An effective trust-region-based approach for symmetric nonlinear systems

This paper presents a new trust-region procedure for solving symmetric nonlinear systems of equations having several variables. The proposed approach takes advantage of the combination of both an effective adaptive trust-region radius and a non-monotone strategy. It is believed that the selection of an appropriate adaptive radius and the application of a suitable non-monotone strategy can improve the efficiency and robustness of the trust-region framework as well as decrease the computational costs of the algorithm by decreasing the required number of subproblems to be solved. The global convergence and the quadratic convergence of the proposed approach are proved without the non-degeneracy assumption of the exact Jacobian. The preliminary numerical results of the proposed algorithm indicating the promising behaviour of the new procedure for solving nonlinear systems are also reported.     

The multistage homotopy analysis method: application to a biochemical reaction model of fractional order

In this paper, a new reliable algorithm called the multistage homotopy analysis method (MHAM) based on an adaptation of the standard homotopy analysis method (HAM) is presented to solve a time-fractional enzyme kinetics. This enzyme–substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The new algorithm is only a simple modification of the HAM, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding systems. Numerical comparisons between the MHAM and the classical fourth-order Runge–Kutta method in the case of integer-order derivatives reveal that the new technique is a promising tool for nonlinear systems of integer and fractional order.     

Hierarchical stochastic production planning for the highest business benefit

This paper addresses the hierarchical stochastic production planning (HSPP) problem of flexible automated workshops (FAWs), each with a number of flexible manufacturing systems (FMSs) the part-transfer between which is a delay of a time period. The problem not only includes uncertainties in the demand, capacities, material supply, processing times, necessity for rework, and scrap, but also considers multiple products and multiple time periods. The objective is to develop a production plan which tells each FMS how many parts to produce and when to produce them so as to obtain the highest business benefit. Herein, the HSPP problem is formulated by a stochastic nonlinear programming model whose constraints are linear but whose objective function is piecewise linear. For the convenience of solving the stochastic nonlinear programming model above, it is approximately transformed into a deterministic nonlinear programming model and further into a linear programming model. Because the scale of the model for a general workshop is too large to be solved by the simplex method on a personal computer within acceptable time, Karmarkar's algorithm and an interaction/prediction algorithm, respectively, are used to solve the model, the former for the medium or small scale problems and the latter for the large scale problems. By the implementation of the above-mentioned algorithms and through many HSPP examples, Karmarkar's algorithm, the interaction/prediction algorithm and the linear programming method in Matlab 5.0 are compared, the result of which shows that the proposed approaches are very effective and suitable for not only “push” production but also “pull” production.     

Analysis of nonlinear electrical circuits using bernstein polynomials

In electrical circuit analysis, it is often necessary to find the set of all direct current (d.c.) operating points (either voltages or currents) of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.     

一类自适应免疫进化算法

基于免疫系统中的进化机理，提出一种自适应免疫进化算法，通过定义扩展半径和突交半径两个新算法参数构造了较小和较大两个邻域，分别利用这两个邻域进行局部和全局搜索，从而形成两层领域搜索机制，以保证算法的全局和局部搜索能力，定义了群体的多样度，并以此自适应调节算法参数以提高算法性能，给出了算法的全局收敛性证明，仿真结果表明，该算法收敛速度快，具有良好的全局寻优和局部求精能力。     

Particle swarm algorithm for solving systems of nonlinear equations

Solving systems of nonlinear equations is one of the most difficult problems in all of numerical computation and in a diverse range of engineering applications. Newton’s method for solving systems of nonlinear equations can be highly sensitive to the initial guess of the solution. In this study, a new particle swarm optimization algorithm is proposed to solve systems of nonlinear equations. Some standard systems are presented to demonstrate the efficiency of this method.     

非线性控制系统综合的频域逆系统方法研究

提出一种不需已知系统微分方程模型的非线性系统综合方法。首先得到对象非线性传递函数的估计,然后利用非线性补偿算法构造前馈补偿器,使复合系统具有近似线性系统的特性,最后采用常规线性系统反馈控制的方法进行控制。仿真结果表明,所提出的频域逆系统综合方法比一般非线性系统自适应控制方法有效。     

复杂负载下数据缓冲区自适应调度方法仿真

传统数据缓冲区调度方法调度时间长、调度结果误差大且不能够完全应对复杂负载问题。因此提出了复杂负载下数据缓冲区自适应调度方法,通过构建模拟数据缓冲区来定义调整的方向,在缓冲数据中,利用操控行为和代替方法之间进行相互不变性推测,获取数据缓冲错失函数;通过引用能力制约条件,将时间分成一些零碎的小片段,利用数据缓冲错失,获取时间约束模型;引入时间约束模型,需要依据时间顺序对事件进行调顺序,结合根据模拟自适应算法所得到的数据,使用雷达资源约束条件能够精准快速地衡量各种数据波束所要求的指令,获取自适应调度模型,为某一个调度间隔选取出最完善的自适应调度方法。通过仿真结果表明:上述方法能够完全应对复杂负载情况的问题,且数据缓冲区自适应调度时间短、调度结果误差小。     

柔性自动化车间生产计划的最优分解

研究了柔性自动化车间生产计划的最优分解问题,首先根据实际需要建立车间生产计划的非线性规划模型,然后为求解方便将其转化成线性规划模型,由于这种模型对于一般车间来讲其规模已经很大,很难在微机上用单纯形法求争,为此,提出分别用卡马卡算法和一种新的基于卡马卡算法的关联预测法来求解车间生产计划的最优分解问题,并编制了相应软件,最后通过算例研究,比较了卡马卡算法、基于卡马卡算法的关联预测法和Matlab中的线性规划法,结果表明所提方法是非常有效的。     

Adaptive particle shape setting and normal calculation methods in fluid rendering

In this paper, we present an adaptive particle shape setting method in Lagrangian-approach based screen space splatting algorithm in real-time fluid rendering. The particle radius will be adjusted according to its Weber number and local density in the rendering process so that a large radius of peaceful fluid particle can help to eliminate a bumpy surface artifact, and a small radius can prevent the obviously spherical shape of particles in splash. The shape of fluid particle will be controlled adaptively on the basis of Weber number too, so that fast moving particles could have an ellipsoidal appearance which describes the splash particle shape in turbulent flow persuasively. We also propose an adaptive normal calculation method to avoid the numerical calculation errors in the normal computation process. The sampling interval will be set in accordance with the viewing distance from camera to the fluid so that fuzzy edges or double image effect in a fixed sampling interval normal computation process could be prevented. Both of the two approaches introduced in this paper take only small amount of computing time and will have little impact on the time consuming property of a real-time fluid rendering application.     

基于自适应权值的点云三维物体重建算法研究

基于三维扫描点云数据的三维物体重建是计算机图形学中非常重要的课题,在计 算机动画、医学图像处理等多方面都有应用。其中基于最小二乘问题的Levenberg-Marquart 算 法和基于极大似然估计的M-Estimator 算法都是不错的方案。但是当点的数量过多过少或者点 云中有噪声时,这些方案产生的结果都会有较大的误差,影响重建的效果。为了解决这两个问 题,结合Levenberg-Marquart 算法和M-Estimator 算法,提出了一种新的算法。该算法结合 Levenberg-Marquart 算法较快的收敛性和M-Estimator 算法的抗噪性,能很好地解决点数量较多 和噪声点影响结果的问题。通过在M-Estimator 的权重函数上进行改进,提出自适应的权值函 数,用灵活变动和自适应的值代替原来的固定值,使算法在噪声等级较高时也能表现良好。最 后将算法应用在球体和圆柱上,并和最新的研究成果进行对比,数据说明算法无论是在点云数 量较多还是在噪声等级较高的情况下都明显优于其他已知算法。     

An Iterative Method for Optimal Feedback Control and Generalized HJB Equation

In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman (GHJB) equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm, which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems. Then, the proposed algorithm solves GHJB equation numerically for points near the origin by considering the linearization of the non-linear equations under a good initial control guess. Finally, the procedure is proved to converge to the optimal stabilizing solution with respect to the iteration variable. In addition, it is shown that the result is a closed-loop control based on this iterative approach. Illustrative examples show that the update control laws will converge to optimal control for nonlinear systems.      

一种新型滑模控制器设计及仿真

对于一类非线性不确定系统,常规滑模控制器存在"抖振"现象和抗外部扰动作用不理想等问题.本文运用自适应模糊系统逼近滑模控制器参数,并引入一个自适应模糊参数连续逼近常规滑模控制器的开关函数,最后给出一种新型自适应模糊滑模控制器,该方法克服函数和边界层法的不足.仿真实验结果表明该方法增强非线性系统的抗干扰能力和鲁棒性,并大大地削弱系统的"抖振"现象.     

Symbolic Computation of Conserved Densities for Systems of Nonlinear Evolution Equations

A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. The algorithm is implemented inMathematica. The programcondens.mautomatically carries out the lengthy symbolic computations for the construction of conserved densities. The code is tested on several well-known partial differential equations from soliton theory. For systems with parameters,condens.mcan be used to determine the conditions on these parameters so that a sequence of conserved densities might exist. The existence of a large number of conservation laws is a predictor for integrability of the system.     

A modified trust region algorithm for nonlinear equations with new updating rule of trust region radius

In this article, we present a trust region algorithm for the nonlinear equations with a new updating rule of the trust region radius, which takes some function of the residual. We show that under the local error bound condition which is weaker than the non-singularity, the new algorithm converges quadratically to some solution of the nonlinear equations. Numerical results show that the new algorithm performs very well for some singular nonlinear equations.     

含有有色噪声的非线性分数阶系统自适应扩展卡尔曼滤波器

研究了含有未知参数的情况下，分别含有分数阶有色过程噪声和有色测量噪声的连续时间非线性分数阶系统状态估计问题.采用Grünwald-Letnikov （G-L）差分方法和1阶泰勒展开公式，对描述连续时间非线性分数阶系统的状态方程进行离散化和线性化.构造由状态量、未知参数和分数阶有色噪声的增广向量，设计自适应分数阶扩展卡尔曼滤波算法实现对有色噪声情况下的连续时间非线性分数阶系统的状态和参数的估计.最后，通过分析两个仿真实例，验证了提出算法的有效性.     

非线性广义系统的右可逆性

研究了广义非线性系统的右可逆性,给出构造性的求逆算法以克服以往结果中需求解非线性方程组的困难,从而使得求逆算法对任意足够光滑的非线性广义系统皆为可行.     

Adaptive fuzzy dynamic surface control for uncertain nonlinear systems

In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of ＂explosion of complexity＂ in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller （SMC）. Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.     

Adaptive identification and control algorithms for nonlinear bacterial growth systems

This paper suggests how nonlinear adaptive control of nonlinear bacterial growth systems could be performed. The process is described by a time-varying nonlinear model obtained from material balance equations. Two different control problems are considered: substrate concentration control and production rate control. For each of these cases, an adaptive minimum variance control algorithm is proposed and its effectiveness is shown by simulation experiments. A theoretical proof of convergence of the substrate control algorithm is given. A further advantage of the nonlinear approach of this paper is that the identified parameters (namely the growth rate and a yield coefficient) have a clear physical meaning and can give, in real time, a useful information on the state of the biomass.     

Adaptive control of linear multivariable systems with high frequency gain matrix hurwitz

A new adaptive control scheme is proposed for multivariable model reference adaptive control （MRAC） systems based on the nonlinear backstepplng approach with vector form. The assumption on a priori knowledge of the high frequency gain matrix in existing results is relaxed and the new required condition for the high frequency gain matrix can be easily checked for certain plants so that the proposed method is widely applicable. This control scheme guarantees the global stability of the closed-loop systems and the tracking error can be arbitrary small. The simulation result for an application example shows the validity of the proposed nonlinear adaptive scheme.