How scaling of the disturbance set affects robust positively invariant sets for linear systems

This paper presents new results on robust positively invariant (RPI) sets for linear discrete‐time systems with additive disturbances. In particular, we study how RPI sets change with scaling of the disturbance set. More precisely, we show that many properties of RPI sets crucially depend on a unique scaling factor, which determines the transition from nonempty to empty RPI sets. We characterize this critical scaling factor, present an efficient algorithm for its computation, and analyze it for a number of examples from the literature. Copyright © 2017 John Wiley & Sons, Ltd.     

The minimal disturbance invariant set: Outer approximations via its partial sums

This paper is concerned with outer approximations of the minimal disturbance invariant set (MDIS) of a discrete-time linear system with an additive set-bounded disturbance. The k-step disturbance reachable sets (Minkowski partial sums) are inner approximations of MDIS that converge to MDIS. Enlarged by a suitable scaling, they can lead to outer approximations of MDIS. Three families of approximations, each based on partial sums, are considered. Theoretical properties of the families are proved and interrelated. Algorithmic questions, including error bounds, are addressed. The results are illustrated by computational data from several examples.     

输入受限的多旋翼无人机轨迹跟踪鲁棒正定不变集设计

针对输入受限的多旋翼无人机轨迹跟踪问题设计了鲁棒正定不变集.考虑多旋翼无人机的非线性动力学模型、外部不确定干扰以及输入饱和约束等因素,首先设计带有干扰抵消项的非线性控制律以保证无人机轨迹跟踪的稳定性,进而基于线性矩阵不等式(LMIs)构造了鲁棒正定不变集.在所设计的控制律作用下,无人机轨迹跟踪误差一旦进入所构造的不变集...     

Convergent Ritz approximations of the set of stabilizing controllers

A necessary and sufficient condition for linear exponential sums to be dense in is derived. Under this condition a Ritz approximation converges, which has been proposed to solve linear control problems. State-space representations of orthonormal basis functions for multivariable systems are given.     

Characterization of rough set approximations in Atanassov intuitionistic fuzzy set theory

The primitive notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation and satisfying many interesting properties. Many types of generalized rough set models have been proposed in the literature. This paper discusses the rough approximations of Atanassov intuitionistic fuzzy sets in crisp and fuzzy approximation spaces in which both constructive and axiomatic approaches are used. In the constructive approach, concepts of rough intuitionistic fuzzy sets and intuitionistic fuzzy rough sets are defined, properties of rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are examined. Different classes of rough intuitionistic fuzzy set algebras and intuitionistic fuzzy rough set algebras are obtained from different types of fuzzy relations. In the axiomatic approach, an operator-oriented characterization of rough sets is proposed, that is, rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of upper and lower intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of crisp/fuzzy relations which produce the same operators.     

基于概念格的粗糙集近似

粗糙集理论的一个重要研究方面是用已定义的概念来近似未定义的概念,而如何构建可定义概念以及如何确定近似运算是这一工作的基础.利用粗糙集这一工具,从概念格的角度来确定可定义概念,并在此基础上研究了概念的粗糙近似.根据粗糙集上下近似的包含关系,得到概念的一种新的上下近似的运算的定义.粗糙集近似理论利用两种不同的近似运算,产生两种不同的近似来描述概念格背景下的对象集合.     

On the minimal robust servo-regulator for nonlinear systems

It is shown in (Huang and Lin, 1991) that the kth-order robust nonlinear servomechanism problem can be solved by a class of linear controllers called kth-order robust servo-regulator. It is further shown in (Huang, 1995) that the kth-order robust servo-regulator, under one additional condition, also solves the (exact) robust nonlinear servomechanism problem. This paper further shows that the minimal dimension of this class of linear controllers is equal to the degree of the minimal polynomial of the k-fold exosystem multiplied by p, where p is the dimension of the regulated output. This result, coupled with a characterization of the minimal polynomial of the k-fold exosystem leads to a straightforward and efficient procedure to synthesize a minimal dimension linear robust servo-regulator.     

Maximal state independent approximations to minimal real change

This paper is devoted to the problem of consistency enforcement for logical databases. The enforcement methods we propose compute the minimal real change in a given DB state, which is sufficient to accomplish the input update and preserve the integrity constraints (IC). For IC expressed in the form of a generalized logic program, this problem is proven to be hard. Meanwhile, we show that it is solvable in linear time under partial interpretations. We propose a method of computing DB state independent correct expansions of the input update and simultaneous optimization of IC with respect to this expansion. We show that under partial interpretations, optimal pairs (greatest correct update expansion/simplest equivalent IC) always exist and can be incrementally computed in square time. This partial solution being correct with respect to the total interpretations, we use it as an approximation in the total case. Moreover, for the class of IC without negation in clause bodies, we prove that this approximation constitutes the optimal pair (greatest correct update expansion/simplest equivalent IC).     

The set of all minimal partial realizations

This paper is concerned with the uniqueness of minimal partial realizations. Earlier papers are typically concerned with the problem of the existence and the determination of a matrix triple(tilde{A},tilde{B},tilde{C})which is a minimal partial realization of a sequence{Y_{1},...,Y_{m}}of Markov parameters. In this paper a parameterized realization(A(y),B, C)(yis a parameter vector) is defined which characterizes the set of all minimal partial realizations of the sequence{ Y_{1},. . . , Y_{m}}. An example is provided and the utility of the parameterization is discussed.     

A hierarchy of LMI inner approximations of the set of stable polynomials

Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for the positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMIs) in the coefficients. As an application of these results, we derive a hierarchy of convex LMI inner approximations (affine sections of the cone of positive definite matrices of size m) of the nonconvex set of Schur stable polynomials of given degree n<m. It is shown that when m tends to infinity the hierarchy converges to a lifted LMI approximation (projection of an LMI set defined in a lifted space of dimension quadratic in n) already studied in the technical literature. An application to robust controller design is described.     

A complete algorithm to find exact minimal polynomial by approximations

Based on an improved parameterized integer relation construction method, a complete algorithm is proposed for finding an exact minimal polynomial from its approximate root. It relies on a study of the error controlling for its approximation. We provide a sufficient condition on the precision of the approximation, depending only on the degree and the height of its minimal polynomial. Our result is superior to the existent error controlling on obtaining an exact rational or algebraic number from its approximation. Moreover, some applications are presented and compared with the subsistent methods.     

Distributed minimum dominating set approximations in restricted families of graphs

A dominating set is a subset of the nodes of a graph such that all nodes are in the set or adjacent to a node in the set. A minimum dominating set approximation is a dominating set that is not much larger than a dominating set with the fewest possible number of nodes. This article summarizes the state-of-the-art with respect to finding minimum dominating set approximations in distributed systems, where each node locally executes a protocol on its own, communicating with its neighbors in order to achieve a solution with good global properties. Moreover, we present a number of recent results for specific families of graphs in detail. A unit disk graph is given by an embedding of the nodes in the Euclidean plane, where two nodes are joined by an edge exactly if they are in distance at most one. For this family of graphs, we prove an asymptotically tight lower bound on the trade-off between time complexity and approximation ratio of deterministic algorithms. Next, we consider graphs of small arboricity, whose edge sets can be decomposed into a small number of forests. We give two algorithms, a randomized one excelling in its approximation ratio and a uniform deterministic one which is faster and simpler. Finally, we show that in planar graphs, which can be drawn in the Euclidean plane without intersecting edges, a constant approximation factor can be ensured within a constant number of communication rounds.     

基于置信优势关系粗糙集的近似集动态更新方法

置信优势关系粗糙集是处理不完备有序信息的重要模型, 上、下近似集的计算是核心内容之一. 在实际应用中, 属性集通常会发生变化. 根据属性集的增加或减少, 首先讨论置信优势类及劣势类变化情况, 随之给出上、下近似集增量式的变化规律, 提出相应的近似集动态更新方法. 通过Matlab 在UCI 数据集上的实验结果表明, 与非增量式方法相比, 所提出的置信优势关系粗糙集下的上、下近似集的增量式更新方法可行、高效.

     

Using response surface approximations in fuzzy set based design optimization

The paper focuses on modelling uncertainty typical of the aircraft industry. The design problem involves maximizing a safety measure of an isotropic plate for a given weight. Additionally, the dependence of the weight on the level of uncertainty, for a specified allowable possibility of failure, is also studied. It is assumed that the plate will be built from future materials, with little information available on the uncertainty. Fuzzy set theory is used to model the uncertainty. Response surface approximations that are accurate over the entire design space are used throughout the design process, mainly to reduce the computational cost associated with designing for uncertainty. All of the problem parameters are assumed to be uncertain, and both a yield stress and a buckling load constraint are considered. The fuzzy set based design is compared to a traditional deterministic design that uses a factor of safety to account for the uncertainty. It is shown that, for the example problem considered, the fuzzy set based design is superior. Additionally, the use of response surface approximations results in substantial reductions in computational cost, allowing the final results to be presented in the form of design charts.Presented as paper 98-1776 at the 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Long Beach, California, April 20-23, 1998     

A framework for robust parametric set membership identification

This paper proposes a new framework for studying robust parametric set membership identification. The authors derive some new results on the fundamental limitations of algorithms in this framework, given a particular model structure. The new idea is to quantify uncertainty only with respect to the (finite dimensional) parametric part of the model and not the (fixed size) unmodeled dynamics. Thus, the measure of uncertainty is different from the measures used in previous robust identification work where system norms are used to quantify uncertainty. As an example, the results are used to assess the fidelity of a certain approximate robust parametric set membership identification algorithm     

最小化决策规则集的计算方法

在决策算法中，并不是所有的决策规则都是必要的，一些过剩的决策规则应该消去，而不影响作决策，因此，研究最小化决策规则集的计算方法是很有意义的．传统的决策算法并没有给出最小化决策规则集的形式化计算方法，为了解决最小化决策规则集的形式化计算问题，引入了最小化决策规则可辨识矩阵概念，提供了基于可辨识矩阵的基本决策规则的最小化决策规则集的计算方法．     

PRT系统的最终有界和正向不变集及其应用

通过构造一个广义正定径向无界的Lyapunov函数和最优化理论,研究了一个在实际中描述血浆运动的PRT混沌系统的最终有界集和正向不变集,得到了三维椭球估计。将得到的变量x,y,z的界应用到混沌同步中,设计一个尽可能简单的线性控制器研究了该系统的完全同步。数值仿真验证了同步理论的有效性。