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Order Terms (order + term)

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Mathematics and Statistics60%

Selected Abstracts

Feedback stabilization of bifurcations in multivariable nonlinear systems,Part II: Hopf bifurcations

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2007
Yong Wang
Abstract In this paper we derive necessary and sufficient conditions of stabilizability for multi-input nonlinear systems possessing a Hopf bifurcation with the critical mode being linearly uncontrollable, under the non-degeneracy assumption that stability can be determined by the third order term in the normal form of the dynamics on the centre manifold. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the Hopf bifurcation of the closed-loop system is supercritical, which is equivalent to local asymptotic stability of the system at the bifurcation point. We prove that under the non-degeneracy conditions, stabilizability is equivalent to the existence of solutions to a third order algebraic inequality of the feedback gains. Explicit conditions for the existence of solutions to the algebraic inequality are derived, and the stabilizing feedback laws are constructed. Part of the sufficient conditions are equivalent to the rank conditions of an augmented matrix which is a generalization of the Popov,Belevitch,Hautus (PBH) rank test of controllability for linear time invariant (LTI) systems. We also apply our theory to feedback control of rotating stall in axial compression systems using bleed valve as actuators. Copyright © 2006 John Wiley & Sons, Ltd. [source]

On the decay of the solutions of second order parabolic equations with Dirichlet conditions

MATHEMATISCHE NACHRICHTEN, Issue 8 2007
Brice FrankeArticle first published online: 8 MAY 200
Abstract We use rearrangement techniques to investigate the decay of the parabolic Dirichlet problem in a bounded domain. The coefficients of the second order term are used to introduce an isoperimetric problem. The resulting isoperimetric function together with the divergence of the first order coefficients and the value distribution of the zero order part are then used to construct a symmetric comparison equation having a slower heat-flow than the original equation. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A new approach to response surface development for detailed gas-phase and surface reaction kinetic model optimization

INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 2 2004
Scott G. Davis
We propose a new method for constructing kinetic response surfaces used in the development and optimization of gas-phase and surface reaction kinetic models. The method, termed as the sensitivity analysis based (SAB) method, is based on a multivariate Taylor expansion of model response with respect to model parameters, neglecting terms higher than the second order. The expansion coefficients are obtained by a first-order local sensitivity analysis. Tests are made for gas-phase combustion reaction models. The results show that the response surface obtained with the SAB method is as accurate as the factorial design method traditionally used in reaction model optimization. The SAB method, however, presents significant computational savings compared to factorial design. The effect of including the partial and full third order terms was also examined and discussed. The SAB method is applied to optimization of a relatively complex surface reaction mechanism where large uncertainty in rate parameters exists. The example chosen is laser-induced fluorescence signal of OH desorption from a platinum foil in the water/oxygen reaction at low pressures. We introduce an iterative solution mapping and optimization approach for improved accuracy. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 94,106, 2004 [source]

Comparison results for nonlinear elliptic equations with lower,order terms

MATHEMATISCHE NACHRICHTEN, Issue 1 2003
Vincenzo Ferone
Abstract We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) + g(x, u) = f, where the principal term is a Leray,Lions operator defined on and g(x, u) is a term having the same sign as u and satisfying suitable growth assumptions. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric. [source]

An implicit QR algorithm for symmetric semiseparable matrices

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 7 2005
Raf Vandebril
Abstract The QR algorithm is one of the classical methods to compute the eigendecomposition of a matrix. If it is applied on a dense n × n matrix, this algorithm requires O(n3) operations per iteration step. To reduce this complexity for a symmetric matrix to O(n), the original matrix is first reduced to tridiagonal form using orthogonal similarity transformations. In the report (Report TW360, May 2003) a reduction from a symmetric matrix into a similar semiseparable one is described. In this paper a QR algorithm to compute the eigenvalues of semiseparable matrices is designed where each iteration step requires O(n) operations. Hence, combined with the reduction to semiseparable form, the eigenvalues of symmetric matrices can be computed via intermediate semiseparable matrices, instead of tridiagonal ones. The eigenvectors of the intermediate semiseparable matrix will be computed by applying inverse iteration to this matrix. This will be achieved by using an O(n) system solver, for semiseparable matrices. A combination of the previous steps leads to an algorithm for computing the eigenvalue decompositions of semiseparable matrices. Combined with the reduction of a symmetric matrix towards semiseparable form, this algorithm can also be used to calculate the eigenvalue decomposition of symmetric matrices. The presented algorithm has the same order of complexity as the tridiagonal approach, but has larger lower order terms. Numerical experiments illustrate the complexity and the numerical accuracy of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd. [source]