Multivariable RBF-ARX model-based robust MPC approach and application to thermal power plant

For a class of smooth nonlinear multivariable systems whose working-points vary with time and the future working-points knowledge are unknown, a combination of a local linearization and a polytopic uncertain linear parameter-varying (LPV) state-space model is built to approximate the present and the future system’s nonlinear behavior, respectively. The combination models are constructed on the basis of a matrix polynomial multi-input multi-output (MIMO) RBF-ARX model identified offline for representing the underlying nonlinear system. A min–max robust MPC strategy is designed to achieve the systems’ output-tracking control based on the approximate models proposed. The closed loop stability of the MPC algorithm is guaranteed by the use of time-varying parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). The effectiveness of the modeling and control methods proposed in this paper is illustrated by a case study of a thermal power plant simulator.     

Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

This article addresses the synchronization of nonlinear master–slave systems under input time‐delay and slope‐restricted input nonlinearity. The input nonlinearity is transformed into linear time‐varying parameters belonging to a known range. Using the linear parameter varying (LPV) approach, applying the information of delay range, using the triple‐integral‐based Lyapunov–Krasovskii functional and utilizing the bounds on nonlinear dynamics of the nonlinear systems, nonlinear matrix inequalities for designing a simple delay‐range‐dependent state feedback control for synchronization of the drive and response systems is derived. The proposed controller synthesis condition is transformed into an equivalent but relatively simple criterion that can be solved through a recursive linear matrix inequality based approach by application of cone complementary linearization algorithm. In contrast to the conventional adaptive approaches, the proposed approach is simple in design and implementation and is capable to synchronize nonlinear oscillators under input delays in addition to the slope‐restricted nonlinearity. Further, time‐delays are treated using an advanced delay‐range‐dependent approach, which is adequate to synchronize nonlinear systems with either higher or lower delays. Furthermore, the resultant approach is applicable to the input nonlinearity, without using any adaptation law, owing to the utilization of LPV approach. A numerical example is worked out, demonstrating effectiveness of the proposed methodology in synchronization of two chaotic gyro systems. © 2015 Wiley Periodicals, Inc. Complexity 21: 220–233, 2016     

State observers for a class of multi-output nonlinear dynamic systems

This note considers the problem of observer design for a class of multi-output nonlinear systems. A new state observer design methodology for linear time-varying multi-output systems is presented. Furthermore, we show that the same methodology can be extended to a class of multi-output nonlinear systems. Some sufficient conditions for the existence of the proposed observer are obtained, which guarantee that the error of state estimation converges asymptotically to zero. An example is given to demonstrate the effectiveness of the proposed methodology.     

非线性再生散度随机效应模型的贝叶斯分析

非线性再生散度随机效应模型是一类非常广泛的统计模型，包括了线性随机效应模型、非线性随机效应模型、广义线性随机效应模型和指数族非线性随机效应模型等．本文研究非线性再生散度随机效应模型的贝叶斯分析．通过视随机效应为缺失数据以及应用结合Gibbs抽样技术和Metropolis-Hastings算法（简称MH算法）的混合算法获得了模型参数与随机效应的同时贝叶斯估计．最后，用一个模拟研究和一个实际例子说明上述算法的可行眭．     

Stabilization for switched nonlinear time-delay systems

This paper investigates the problem of stabilization for a class of switched nonlinear systems with time-delay. Based on the differential mean value theorem (DMVT), the switched nonlinear systems are transformed into switched linear parameter varying (LPV) systems. By using multiple Lyapunov function approach and convexity principle, and via observer-based output feedback, a sufficient condition for the stabilization of the original system is proposed, which has been expressed in terms of linear matrix inequalities (LMIs). Further, the control method is extended to a class of switched nonlinear systems with norm-bounded uncertainties. A new sufficient condition is proposed, which guarantees the class of uncertain switched systems, is asymptotically stabilizable. Finally, two examples are given to illustrate the effectiveness of the proposed approaches.     

Air path identification of diesel engines by LPV techniques for gain scheduled control

Modelling is a key element to improve the performance of engine control systems, but many factors like non-linearity and complexity complicate the derivation of sufficiently precise physical models. This motivates an increasing interest in data based models. Linear models can successfully represent the engine operation in some reduced regions, but tend to fail when large operating regions must be considered. This motivates the interest in deriving and using gain scheduling models or their natural extension, the linear parameter varying (LPV) models. In this article we propose to model the air path of diesel engines using input–output LPV models with a physically motivated structure and parameters estimated from data. These models are shown to combine good precision with simplicity and allow the systematic design of optimal and robust control systems, and can be determined in a very short time if sufficient data are available.     

Decoupling correlated and uncorrelated parametric uncertainty contributions for nonlinear models

For models with correlated parameters, the amount of uncertainty (generally measured by variance) in a model output contributed by a specific parameter encompasses two components: (1) the uncertainty contributed by the variations (used to represent uncertainty in the parameter) correlated with other parameters; and (2) the uncertainty contributed by the variations unique to the parameter of interest (i.e., uncorrelated variations or variations that cannot be explained by any other parameters in the model). A regression-based method has been proposed previously by Xu and Gertner (2008) [1] to decouple the correlated and uncorrelated contributions to uncertainties in model outputs by each parameter for linear models. Based on a modified version of the popular Fourier Amplitude Sensitivity Test (FAST), this paper develops a general approach for the quantification of the correlated and uncorrelated parametric uncertainty contributions in linear, nonlinear and non-monotonic models with linear or nonlinear dependence among parameters. The decoupling of correlated and uncorrelated contributions can help us determine if the uncertainty contributed by a specific parameter results from the uncertainty in itself or from its correlations with other parameters. Thus, this decoupling can be very useful in improving the understanding our modeled systems.     

Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach

State-dependent Riccati equation (SDRE) techniques are rapidly emerging as general design and synthesis methods of nonlinear feedback controllers and estimators for a broad class of nonlinear regulator problems. In essence, the SDRE approach involves mimicking standard linear quadratic regulator (LQR) formulation for linear systems. In particular, the technique consists of using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficient matrices. Theoretical advances have been made regarding the nonlinear regulator problem and the asymptotic stability properties of the system with full state feedback. However, there have not been any attempts at the theory regarding the asymptotic convergence of the estimator and the compensated system. This paper addresses these two issues as well as discussing numerical methods for approximating the solution to the SDRE. The Taylor series numerical methods works only for a certain class of systems, namely with constant control coefficient matrices, and only in small regions. The interpolation numerical method can be applied globally to a much larger class of systems. Examples will be provided to illustrate the effectiveness and potential of the SDRE technique for the design of nonlinear compensator-based feedback controllers.     

Data envelopment analysis with nonlinear virtual inputs and outputs

An underlying assumption in DEA is that the weights coupled with the ratio scales of the inputs and outputs imply linear value functions. In this paper, we present a general modeling approach to deal with outputs and/or inputs that are characterized by nonlinear value functions. To this end, we represent the nonlinear virtual outputs and/or inputs in a piece-wise linear fashion. We give the CCR model that can assess the efficiency of the units in the presence of nonlinear virtual inputs and outputs. Further, we extend the models with the assurance region approach to deal with concave output and convex input value functions. Actually, our formulations indicate a transformation of the original data set to an augmented data set where standard DEA models can then be applied, remaining thus in the grounds of the standard DEA methodology. To underline the usefulness of such a new development, we revisit a previous work of one of the authors dealing with the assessment of the human development index on the light of DEA.     

非线性随机效应模型的异方差性检验

随机效应模型广泛应用于刻画重复测量数据的特征．在该模型中,随机误差的方差包括受试群体内部及受试群体之间两项方差．Ｚｈａｎｇ和 Ｗｅｉｓｓ ２０００年研究了线性随机效应模型的异方差检验,本文对非线性随机效应模型,分别讨论了群体内、群体间和多变量的异方差性的检验问题,得到了检验的ｓｃｏｒｅ统计量,并讨论了三种情形下,相应的ｓｃｏｒｅ函数之间的关系．最后给出一个数值例子说明上述方法的有用性．     

Automated generation of LFT-based parametric uncertainty descriptions from generic aircraft models

A computer assisted modelling methodology is developed for the generation of linearized models with parametric uncertainties described by Linear Fractional Transformations (LFTs). The starting point of the uncertainty modelling is a class of generic nonlinear aircraft models with explicit parametric dependence used for simulation purposes. The proposed methodology integrates specialized software tools for object-oriented modelling, for simulation, and for numerical as well as symbolic computations. The methodology has many generic features being applicable to similar nonlinear model classes.     

具有随机效应和AR(1)误差的非线性纵向数据模型中组间方差和自相关系数的齐性检验

组间方差和自相关系数的齐性是纵向数据分析的基本假设之一,然而这种假设需要进行统计检验. Zhang \&; Weiss$^{[15]}$ 讨论了线性随机效应模型的组间和组内方差齐性的检验问题;林金官 \&; 韦博成$^{[10]}$ 研究了具有AR(1)误差但没有随机效应的非线性模型的自相关系数的齐性检验.该文研究具有随机效应和AR(1)误差的非线性模型的组间方差和自相关系数的齐性检验问题,构造了几个score检验统计量, 并通过Monte Carlo模拟方法研究了检验统计量的性质.最后利用该文的方法分析一组实际数据和一组模拟数据.     

The application of optimal control methodology to nonlinear programming problems

Dynamic programming techniques have proven to be more successful than alternative nonlinear programming algorithms for solving many discrete-time optimal control problems. The reason for this is that, because of the stagewise decomposition which characterizes dynamic programming, the computational burden grows approximately linearly with the numbern of decision times, whereas the burden for other methods tends to grow faster (e.g.,n ³ for Newton's method). The idea motivating the present study is that the advantages of dynamic programming can be brought to bear on classical nonlinear programming problems if only they can somehow be rephrased as optimal control problems.As shown herein, it is indeed the case that many prominent problems in the nonlinear programming literature can be viewed as optimal control problems, and for these problems, modern dynamic programming methodology is competitive with respect to processing time. The mechanism behind this success is that such methodology achieves quadratic convergence without requiring solution of large systems of linear equations.     

Temperature prediction at critical points in district heating systems

Current methodologies for the optimal operation of district heating systems use model predictive control. Accurate forecasting of the water temperature at critical points is crucial for meeting constraints related to consumers while minimizing the production costs for the heat supplier. A new forecasting methodology based on conditional finite impulse response (cFIR) models is introduced, for which model coefficients are replaced by coefficient functions of the water flux at the supply point and of the time of day, allowing for nonlinear variations of the time delays. Appropriate estimation methods for both are described. Results are given for the test case of the Roskilde district heating system over a period of more than 6 years. The advantages of the proposed forecasting methodology in terms of a higher forecast accuracy, its use for simulation purposes, or alternatively for better understanding transfer functions of district heating systems, are clearly shown.     

Parameter-dependent H∞ filter design for LPV systems and an autopilot application

This paper considers the design problem of parameter dependent H_∞ filters for linear parameter varying (LPV) systems whose parameters are measurable. Conditions for existence of parameter-dependent Lyapunov function are proposed via parametrical linear matrix inequality (LMI) constraints. Based on the solutions to the LMIs, an algorithm for the gain matrices of LPV filter is presented. The design method is applied to a missile system to demonstrate the effectiveness.     

Stabilization of nonlinear systems in compound critical cases

In this paper, we study the stabilization of nonlinear systems in critical cases by using the center manifold reduction technique. Three degenerate cases are considered, wherein the linearized model of the system has two zero eigenvalues, one zero eigenvalue and a pair of nonzero pure imaginary eigenvalues, or two distinct pairs of nonzero pure imaginary eigenvalues; while the remaining eigenvalues are stable. Using a local nonlinear mapping (normal form reduction) and Liapunov stability criteria, one can obtain the stability conditions for the degenerate reduced models in terms of the original system dynamics. The stabilizing control laws, in linear and/or nonlinear feedback forms, are then designed for both linearly controllable and linearly uncontrollable cases. The normal form transformations obtained in this paper have been verified by using code MACSYMA.     

A NARMAX model-based state-space self-tuning control for nonlinear stochastic hybrid systems

A novel state-space self-tuning control methodology for a nonlinear stochastic hybrid system with stochastic noise/disturbances is proposed in this paper. via the optimal linearization approach, an adjustable NARMAX-based noise model with estimated states can be constructed for the state-space self-tuning control in nonlinear continuous-time stochastic systems. Then, a corresponding adaptive digital control scheme is proposed for continuous-time multivariable nonlinear stochastic systems, which have unknown system parameters, measurement noise/external disturbances, and inaccessible system states. The proposed method enables the development of a digitally implementable advanced control algorithm for nonlinear stochastic hybrid systems.     

Robust Stability and Stabilization of a Class of Nonlinear Itô-Type Stochastic Systems via Linear Matrix Inequalities

This article presents a new approach to robust quadratic stabilization of nonlinear stochastic systems. The linear rate vector of a stochastic system is perturbed by a nonlinear function, and this nonlinear function satisfies a quadratic constraint. Our objective is to show how linear constant feedback laws can be formulated to stabilize this type of stochastic systems and, at the same time maximize the bounds on this nonlinear perturbing function which the system can tolerate without becoming unstable. The new formulation provides a suitable setting for robust stabilization of nonlinear stochastic systems where the underlying deterministic systems satisfy the generalized matching conditions. Our sufficient conditions are written in matrix forms, which are determined by solving linear matrix inequalities (LMIs), which have significant computational advantage over any other existing techniques. Examples are given to demonstrate the results.     

Experimental study of steady-state localization in coupled beams with active nonlinearities

Summary Steady-state nonlinear motion confinement is experimentally studied in a system of weakly coupled cantilever beams with active stiffness nonlinearities. Quasistatic swept-sine tests are performed by periodically forcing one of the beams at frequencies close to the first two closely spaced modes of the system, and experimental nonlinear frequency response curves for certain nonlinearity levels are generated. Of particular interest is the detection of strongly localized steady-state motions, wherein vibrational energy becomes spatially confined mainly to the directly excited beam. Such motions exist in neighborhoods of strongly localized antiphase nonlinear normal modes (NNMs) which bifurcate from a spatially extended NNM of the system. Steady-state nonlinear motion confinement is an essentially nonlinear phenomenon with no counterpart in linear theory, and can be implemented in vibration and shock isolation designs of mechanical systems.Presently Assistant Professor of Aerospace and Mechanical Engineering, Boston University (from January 1995).     

一类具有分离变量的非线性离散系统的镇定控制器

在控制理论和控制工程中，镇定控制器的设计是一个经典问题。许多有关这个问题的结论一般都是针对线性系统。对于非线性系统，很少见到有构造性结果能用于控制工程中。本针对一类广泛的非线性控制系统，我们构造了一些控制器，这些判据在工程实际问题中将具有一定的指导意义。