Root-restricted Kleenean rotations

We generalize the Kleene theorem to the case where nonassociative products are used. For this purpose, we apply rotations restricted to the root of binary trees.     

Adaptive discrete neural observer design for nonlinear systems with unknown time‐delay

This paper focuses on the adaptive observer design for nonlinear discrete‐time MIMO systems with unknown time‐delay and nonlinear dynamics. The delayed states involved in the system are arguments of a nonlinear function and only the estimated delay is utilized. By constructing an appropriate Lyapunov–Krasovskii function, the delay estimation error is considered in the observer parameter design. The proposed method is then extended to the system with a nonlinear output measurement equation and the delayed dynamics. With the help of a high‐order neural network (HONN), the requirement for a precise system model, the linear‐in‐the‐parameters (LIP) assumption of the delayed states, the Lipschitz or norm‐boundedness assumption of unknown nonlinearities are removed. A novel converse Lyapunov technical lemma is also developed and used to prove the uniform ultimate boundedness of the proposed observer. The effectiveness of the proposed results is verified by simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

一种提取目标图像最小外接矩形的快速算法

在图像分类与识别算法研究中,目标几何特征的提取通常需要计算目标图像的最小外接矩形以获取长、宽等属性。针对该特点,提出一种利用顶点链码与离散格林理论相结合的方式提取目标图像的最小外接矩形的算法。该算法只需根据顶点链中垂直或水平方向上的点坐标即可求出目标的面积、形心和主轴。基于顶点链码和离散格林的主轴法和旋转法可快速求出目标的最小外接矩形。实验结果表明,旋转法的运算速度是现有算法的2倍左右,主轴法的速度又比旋转法快速2倍左右。     

Connecting the 3D DGS Calques3D with the CAS Maple

Many (2D) Dynamic Geometry Systems (DGSs) are able to export numeric coordinates and equations with numeric coefficients to Computer Algebra Systems (CASs). Moreover, different approaches and systems that link (2D) DGSs with CASs, so that symbolic coordinates and equations with symbolic coefficients can be exported from the DGS to the CAS, already exist. Although the 3D DGS Calques3D can export numeric coordinates and equations with numeric coefficients to Maple and Mathematica, it cannot export symbolic coordinates and equations with symbolic coefficients. A connection between the 3D DGS Calques3D and the CAS Maple, that can handle symbolic coordinates and equations with symbolic coefficients, is presented here. Its main interest is to provide a convenient time-saving way to explore problems and directly obtain both algebraic and numeric data when dealing with a 3D extension of “ruler and compass geometry”. This link has not only educational purposes but mathematical ones, like mechanical theorem proving in geometry, geometric discovery (hypotheses completion), geometric loci finding… As far as we know, there is no comparable “symbolic” link in the 3D case, except the prototype 3D-LD (restricted to determining algebraic surfaces as geometric loci).     

Multiple robust H∞ controller design using the nonsmooth optimization method

This paper proposes a systematic technique to design multiple robust H_∞ controllers. The proposed technique achieves a desired robust performance objective, which is impossible to achieve with a single robust controller, by dividing the uncertainty set into several subsets and by designing a robust controller to each subset. To achieve this goal with a small number of divisions of the uncertainty set, an optimization problem is formulated. Since the cost function of this optimization problem is not a smooth function, a numerical nonsmooth optimization algorithm is proposed to solve this problem. This method avoids the use of Lyapunov variables, and therefore it leads to a moderate size optimization problem. A numerical example shows that the proposed multiple robust control method can improve the closed‐loop performance when a single robust controller cannot achieve satisfactory performance. Copyright © 2009 John Wiley & Sons, Ltd.     

A Kharitonov‐like theorem for robust stability independent of delay of interval quasipolynomials

In this paper, a Kharitonov‐like theorem is proved for testing robust stability independent of delay of interval quasipolynomials, p(s)+∑eq_k(s), where p and q_k's are interval polynomials with uncertain coefficients. It is shown that the robust stability test of the quasipolynomial basically reduces to the stability test of a set of Kharitonov‐like vertex quasipolynomials, where stability is interpreted as stability independent of delay. As discovered in (IEEE Trans. Autom. Control 2008; 53 :1219–1234), the well‐known vertex‐type robust stability result reported in (IMA J. Math. Contr. Info. 1988; 5 :117–123) (See also (IEEE Trans. Circ. Syst. 1990; 37 (7):969–972; Proc. 34th IEEE Conf. Decision Contr., New Orleans, LA, December 1995; 392–394) does contain a flaw. An alternative approach is proposed in (IEEE Trans. Autom. Control 2008; 53 :1219–1234), and both frequency sweeping and vertex type robust stability tests are developed for quasipolynomials with polytopic coefficient uncertainties. Under a specific assumption, it is shown in (IEEE Trans. Autom. Control 2008; 53 :1219–1234) that robust stability independent of delay of an interval quasipolynomial can be reduced to stability independent of delay of a set of Kharitonov‐like vertex quasipolynomials. In this paper, we show that the assumption made in (IEEE Trans. Autom. Control 2008; 53 :1219–1234) is redundant, and the Kharitonov‐like result reported in (IEEE Trans. Autom. Control 2008; 53 :1219–1234) is true without any additional assumption, and can be applied to all quasipolynomials. The key idea used in (IEEE Trans. Autom. Control 2008; 53 :1219–1234) was the equivalence of Hurwitz stability and ?_‐o‐stability for interval polynomials with constant term never equal to zero. This simple observation implies that the well‐known Kharitonov theorem for Hurwitz stability can be applied for ?_‐o‐stability, provided that the constant term of the interval polynomial never vanishes. However, this line of approach is based on a specific assumption, which we call the CNF‐assumption. In this paper, we follow a different approach: First, robust ?_‐o‐stability problem is studied in a more general framework, including the cases where degree drop is allowed, and the constant term as well as other higher‐orders terms can vanish. Then, generalized Kharitonov‐like theorems are proved for ?_‐o‐stability, and inspired by the techniques used in (IEEE Trans. Autom. Control 2008; 53 :1219–1234), it is shown that robust stability independent of delay of an interval quasipolynomial can be reduced to stability independent of delay of a set of Kharitonov‐like vertex quasipolynomials, even if the assumption adopted in (IEEE Trans. Autom. Control 2008; 53 :1219–1234) is not satisfied. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison of two novel MRAS based strategies for identifying parameters in permanent magnet synchronous motors

Two model reference adaptive system (MRAS) estimators are developed for identifying the parameters of permanent magnet synchronous motors (PMSM) based on the Lyapunov stability theorem and the Popov stability criterion, respectively. The proposed estimators only need online measurement of currents, voltages, and rotor speed to effectively estimate stator resistance, inductance, and rotor flux-linkage simultaneously. The performance of the estimators is compared and verified through simulations and experiments, which show that the two estimators are simple, have good robustness against parameter variation, and are accurate in parameter tracking. However, the estimator based on the Popov stability criterion, which can overcome parameter variation in a practical system, is superior in terms of response speed and convergence speed since there are both proportional and integral units in the estimator, in contrast to only one integral unit in the estimator based on the Lyapunov stability theorem. In addition, the estimator based on the Popov stability criterion does not need the expertise that is required in designing a Lyapunov function.     

出具证明编译器中线性整数命题证明的自动生成

近年来,出具证明编译器作为构建高可信软件的重要途径,逐渐成为编译器理论和形式化验证的研究热点.在其理论框架中,编译器需要借助自动定理证明技术,自动地证明验证条件并生成机器可检查的证明项,因此好的自动定理证明器对出具证明编译器至关重要.本文基于Simplex算法在出具证明编译器的框架内设计并实现了一个支持线性整数命题求解的自动定理证明器,并且提出一套证明项构造方法,将其应用于自动定理证明器中可生成Coq可检查的证明.     

Anti-periodic fractional boundary value problems

We study a class of anti-periodic boundary value problems of fractional differential equations. Some existence and uniqueness results are obtained by applying some standard fixed point principles. Several examples are given to illustrate the results.