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71.
Jean Marcel Pallo 《Information Processing Letters》2010,111(1):46-50
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. 相似文献
72.
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. 相似文献
73.
74.
Eugenio Roanes-Lozano Nicolas van Labeke Eugenio Roanes-Macías 《Mathematics and computers in simulation》2010
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). 相似文献
75.
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. 相似文献
76.
Onur Toker 《国际强度与非线性控制杂志
》2010,20(6):623-638
》2010,20(6):623-638
In this paper, a Kharitonov‐like theorem is proved for testing robust stability independent of delay of interval quasipolynomials, p(s)+∑eqk(s), where p and qk'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. 相似文献
77.
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. 相似文献
78.
79.
Bashir Ahmad 《Computers & Mathematics with Applications》2011,62(3):1150-1156
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. 相似文献
80.
We proved some almost sure limit theorems for standard strongly dependent Gaussian sequences in nonstationary cases under some mild conditions. 相似文献