Accelerated monotone iterative methods for a boundary value problem of second-order discrete equations

An accelerated monotone iterative method for a boundary value problem of second-order discrete equations is presented. This method leads to an existence-comparison theorem as well as a computational algorithm for the solutions. The monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration, and the rate of convergence of the iterations is either quadratic or nearly quadratic depending on the property of the nonlinear function. Some numerical results are presented to illustrate the monotone convergence of the iterative sequences and the rate of convergence of the iterations.     

A revised Kleinman algorithm to solve algebraic Riccati equation of singularly perturbed systems

In this paper, we show that the Kleinman algorithm can be used well to solve the algebraic Riccati equation (ARE) of singularly perturbed systems, where the quadratic term of the ARE may be indefinite. The quadratic convergence property of the Kleinman algorithm is proved by using the Newton-Kantorovich theorem when the initial condition is chosen appropriately. In addition, the numerical method to solve the generalized algebraic Lyapunov equation (GALE) appearing in the Kleinman algorithm is given.     

On adaptive minimum variance regulation for non-minimum phase plants

Adaptive minimum variance control is applied to nonminimum phase plants augmented with adaptive compensators. The objective of the compensators is to achieve, asymptotically, a minimum phase property for the augmented plant. With this property, the minimum variance controller gives a stabilizing control signal. The scheme proposed has interpretations as an adaptive quadratic index minimizing procedure and also as an adaptive pole assignment algorithm. The advantage over other adaptive quadratic index minimizing procedures is simply that the weightings are made adaptive so as to guarantee convergence. One feature not shared by other adaptive pole assignment schemes is that they conveniently specialize to simple minimum variance schemes when, for these, control energy constraints are not violated. This paper presents only the discrete-time adaptive regulator version. Companion papers give a full global convergence theory and pre-processing augmentations for the stochastic tracking scheme versions.     

An integrated optimal control algorithm for discrete-time nonlinear stochastic system

Consider a discrete-time nonlinear system with random disturbances appearing in the real plant and the output channel where the randomly perturbed output is measurable. An iterative procedure based on the linear quadratic Gaussian optimal control model is developed for solving the optimal control of this stochastic system. The optimal state estimate provided by Kalman filtering theory and the optimal control law obtained from the linear quadratic regulator problem are then integrated into the dynamic integrated system optimisation and parameter estimation algorithm. The iterative solutions of the optimal control problem for the model obtained converge to the solution of the original optimal control problem of the discrete-time nonlinear system, despite model-reality differences, when the convergence is achieved. An illustrative example is solved using the method proposed. The results obtained show the effectiveness of the algorithm proposed.     

Solving equations via the trust region and its application to a class of stochastic linear complementarity problems

Equations with box constraints are applied in many fields, for example the complementarity problem. After studying the existing methods, we find that quadratic convergence of majority algorithms is based on the solvability of the equations. But whether the equations are solvable is previously unknown. So, it is necessary to design an algorithm which has fast quadratic convergence. The quadratic convergence does not depend on the solvability of the equations. In this paper, we propose a new method for solving equations. The global and local quadratic convergence of the proposed algorithm are established under some suitable assumptions. We apply the proposed algorithm to a class of stochastic linear complementarity problems. Numerical results show that our method is valid.     

A control method to make LQR robust: A planes cluster approaching mode

Linear quadratic regulator (LQR) is an optimal controller being used for linear systems, and it can minimize the comprehensive quadratic performance index (QPI) with respect to convergence error and control consumption. However, LQR lacks the robust property to cope with parameter perturbations and external disturbances. Aiming at the above deficiency of LQR, a robust LQR (RLQR) is proposed for linear systems under the guideline of planes cluster approaching mode (PCAM). In the proposed RLQR, one nonlinear item is introduced into control law, and it cooperates with the other linear item to guarantee the global asymptotic stability in the presence of equivalent disturbances. The conditions of global asymptotic stability are deduced by the method of Lyapunov function. Simulation results present that, the chosen LTI plant using RLQR possesses smaller QPI in the existence of timevarying disturbances, compared with the conventional LQR and sliding mode controller (SMC).     

一种广义次成分提取算法及其收敛性分析

广义次成分分析(generalized minor component analysis,GMCA)在现代信号处理的许多领域具有重要作用.目前现有的大多算法不能同时具备与算法对应的信息准则,以及收敛性、自稳定性和多个广义次成分提取的性能.针对上述问题,利用一种新的信息传播规则,推导出一种广义次成分提取算法,并采用确定离散时间方法(deterministic discrete time,DDT)对算法的全局收敛性能进行分析;同时,通过理论分析算法的收敛性能与算法初始状态的关系,表明算法具有自稳定性.进一步地,探索了算法在多重广义次成分提取方面的应用.相比之前的算法,所提算法具有更快的收敛速度.Matlab仿真验证了所提出算法的各项性能.     

Extremum seeking by a dynamic plant using mixed integral sliding mode controller with synchronous detection gradient estimation

This paper presents a continuous‐time optimization method for an unknown convex function restricted to a dynamic plant with an available output including a stochastic noise. For solving the problem, we propose an extremum seeking algorithm based on a modified synchronous detection method for computing a stochastic gradient descent approach. In order to reject from the beginning the undesirable uncertainties and perturbations of the dynamic plant, we employ the standard deterministic integral sliding mode control transforming the initial dynamic plant to the static one, and after (in fact, from the beginning of the process), we apply the gradient decedent technique. We consider time‐decreasing parameters for compensating the stochastic dynamics. We prove the stability and the mean‐square convergence of the method. To validate the exposition, we perform a numerical example simulation.     

基于伪谱法的滑翔轨迹多级迭代优化策略

伪谱法可实时求解具有高度非线性动态特性的飞行器最优轨迹;以X-51A相似飞行器模型为研究对象,采用增量法与查表插值建立纵向气动力模型,伪谱法与序列二次规划算法求解滑翔轨迹最优控制问题;提出使用多级迭代优化策略,为序列二次规划算法求解伪谱法参数化得到的大规模非线性规划问题提供初值,弥补序列二次规划算法在求解大规模非线性规划问题过程中,出现的初值敏感、收敛速度减慢等问题。通过与传统方法求解出的状态量与控制量仿真飞行状态进行对比,证明了多级迭代优化策略的有效性和高效性,该策略在实际工程应用中取得了良好效果。     

时滞非线性系统的采样迭代学习控制

针对一类输入时滞非线性系统, 提出了一种采样迭代学习控制算法, 该算法不含跟踪误差的微分信号, 给出了学习算法收敛的充分条件, 当不存在初始误差、不确定扰动时, 算法在采样点处能实现对期望输出信号的完全跟踪, 否则, 跟踪误差一致有界, 仿真结果表明了该算法的有效性.     

Newton's method for solving parametric linear quadratic control problems

Newton's method is applied to parametric linear quadratic control problems, including the optimal output feedback problem and the optimal decentralized control problem. Newton's equations are obtained as a system of coupled linear matrix equations. They are solved iteratively using the conjugate gradient method. In order to reduce the amount of work associated with the procedure, an inexact newtonian algorithm is also considered. In this algorithm, an approximate solution of the Newton equations is computed in such a way that the asymptotic convergence rate is quadratic.     

Optimization of passive microwave devices through geometrical parameterization—Application to the design of a cylindrical dual‐mode cavity filter

A new algorithm, based on geometrical parameterization and finite element method is presented for the optimization of microwave devices. Using geometrical parameterization, the field quantities are expressed as a polynomial in design parameters. Automatic differentiation is used for calculation of higher order derivatives. To ensure continuous gradients, an integrated mesh deformation algorithm is deployed to morph initial finite elements mesh into the perturbed geometry. The resulting parametric model is deployed through quadratic surface reconstruction to find local minimum at each stage. The convergence of the optimization through the reconstructed surfaces is discussed. As an example, a 5‐pole dual‐mode cavity filter is designed and optimized using the presented algorithm. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.     

求解Minimax优化问题的Newton型算法

Newton法是求解无约束优化问题的最有效的算法,但由于需要计算目标函数的Hesse矩阵计算量大,因此人们大多采用拟Newton(变度量法)求解无约束问题。近些年来,由于自动微分(Automatic Differentiation)技术的提出和计算机速度与内存的不断提高,     

线性离散系统的快速辨识与自适应控制

利用输出误差向量组成一正定二次型目标函数,然后应用各种梯度法计算待估的参数。为改进迭代计算的收敛特性,文中建议增加输出误差向量的维数。本方法的主要优点在于利用系统输入输出的有限数据即可求得参数真值。文中还说明本方法也可用于模型参考自适应控制系统的设计。     

An optimal tracking neuro-controller for nonlinear dynamic systems

Multilayer neural networks are used to design an optimal tracking neuro-controller (OTNC) for discrete-time nonlinear dynamic systems with quadratic cost function. The OTNC is made of two controllers: feedforward neuro-controller (FFNC) and feedback neuro-controller (FBNC). The FFNC controls the steady-state output of the plant, while the FBNC controls the transient-state output of the plant. The FFNC is designed using a novel inverse mapping concept by using a neuro-identifier. A generalized backpropagation-through-time (GBTT) algorithm is developed to minimize the general quadratic cost function for the FBNC training. The proposed methodology is useful as an off-line control method where the plant is first identified and then a controller is designed for it. A case study for a typical plant with nonlinear dynamics shows good performance of the proposed OTNC.     

一种新型高效的计算机寻优算法

提出一种全新的寻找无约束最优解的计算机算法。该算法能使得目标函数梯度的模逐渐收缩到零,以达到目标函数极小化,因此命名“梯度收缩法”。它同时利用了牛顿法和共轭梯度法的优点,应用目标函数的二阶导数,收敛很快,且具有牛顿法的“二次终止”特性。但Hessian矩阵奇异时,牛顿法将无法进行下去,该文算法可以克服这个缺点且能快速确定是否收敛到一个鞍点。     

基于改进模糊神经网络的软测量建模方法

提出了一种改进的模糊神经网络软测量建模方法，采用规则化的平均输出隶属度函数作为模糊基函数进行反模糊化运算；在训练网络时,部分参数采用Levenberg-Marquardt算法来训练，另一部分采用一阶梯度下降法．最后用该建模方法建立了聚合反应中熔融指数的软测量模型，并与一般的模糊神经网络软测量模型进行比较．结果表明改进的模糊神经网络对初始值的选择不敏感,具有很好的收敛性，同时还能达到指定的预测精度，很适合工程应用．     

A new version of Kovarik’s approximate orthogonalization algorithm without matrix inversion

In 1970 Kovarik proposed approximate orthogonalization algorithms. One of them (algorithm B) has quadratic convergence but requires at each iteration the inversion of a matrix of similar dimension to the initial one. An attempt to overcome this difficulty was made by replacing the inverse with a finite Neumann series expansion involving the original matrix and its adjoint. Unfortunately, this new algorithm loses the quadratic convergence and requires a large number of terms in the Neumann series which results in a dramatic increase in the computational effort per iteration. In this paper we propose a much simpler algorithm which, by using only the first two terms in a different series expansion, gives us the desired result with linear convergence. Systematic numerical experiments for collocation and Toeplitz matrices are also described.     

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm.     

Interval regression analysis using quadratic loss support vector machine

Support vector machines (SVMs) have been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate interval linear and nonlinear regression models combining the possibility and necessity estimation formulation with the principle of quadratic loss SVM. This version of SVM utilizes quadratic loss function, unlike the traditional SVM. For data sets with crisp inputs and interval outputs, the possibility and necessity models have been recently utilized, which are based on quadratic programming approach giving more diverse spread coefficients than a linear programming one. The quadratic loss SVM also uses quadratic programming approach whose another advantage in interval regression analysis is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression. However, this is not a computationally expensive way. The quadratic loss SVM allows us to perform interval nonlinear regression analysis by constructing an interval linear regression function in a high dimensional feature space. The proposed algorithm is a very attractive approach to modeling nonlinear interval data, and is model-free method in the sense that we do not have to assume the underlying model function for interval nonlinear regression model with crisp inputs and interval output. Experimental results are then presented which indicate the performance of this algorithm.