摘要:

A theoretical framework for proposed “weak Tau” type of approximation schemes is considered in the context of least-squares parameter estimation problems for partial differential equations. A convergence theory which includes parameter estimate convergence and method stability is developed. Numerical results demonstrating the possible advantages of these ideas are also presented.

ISSN:0163-0563    

DOI:10.1080/01630569108816418

出版商:Marcel Dekker, Inc.    

年代:1991

数据来源: Taylor

摘要:

Wavelet based Galerkin approximation schemes for the closed-loop solution of optimal linear-quadratic regulator problems for distributed parameter systems are developed. The methods are based upon the finite dimensional approximation of the associated operator algebraic Riccati equation in Galerkin sub-spaces spanned by families of compactly supported wavelet functions. An overview of the aspects of the theory of wavelet transforms which are useful in the development of Galerkin schemes has been provided. A brief outline of optimal linear-quadratic control theory for infinite dimensional systems together with the associated approximation and convergence theories have also been included. The results of numerical studies involving two examples, control of a one dimensional heat/diffusion equation and vibration damping in a visco-thermoelastic rod, are presented and discussed. Comparisons with existing methods using both spline and modal functions are made.

ISSN:0163-0563    

DOI:10.1080/01630569108816419

出版商:Marcel Dekker, Inc.    

年代:1991

数据来源: Taylor

摘要:

This paper deals with the development and analysis of well-posed models and computational algorithms for control of a class of partial differential equations that descrive the motions of thermo-viscoelastic structures. We first present an abstract “state space” framework and general well-posedness result that can be applied to a large class of thermo-elastic and thermo-viscoelastic models. This state space framework is used in the development of a computational scheme to be used in the solution of an LQR control problem. A detailed convergence proof is provided for the viscoelastic model, and several numerical results are presented to illustrate the theory and to analyze problems for which the theory is incomplete.

ISSN:0163-0563    

DOI:10.1080/01630569108816420

出版商:Marcel Dekker, Inc.    

年代:1991

数据来源: Taylor

摘要:

We study the problem of interpolating scattered data in Euclidean spaces by linear combinations of translates of conditionally positive definite functions. We show that certain symmetric linear combinations of these functions give rise to nonsingular interpolation matrices. We also estimate the norms of inverses of these matrices.

ISSN:0163-0563    

DOI:10.1080/01630569108816421

出版商:Marcel Dekker, Inc.    

年代:1991

数据来源: Taylor

摘要:

Both continuous and discrete – time Galerkin methods are analysed for the numerical approximation of a single phase semilinear Stefan problem with a nonlinear source term. Optimal rates of convergence inL2HlandH2– norms are derived for both the cases.

ISSN:0163-0563    

DOI:10.1080/01630569108816422

出版商:Marcel Dekker, Inc.    

年代:1991

数据来源: Taylor

摘要:

This paper is concerned with a class of optimal control problems with state and control constraints which have one state variable but several control variables. The variables can appear linearly or not linearly, and the performance index and the function in the state equation are able to be non-convex in their variables. In order to overcome difficulities in solving such problems that are caused by state constraints, the Method of Orienting Curves is developed. By this method, the optimal trajectory is constructed as a path which consists of parts of orienting curves, boundary arcs, and finally, of the final curve. This method can be applied tho solve a lot of practical problems, for example, optimal control of hydroelectric power plants, Zemerlo's navigation problem with state constraints …. Here, an inventory problems is considered as application example.

ISSN:0163-0563    

DOI:10.1080/01630569108816423

出版商:Marcel Dekker, Inc.    

年代:1991

数据来源: Taylor

摘要:

The linear Cauchy problemforwith a linear pseudo-differential operatorL(D) whose symbol is analytic in a domainis discussed in the framework of spacesandThe spaceis the space of tempered distributions whose Fourier transform is supported by a subset ofG, andis its dual space. Theorems of existence and uniqueness are presented and methods of approximating the solutions are developed. Applications to some concrete problems are described.

ISSN:0163-0563    

DOI:10.1080/01630569108816424

出版商:Marcel Dekker, Inc.    

年代:1991

数据来源: Taylor

摘要:

In this paper we study second-order optimality conditions for the multi-objective programming problems with both inequality constraints and equality constraints. Two weak second-order constraint qualifications are introduced, and based on them we derive several second-order necessary conditions for a local weakly efficient solution. Two second-order sufficient conditions are also presented.

ISSN:0163-0563    

DOI:10.1080/01630569108816425

出版商:Marcel Dekker, Inc.    

年代:1991

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630569108816417

出版商:Marcel Dekker, Inc.    

年代:1991

数据来源: Taylor