一种基于LPV系统的$H_infty$切换控制器设计方法

针对线性参数变化(LPV)系统提出一种切换控制器参数化设计方法.基于Youla参数化思想,将控制器设计过程分解为两个步骤.首先,设计一个中心控制器保证闭环系统的全局$H_\infty$性能;其次,将参数变化区域划分为若干个子区域,在每个子区域中将中心控制器进行线性分式变换,得到切换控制器自由参数的状态空间实现,将切换控制器转换为自由参数之间的切换.基于所提出的切换LPV控制器线性分式变换实现方法,不仅可以保证在任意切换的情况下子系统各自局部的$H_\infty$性能,而且可以保证整个闭环系统满足某一整体的$H_\infty$性能,并通过仿真结果验证了所提出方法的有效性.     

对角CARIMA模型多变量广义预测控制改进算法

为了增强多变量广义预测控制算法(MGPC)的实用性,对其实现形式进行了进一步的简化.利用对角CARIMA模型的结构特点,先对系统中单个输出变量期望值的自由响应部分进行分解推导,将其表达成自由响应项系数与系统输入输出变量已知值乘积的形式,得到此输出变量的预测表达式,然后将系统所有输出变量的预测表达式代入目标函数中,得到的控制增量等于控制器系数与参考轨迹、过程输入输出历史数据的乘积.控制器系数只与模型参数及设计参数有关,求解控制量时不再需要进行模型输出预报,控制器结构简单,实现容易.对比实验结果表明了该方法保持了常规MGPC方法的优秀控制性能.     

利用表达式控制器轻松创建复杂动画

表达式控制器是3DSMAX中功能非常强大的动画制作手段.使用表达式控制器能够使动画的控制更加简洁准确.它能使复杂的动画设置自动完成。表达式控制器提供了一种通过数学方式创建动画的能力。它可以控制物体的基本建立参数(如长度、半径等).控制变换和修改(如移动放缩等)。     

附加自由曲面构造框架及其有效性维护的研究*

在对HUST-CAID(哈尔滨理工大学计算机辅助工业造型设计)系统进行研究的基础上,首先引入了自由曲面特征,然后结合HUST-CAID系统定义了自由曲面特征的分类和参数化,应用这种分类和参数化的方法创建了一个自由曲面特征,提出了一种基于FFDP配置的附加自由曲面特征的构造框架。此框架可以使自由曲面整体模型的构造完全参数化。最后建立了基于这个框架构造的自由曲面附加特征的有效性维护机制,从而达到对自由曲面附加特征进行有效性维护的目的。     

关于一种变参数PID控制器的分析与研究

分析了变参数PID控制器各个参数随着误差信号的变化趋势,得到它们的关系表达式.通过这个关系式去实现变参数PID控制器的参数校正.仿真结果表明能得到比常规非变参数PID控制器性能更好.     

基于LMI 的线性时滞系统输出动态反馈镇定

考虑线性时滞系统的输出动态反馈镇定问题.利用自由参数矩阵对闭环系统进行适当变换,并结合相应的Lyapunov-Krasovskii泛函得到了时滞相关的控制器存在性判据.利用控制器参数化方法,将控制器参数与泛函参数的求解归结为线性矩阵不等式解的形式,从而克服了时滞无关性及求解非凸优化问题所导致的保守性.仿真算例验证了结论的有效性.     

一类参数不确定性系统的鲁棒控制

讨论了带有分母多项式摄动的参数不确定性系统的鲁棒镇定问题,给出了这类参数 不确定性系统存在鲁棒控制器的一个充分条件,并且当这个条件被满足时,得到了部分鲁棒 控制器的一个参数化公式.     

一种新的H∞固定阶控制器综合方法

提出了只通过一个Ｒｉｃｃａｔｉ方程求解Ｈ∞固定阶控制器的方法，在获得系统与控制器的增广系统后，得到了一个和控制器参数有关的假想控制输入，在其特定形式下得到一个全信息控制问题，由于增广系统是奇异的，根据范数约束得到的Ｒｉｃｃａｔｉ方程是和一个常数有关的，从而较为简单的处理奇异问题，因为假想输入的是扰动和状态变量的反馈形式，故可参数化控制器，最后的结果表明如果参数阵满足某些条件，则固定阶控制器是存在的     

给定阶控制器■_1优化设计方法

研究了基于多输入多输出离散时间系统的给定阶控制器l1优化设计问题.基于You la参数化法,对自由参数Q分为多项式和有理多项式两种情况进行了讨论,并将有理式的情形转化为多项式的形式,最后将给定阶的控制器优化问题归结为求解标准的线性规划问题.在给定控制器阶次的条件下,得到使闭环系统内部稳定并使相应的l1范数最小的最优控制器.最后给出了算例来验证算法的有效性.*     

不确定性线性多变量系统的鲁棒分散控制

本文首先给出了被给定控制器所稳定的系统的(自出)参数化表达式,接着探讨了三类不确知线性多变量系统的鲁棒分散控制器存在的充分及必要条件。     

Combinatorial Construction of Seamless Parameter Domains

The problem of seamless parametrization of surfaces is of interest in the context of structured quadrilateral mesh generation and spline-based surface approximation. It has been tackled by a variety of approaches, commonly relying on continuous numerical optimization to ultimately obtain suitable parameter domains. We present a general combinatorial seamless parameter domain construction, free from the potential numerical issues inherent to continuous optimization techniques in practice. The domains are constructed as abstract polygonal complexes which can be embedded in a discrete planar grid space, as unions of unit squares. We ensure that the domain structure matches any prescribed parametrization singularities (cones) and satisfies seamlessness conditions. Surfaces of arbitrary genus are supported. Once a domain suitable for a given surface is constructed, a seamless and locally injective parametrization over this domain can be obtained using existing planar disk mapping techniques, making recourse to Tutte's classical embedding theorem.     

具有指定闭环特征值的离散时间最优调节器的设计

本文研究了LQ最优调节器的逆问题。在控制变量加权矩阵R给定的条件下,通过引入一组自由变量,给出了满足闭环系统特征值要求的状态加权矩阵Q的一种参数化表示结果。基于这一结果,文中研究了一类系统的LQ最优调节器之逆问题的解析解法。通过所求得的自由变量解,就可以直接确定系统的最优状态反馈控制器。     

LQ最优控制系统中加权阵的确定

本文研究了LQ最优调节器的逆问题.在控制变量加权矩阵R给定的条件下,通过引入 一组自由变量,给出了满足闭环系统特征值要求的状态加权矩阵Q的一种参数化表示结果.基 于这种结果,研究了LQ逆问题的矩阵变换解法和一类系统的LQ逆问题的解法.此外,文中 还给出了不求解代数矩阵Riccati方程确定系统的最优状态反馈系数矩阵K的方法.     

Parametrization of Bézier-type B-spline curves and surfaces

Sections of parametric surfaces defined by equally spaced parameter values can be very unevenly spaced physically. This can cause practical problems when the surface is to be drawn or machined automatically. This paper describes a method for imposing a good parametrization on a curve constructed by Bézier's method and based on B-splines. The extension of the method to the parametrization of surfaces is considered briefly.     

Adaptive observers for a class of uniformly observable systems with nonlinear parametrization and sampled outputs

In this paper, we propose an adaptive observer for a class of uniformly observable nonlinear systems with nonlinear parametrization and sampled outputs. A high gain adaptive observer is first designed under the assumption that the output is continuously measured and its exponential convergence is investigated, thanks to a well defined persistent excitation condition. Then, we address the case where the output is available only at (non uniformly spaced) sampling instants. To this end, the continuous-time output observer is redesigned leading to an impulsive observer with a corrective term involving instantaneous state impulses corresponding to the measured samples and their estimates. Moreover, it is shown that the proposed impulsive observer can be put under the form of a hybrid system composed of a continuous-time observer coupled with an inter-sample output predictor. Two design features are worth to be emphasized. Firstly, the observer calibration is achieved through the tuning of a scalar design parameter. Secondly, the exponential convergence to zero of the observation and parameter estimation errors is established under a well defined condition on the maximum value of the sampling partition diameter. More specifically, the observer design is firstly carried out in the case of linear parametrization before being extended to the nonlinear one. The theoretical results are corroborated through simulation results involving a typical bioreactor.     

基于Generative Component的中国古建筑参数化设计

为有效分析古建筑,利用参数化建模软件Generative Component（GC）,结合编程设计对中国古建筑主要结构和构件进行参数化分析,找出其内在结构的规律性及各构件之间的参数关系,实现古建筑的数字化、参数化描述,生成参数可修改的结构化三维模型.     

Scale‐Invariant Directional Alignment of Surface Parametrizations

Various applications of global surface parametrization benefit from the alignment of parametrization isolines with principal curvature directions. This is particularly true for recent parametrization‐based meshing approaches, where this directly translates into a shape‐aware edge flow, better approximation quality, and reduced meshing artifacts. Existing methods to influence a parametrization based on principal curvature directions suffer from scale‐dependence, which implies the necessity of parameter variation, or try to capture complex directional shape features using simple 1D curves. Especially for non‐sharp features, such as chamfers, fillets, blends, and even more for organic variants thereof, these abstractions can be unfit. We present a novel approach which respects and exploits the 2D nature of such directional feature regions, detects them based on coherence and homogeneity properties, and controls the parametrization process accordingly. This approach enables us to provide an intuitive, scale‐invariant control parameter to the user. It also allows us to consider non‐local aspects like the topology of a feature, enabling further improvements. We demonstrate that, compared to previous approaches, global parametrizations of higher quality can be generated without user intervention.     

Data driven local coordinates for multivariable linear systems and their application to system identification

In this paper we introduce a new parametrization for state-space systems: data driven local coordinates (DDLC). The parametrization is obtained by restricting the full state-space parametrization, where all matrix entries are considered to be free, to an affine plane containing a given nominal state-space realization. This affine plane is chosen to be perpendicular to the tangent space to the manifold of observationally equivalent state-space systems at the nominal realization. The application of the parametrization to prediction error identification is exemplified. Simulations indicate that the proposed parametrization has numerical advantages as compared to e.g. the more commonly used observable canonical form.     

Optimal control problems with multiple characteristic time points in the objective and constraints

In this paper, we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points. These time points can be either fixed or variable. Using the control parametrization technique and a time scaling transformation, this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems. Each of these approximate problems can be viewed as a finite dimensional optimization problem. New gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be applied to solve each approximate optimal parameter selection problem. For illustration, two numerical examples are solved.     

Normal Parametrizations of Algebraic Plane Curves

In this paper we present a theoretical and algorithmic analysis on the normality of rational parametrizations of algebraic plane curves over arbitrary fields of characteristic zero. If the field is algebraically closed we give an algorithm to decide whether a parametrization is proper and, if not, a normal parametrization is computed. If the field is not algebraically closed the problem is more complicated, and a degenerated situation may appear. We classify the degenerations in strong and weak degenerations, and an algorithm to decide this phenomenon is derived. Furthermore, we prove that if the parametrization is strongly degenerated then the curve cannot be normally parametrized, but weak degenerations can be resolved, and an algorithm to reparametrize the input weakly degenerated parametrization into a non-degenerated one is given. In addition, we show how these results can be applied and improved to the case of real rational curves. In this case, we present an algorithm that decides whether a given real parametrization can be normally parametrized over the reals, and that computes such a parametrization if it exists.