patient suffering from idiopathic ventricular tachycardia in which a sinus rhythm sequence was followed by a ventricular extrasystolic beat.     

Design of robust gain-scheduled PI controllers for nonlinear processes

Gain-scheduling has proven to be a successful design methodology in many engineering applications. However, in the absence of a sound theoretical analysis, these designs come with no guarantees of robust stability, performance or even nominal stability of the overall gain-scheduled deign.This paper presents such an analysis for one type of nonlinear gain-scheduled control system based on the process input for nonlinear chemical processes. A methodology is also proposed for the design and optimization of the robust gain-scheduled PI controller. Conditions which guarantee robust stability and performance are formulated as a finite set of linear matrix inequalities (LMIs) and hence, the resulting problem is numerically tractable. Issues of modeling error and input-saturation are explicitly incorporated into the analysis. A simulation study of a nonlinear continuous stirred tank reactor (CSTR) process indicates that this approach can produce efficient sub-optimal robust gain-scheduled controllers.     

Kernel machine-based rank-lifting regularized discriminant analysis method for face recognition

To address two problems, namely nonlinear problem and singularity problem, of linear discriminant analysis (LDA) approach in face recognition, this paper proposes a novel kernel machine-based rank-lifting regularized discriminant analysis (KRLRDA) method. A rank-lifting theorem is first proven using linear algebraic theory. Combining the rank-lifting strategy with three-to-one regularization technique, the complete regularized methodology is developed on the within-class scatter matrix. The proposed regularized scheme not only adjusts the projection directions but tunes their corresponding weights as well. Moreover, it is shown that the final regularized within-class scatter matrix approaches to the original one as the regularized parameter tends to zero. Two public available databases, namely FERET and CMU PIE face databases, are selected for evaluations. Compared with some existing kernel-based LDA methods, the proposed KRLRDA approach gives superior performance.     

Nonlinear model predictive control for models in quasi‐linear parameter varying form

This article presents a nonlinear model predictive control (NMPC) approach based on quasi‐linear parameter varying (quasi‐LPV) representations of the model and constraints. Stability of the proposed algorithm is ensured by the offline solution of an optimization problem with linear matrix inequality constraints in conjunction with an online terminal state constraint. Furthermore, an iterative approach is presented with which the NMPC optimization problem can be handled by solving a series of Quadratic Programs at each time step, this being highly computationally efficient. A practical and simple way of obtaining quasi‐LPV representations of the system using velocity‐based linearization is presented in two examples.     

A randomized method for solving discrete ill-posed problems

An approach is proposed to the stable solution of discrete ill-posed problems on the basis of a combination of random projection of the initial ill-conditioned matrix with an ill-defined numerical rank and the pseudo-inversion of the resultant matrix. To select the dimension of the projection matrix, we propose to use criteria for the selection of a model and a regularization parameter. The results of experimental studies based on the well-known examples of discrete ill-posed problems are presented. Their solution errors are close to the Tikhonov regularization error, but a matrix dimension reduction owing to projection reduces the expenditures for computations, especially at high noise levels.     

一种空间飞行器姿态控制非线性模型的预测控制新算法

空间飞行器的姿态控制受到诸如带时延的非线性动态特性、模型和参数的不确定性等因素的影响 ,其控制相当复杂。传统的控制技术 (如PID控制 )对控制对象的过程模型要求较高 ,且不能解决过程控制中非线性、时变、控制输入的约束性等因素的影响 ,其控制所能达到的性能和效率也远不够满足当前飞行器的控制要求。该文将介绍一种新型的基于控制输入的函数空间最优化的模型预测控制算法 ,称为函数空间模型预测控制 (F -MPC)。该法可用于线性和非线性系统 ,对过程模型要求不高 ,能在控制输入约束条件存在的情况下通过在线优化使系统很好地跟踪期望轨迹 ,并且解决了PID控制所遇到的问题。同时 ,将该算法用于空间飞行器的姿态控制仿真 ,仿真结果表明控制效果很好。