Dual bases for spline spaces on cells

The purpose of this paper is twofold. First, we extend the basic dimension result for spline spaces on simple cells to a class of spline spaces which satisfy additional smoothness conditions at the interior vertex. This extension is useful for the study of super spline spaces. Secondly, and more importantly, we show how to choose minimal determining sets of Bézier coordinates for these spaces. These in turn are useful for constructing explicit locally supported bases for spline spaces on general triangulations.     

A remez type algorithm for generalized spline spaces

Best uniform approximation by generalized spline spaces was studied by Nürnberger, Schumaker, Sommer, and Strauß [5]. In this paper we describe a Remez type algorithm for computing best spline approximations. Although some of the proofs are quite different we are able to prove results similar to the convergence of the Remez algorithm for polynomial spline functions by Nürnberger and Sommer [8].     

Optimal approximate conversion of spline surfaces

The paper introduces an effective method for approximate conversion of spline surfaces. The method uses mainly geometric continuity conditions, parameter transformations and nonlinear optimization techniques. Degree reduction to bicubic and biquintic surfaces is introduced, curvature oriented segmentation is developed. The method can be extended to merging spline surfaces and to spline approximation of offset surfaces.     

Optimal guaranteed cost control of a class of hybrid systems with mode-dependent mixed time delays

In this paper, the guaranteed cost control problem is investigated for a class of nonlinear systems with Markovian jumping parameters and mixed time delays. The time delays involved consist of the mode-dependent discrete time delay and the distributed time delay with mode-dependent upper and lower boundaries; the associated cost function is a quadratic function, and nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov–Krasovskii functionals and some analytic techniques, the sufficient conditions for the existence of guaranteed cost controllers are derived for the systems and related cost function. Moreover, a linear matrix inequality (LMI) based approach to design the optimal guaranteed cost controller is formulated to minimise the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.     

一类脉冲切换系统的最优控制

研究一类脉冲依赖于状态的脉冲切换系统的最优控制问题. 考虑了目标函数的两种情况: 当目标函数光滑时, 通过将跳跃瞬间转化为一个新的待优化参数, 得到了该脉冲切换系统的必要最优性条件; 当目标函数不光滑时, 利用非光滑分析的知识, 得到了广义微分形式的必要最优性条件. 算例分析验证了所提出方法的有效性.     

On a class of minimum energy controls related to spline functions

The problem of determining a minimum energy control for a dynamically interconnected set ofpsingle input-single output finite-dimensional linear time-varying dynamical systems, for which the outputs are constrained to assume prescribed values at different points in time, is considered. It is shown that the solution (optimal controller) is obtained by performing a linear operation on an appropriate vector-valued generalized interpolating spline.     

一类不稳定时滞过程的最优控制

本文对控制能量存在约束条件下一类不稳定时滞过程的最优控制问题进行了探讨. 首先基于不稳定过程的互质分解, 由敏感度函数和控制敏感度函数定义了一个包含跟踪误差和控制能量在内的性能指标, 然后应用谱分解最小化该性能指标, 从而为一类不稳定时滞过程导出了一种最优的控制器设计方法, 可使系统在控制能量存在约束时获得最优的控制性能. 仿真研究进一步说明了该方法的有效性.     

Optimal parallel initialization algorithms for a class of priorityqueues

An adaptive parallel algorithm for inducing a priority queue structure on an n-element array is presented. The algorithm is extended to provide optimal parallel construction algorithms for three other heap-like structures useful in implementing double-ended priority queues, namely min-max heaps, deeps, and min-max-pair heaps. It is shown that an n-element array can be made into a heap, a deap, a min-max heap, or a min-max-pair heap in O(log n+(n /p)) time using no more than n/log n processors, in the exclusive-read-exclusive-write parallel random-access machine model     

Optimal neuronal tuning for finite stimulus spaces

The efficiency of neuronal encoding in sensory and motor systems has been proposed as a first principle governing response properties within the central nervous system. We present a continuation of a theoretical study presented by Zhang and Sejnowski, where the influence of neuronal tuning properties on encoding accuracy is analyzed using information theory. When a finite stimulus space is considered, we show that the encoding accuracy improves with narrow tuning for one- and two-dimensional stimuli. For three dimensions and higher, there is an optimal tuning width.     

Optimal mixed sensitivity for SISO-distributed plants

The authors extend previous results for the single-input/single-output (SISO) mixed sensitivity problem for distributed parameter systems to a more general setting in which the transfer function of the plant to be controlled has both irrational stable and irrational unstable parts. These developments were originally motivated by the computation of the infimal H^∞-norm of the weighted mixed sensitivity for the irrational transfer function model of a damped flexible beam     

Observability conditions for a class of mixed distributed and lumped parameter systems

Observability of a class of mixed distributed and lumped parameter systems with respect to physically realizable measurements is studied. Measurements are made either on the lumped subsystem or at interior points of the spatial domain. In both cases algebraic observability conditions are determined and the results applied to a transportation lag system.     

Optimal damping coefficient for a class of continuous contact models

Multibody System Dynamics - In this study, we develop an analytical formula to approximate the damping coefficient as a function of the coefficient of restitution for a class of continuous contact...     

一类离散线性切换系统的最优控制

研究了一类离散线性切换系统在切换时间、切换次数固定的情况下的二次最优控制问题.利用离散动态规划的方法,将多级决策过程分解成一系列易于求解的单级决策过程,求出最优控制序列和最优切换序列,并给出算法.最后通过一个数值例子来说明所提出的方法的有效性.     

Optimal control laws for a class of constrained linear-quadratic problems

In general it seems impossible to specify the form of the solution of the linear-quadratic optimal control problem when there are control constraints. This paper deals with a restricted class of quadratic performance criteria, for which the optimal feedback control law is shown to be linear-in-half-spaces when the control is constrained to take values in a closed cone $\text{Γ ?}\text{R}{}^{\mathrm{<mtext>m</mtext>}}$. The time-varying vector quantities which are required for implementation of the optimal control law may be pre-computed by solving two initial-value problems for certain nonlinear first-order ordinary differential equations, and maximizing a quadratic function over the cone Γ at each time. The instants at which the solutions of these initial-value problems blow up are precisely the ‘escape times’ at which the performance criterion becomes unbounded below on some half-space. Analogues of the familiar Riccati equation are also presented.     

Optimal nonlinear estimation for a class of discrete-time stochastic systems

Recursive estimation for nonlinear discrete-time stochastic systems with additive white Gaussian observation noise is investigated. It is proved that for certain classes of systems, described either by finite Volterra series expansions or by state-linear realizations under certain algebraic conditions, the optimal conditional mean estimator is recursive and of fixed finite dimension. An example is presented to illustrate the structure of the estimators.     

Conceptualising mixed spaces of interaction for designing continuous interaction

Recent progress in the overlay and registration of digital information on the users workspace in a spatially meaningful way has allowed mixed reality (MR) to become a more effective operational medium. However, research in software structures, design methods and design support tools for MR systems is still in its infancy. In this paper, we propose a conceptual classification of the design space to support the development of MR systems. The proposed design space (DeSMiR) is an abstract tool for systematically exploring several design alternatives at an early stage of interaction design, without being biassed towards a particular modality or technology. Once the abstract design possibilities have been identified and a concrete design decision has been taken (i.e. a specific modality has been selected), a concrete MR application can be considered in order to analyse the interaction techniques in terms of continuous interaction properties. We suggest that our design space can be applied to the design of several kinds of MR applications, especially those in which very little user focus distraction can be tolerated, and where smooth connections and interactions between real and virtual worlds is critical for the system development. An image-guided surgery system (IGS) is used as a case study.

Schauder bases and approximation property in fuzzy normed spaces

Our aim in this article is to introduce and study the notion of weak and strong Schauder bases in fuzzy normed spaces. Further, we introduce strong and weak fuzzy approximation properties and set a relationship between these two new notions which may provide an acceleration to the structural analysis of fuzzy normed spaces.