输出概率密度函数鲁棒弹性最优跟踪控制

研究了一类随机动态系统的鲁棒弹性最优跟踪控制问题。在采用B样条神经网络模型逼近随机动态系统的输出概率密度函数(PDF)的基础上,同时考虑系统模型和控制器增益不确定性,结合Lyapunov稳定性理论和线性矩阵不等式(LMI)技术,引入增广控制作用,设计基于广义状态反馈的鲁棒弹性最优跟踪控制器,目的是使系统的输出PDF跟踪给定PDF。通过求解LMI,所得控制器不仅能实现跟踪目的,而且能确保该随机动态系统全局稳定并满足一定的线性二次型性能指标上界。仿真结果表明该方法简单易行,且无需任何设计参数调整。     

一类仿射非线性系统的概率密度函数形状控制

针对一类仿射非线性有界动态随机系统,提出一种最优概率密度函数（PDF）跟踪控制算法,使得系统的输出PDF跟踪给定的PDF．首先利用线性B样条解耦得到仿射非线性状态方程和PDF逼近方程,使PDF跟踪转化为状态方程输出权值的跟踪;然后采用线性时变序列逼近方法将非线性系统转化为线性时变系统,通过对线性系统的迭代运算得到非线性系统的最优跟踪控制器,从而实现最优PDF跟踪．理论分析和仿真实验均表明了所提出算法的有效性．     

基于LMI的参数随机变化系统的概率密度函数控制

针对模型参数在有界区域内随机变化的系统, 基于平方根 B 样条模型, 提出了输出概率密度函数 (Probability density function, PDF) 跟踪控制策略. 目标是控制系统输出的概率密度函数跟踪给定的概率密度函数. 通过 B 样条逼近建立了输出 PDF 和权值之间的对应关系, 把 PDF 的跟踪转化为权值的跟踪, 同时系统转化为 MIMO 系统,从而权值向量的跟踪就转化为 MIMO 系统的跟踪问题, 接着给出了系统输出概率密度函数跟踪给定概率密度函数的控制器存在的充分条件, 通过求解线性矩阵不等式完成状态反馈和输出反馈跟踪控制器的设计, 得到了系统具有 Hinfinity 范数界 Gamma 鲁棒镇定的结果. 仿真结果表明本文提出的控制算法是有效的.     

基于完备能量模型的B样条曲面造型技术

鉴于传统能量模型物理意义的不明确性,对比薄板弹性变形的能量泛函,建立了变形曲面的完备能量模型, 着重解决B样条曲面能量法造型的若干关键技术.完备能量模型可以充分表达曲面刚度并明确设计参数的物理意义及选取标准.通过引入曲面构形及曲面位移模式描述变形曲面;基于完备能量模型推导统一的曲面造型控制方程;采用有限元方法求解控制方程.在单元划分方式上,以双三次准均匀B样条单元划分曲面,有利于简支与固支约束条件的处理.     

生物信息学中蛋白质结构的B样条结构曲线计算模型研究

蛋白质结构建模是生物信息学中一个基础而重要的问题．根据蛋白质分子自身的链式结构特点,基于蛋白质分子主链(即骨架)上的Ca原子,运用B样条空间曲线理论,提出了一种蛋白质骨架结构生物信息学分析模型——B样条结构曲线(BSSC)模型．利用BSSC模型的连续性、可控性、可扩展性等特点,可对蛋白质结构相关的诸多生物信息学问题进行分析和研究．     

一类模型不确定系统的最优跟踪性能

在内模控制(IMC)结构下，对控制能量存在约束时一类不确定系统所能达到的最优跟踪性能进行了探讨．首先针对一类相加模型误差的描述，定义了一个平均意义上的包含跟踪误差和控制能量的性能指标．然后通过谱分解极小化该性能指标，导出一个最优的控制器设计方法，可以兼顾模型不确定性和控制能量约束，在实际控制系统设计中可用来对最优跟踪性能和控制能量进行预估．     

一类模糊时滞系统输出跟踪控制

基于T-S模糊模型和变结构控制策略,研究了一类带有参数不确定项的模糊时滞系统输出跟踪问题。利用变结构控制理论选择滑动模,针对系统时滞项为已知和未知的两种情况,根据可达条件提出了一种变结构控制方法。该方法确保系统的运动轨迹在有限的时间内到达滑模面并一直保持在滑模面上。根据ISS理论和LMI方法研究了系统状态全局有界的充分条件。通过仿真实例验证了所提方法的正确性和有效性。     

基于层次B样条的网格模型变形技术

针对常用的网格模型提出了一个基于层次B样条控制的三维网格空间变形框架．首先由用户交互地选取编辑区域,由程序完成编辑区域的参数化和均匀重采样;然后用层次B样条光顺拟合这些均匀采样点,所得的R样条曲面作为网格模型的基曲面,计算待编辑区域中网格顶点相对该B样条基曲面的局部坐标,该局部坐标平移、旋转不变,可视为模型的内蕴几何特征,并作为变形操作中的不变量．用户通过编辑层次B样条基曲面或者直接编辑三维网格模型,可实现多分辨率变形．实验结果表明：该方法操作直观方便,无论对整体还是局部变形,都能取得可控、可靠的变形效果,且采刚B样条曲面的控制手段易于与已有的造型系统合成．     

基于B样条曲线的植物模型建立方法

本文分析了植物模型的结构,尝试通过B样条曲线曲面来描述植物的终端节点,并分析了采用这种描述结构时的植物生长模型和风动模型的可能性,植物的生长模型主要通过模拟生态过程,即植物的终端节点通过光合作用产生的能量和能量对植物生长的影响等关系来建立了这些行为模型,最后提供了这种算法的验证结果。     

不匹配不确定性系统的近似变结构输出跟踪控制

针对一类具有不匹配不确定性的非线性系统,提出一种结合变结构控制方法及自适应控制方法输出跟踪控制器。首先提出一种保证不确定性系统跟踪误差指数稳定的近似变结构控制器;进而得到一种具有不确定性范数上界估计能力的自适应近似变结构控制器,并证明了所提出的自适应近似变结构控制器使跟踪误差在时间趋于无穷时收敛于零。     

Linearized controller design for the output probability density functions of non-Gaussian stochastic systems

1 Introduction There are many practical systems that require the control of the shape of the output probability den- sity function rather than just their mean values and variances. These systems are seen in papermaking processes[1,2], chemical engineering, material science, combustion ?ame distribution systems and food pro- cessing industries. For example, in chemical engineer- ing the control of particle size distribution has al- ways been regarded as an important area of research[3], whilst …     

Optimal probability density function control for NARMAX stochastic systems

This paper presents a new control strategy for a class of non-Gaussian stochastic systems so that the output probability density function (PDF) of the system can be made to follow a desired PDF. The system considered is represented by an Nonlinear AutoRegressive and Moving Average with eXogenous (NARMAX) inputs with input channel time-delay and non-Gaussian noise. A multi-step-ahead nonlinear cumulative cost function is used to improve tracking performance. For this purpose, a relationship between the PDFs of all the inputs and the PDFs of multiple-step-ahead output is formulated by constructing an auxiliary multivariate mapping. By minimizing this performance function, a new explicit predictive controller design algorithm is established with less conservatism than some previous results. Furthermore, an improved approach is developed to guarantee the local stability of the closed-loop system by tuning the weighting parameters recursively. Simulations are given to demonstrate the effectiveness of the proposed control algorithm and desired results have been obtained.     

Generalized discrete-time PI control of output PDFs using square root B-spline expansion

A new control approach is proposed for the probability density function (PDF) control of non-Gaussian stochastic systems using PI controllers. Using the square root output PDF model and the weight dynamics, the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics, where LMI techniques are used to design a generalized PI controller such that stability, state constraints and tracking performances can be guaranteed simultaneously.     

Constrained discrete-time PI controller design for output PDFs of stochastic systems with time delays

This article presents a new proportional-integral (PI) tracking control strategy for non-Gaussian stochastic systems based on a square root B-spline model for the output probability density functions (PDFs). Following the square root B-spline approximation to the measured output PDF, a non-linear discrete-time dynamical model can be established between the control input and the weights related to the PDFs. It is noted that the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics. For the non-linear discrete-time weight model including time-delay terms and exogenous disturbances, convex linear matrix inequality optimisation algorithms are used to design a generalised PI controller such that stabilisation, state constraint and tracking performance can be guaranteed simultaneously. Furthermore, in order to enhance the robustness, the peak-to-peak measure index is applied to optimise the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.     

Feedback control of nonlinear stochastic systems for targeting a specified stationary probability density

In the present paper, an innovative procedure for designing the feedback control of multi-degree-of-freedom (MDOF) nonlinear stochastic systems to target a specified stationary probability density function (SPDF) is proposed based on the technique for obtaining the exact stationary solutions of the dissipated Hamiltonian systems. First, the control problem is formulated as a controlled, dissipated Hamiltonian system together with a target SPDF. Then the controlled forces are split into a conservative part and a dissipative part. The conservative control forces are designed to make the controlled system and the target SPDF have the same Hamiltonian structure (mainly the integrability and resonance). The dissipative control forces are determined so that the target SPDF is the exact stationary solution of the controlled system. Five cases, i.e., non-integrable Hamiltonian systems, integrable and non-resonant Hamiltonian systems, integrable and resonant Hamiltonian systems, partially integrable and non-resonant Hamiltonian systems, and partially integrable and resonant Hamiltonian systems, are treated respectively. A method for proving that the transient solution of the controlled system approaches the target SPDF as t→∞ is introduced. Finally, an example is given to illustrate the efficacy of the proposed design procedure.     

Shaping of Output PDF Based on the Rational Square-root B-spline Model

This paper presents a new method for the modeling and control of the output probability density functions (PDFs) of linear stochastic systems.At first,a new PDF approximation method, namely the rational square-root B-spline model is proposed and the innovative concept of pseudo- weights is introduced.The new model is then compared with the existing B-spline models in terms of feasible domains.Next,a controller is developed to realize the output PDF tracking performance. An alternative minimal entropy control strategy is also provided for the case that no target PDF is available.Finally,illustrative examples indicate the effectiveness of the proposed algorithms.     

Control of quasi non-integrable Hamiltonian systems for targeting a specified stationary probability density

An innovative design procedure for the feedback control of quasi non-integrable Hamiltonian systems to target a specified stationary probability density function (SPDF) is proposed based on the averaged Fokker–Planck–Kolmogorov equation. The control force is split into a conservative part and a dissipative part. The conservative part is designed to make the controlled system and the target SPDF having the same Hamiltonian structure. The dissipative part is then determined to make the target SPDF to be the stationary solution of the controlled system. Then, a Lyapunov function method is adopted for proving that the transient solution of the controlled system approaches to the target SPDF as time t → ∞. The simulation result for an example shows the effectiveness of the proposed control strategy.     

基于有理平方根B样条模型的概率密度函数形状控制

This paper presents a new method for the modeling and control of the output probability density functions (PDFs) of linear stochastic systems. At first, a new PDF approximation method, namely the rational square-root B-spline model is proposed and the innovative concept of pseudoweights is introduced. The new model is then compared with the existing B-spline models in terms of feasible domains. Next, a controller is developed to realize the output PDF tracking performance. An alternative minimal entropy control strategy is also provided for the case that no target PDF is available. Finally, illustrative examples indicate the effectiveness of the proposed algorithms.     

随机部分可积拟哈密顿系统的概率密度追踪控制

目前非线性随机系统的控制方法存在设计复杂,计算成本高,以及缺乏稳定性或收敛性证明等缺点,针对这些问题,本文在作者前期研究的基础上发展了一种全新的针对部分可积的非线性随机系统的反馈控制,使得受控系统输出的稳态概率密度逼近事先给定的目标概率密度,并利用Lyapunov函数法证明受控系统的收敛性.数学仿真结果证明了这种方法的可行性和正确性.     

反馈线性的非线性系统的分步输出变结构控制

针对一类存在参数不确定性的反馈线性的非线性动态系统,通过构造两个滑模流形,即误差跟踪的线性函数和中间控制变量与其实际值之间的误差,给出了输出跟踪控制律．并设计一个变结构控制律使闭环系统的轨迹渐近趋于滑模区,对于所有滑模区上的轨迹,跟踪误差趋于零．