共查询到20条相似文献,搜索用时 31 毫秒
1.
Yuan-Hua Ni 《应用数学学报(英文版)》2010,26(2):251-266
This paper deals with the output feedback H∞ control problem for a class of nonlinear stochastic systems. Based on the latest developed theory of stochastic dissipation, a notable result about the nonlinear H∞ output feedback control of deterministic system is generalized to the stochastic case. Finally, in the cases of state feedback and output feedback, two families of controllers are provided respectively. 相似文献
2.
L. W. White 《Journal of Optimization Theory and Applications》1982,36(2):277-288
The feedback operator of a linear pseudoparabolic problem with quadratic criterion is obtained by decoupling of the optimality condition. The feedback operator is shown to be related to the solution of a Riccati equation formulated in theB*-algebra of bounded linear operators onL
2(). This approach shows that the linear feedback operator may be considered as a bounded operator fromL
2() intoH
0
1
(). Finally, we give a theorem establishing the convergence behavior for the feedback operators for these problems as they formally approach an analogous problem of parabolic type.This work was supported in part by the National Science Foundation, Grant No. MCS-7902037. 相似文献
3.
Summary The error in the estimate of thekth eigenvalue of a regular Sturm-Liouville problem obtained by Numerov's method with mesh lengthh isO(k
6
h
4). We show that a simple correction technique of Paine, de Hoog and Anderssen reduces the error to one ofO(k
3
h
4). Numerical examples demonstrate the usefulness of this correction even for low values ofk. 相似文献
4.
Summary It is shown that a simple asymptotic correction technique of Paine, de Hoog and Anderssen reduces the error in the estimate of thekth eigenvalue of a regular Sturm-Liouville problem obtained by the finite element method, with linear hat functions and mesh lengthh, fromO(k
4
h
2) toO(k h
2). The result still holds when the matrix elements are evaluated by Simpson's rule, but if the trapezoidal rule is used the error isO(k
2
h
2). Numerical results demonstrate the usefulness of the correction even for low values ofk. 相似文献
5.
Shuping Ma Chenghui Zhang Zhaolin Cheng 《Journal of Computational and Applied Mathematics》2008,217(1):194-211
The robust memoryless state feedback H∞ control problem for uncertain time-delay discrete-time singular systems is discussed. Under a series of equivalent transformation, the equivalence of this problem and the robust state feedback H∞ control problem for standard state-space uncertain time-delay discrete-time systems is presented. In terms of matrix inequality, the delay-dependent sufficient condition for the solution of this problem is given, the design method of the memoryless state feedback controller and the controller are also given. 相似文献
6.
K. G. Arvanitis P. N. Paraskevopoulos 《Journal of Optimization Theory and Applications》1995,87(2):235-267
This paper deals with the problem of designing multirate-output contrlleers for sampled-dataH
-optimal control of linear continuous-time systems. Two formulations of the problem are studied. In the first, the intersample behavior of the disturbance and the controlled output signals is not considered, whereas in the second the continuous-time nature of these signals is taken into account. It is shown that, in both cases and unter appropriate conditions, it is plausible to reduce the repective initial problem to an associated discrete-timeH
-optimization problem for which a fictitious static state feedback controller is to be designed. This fact has a beneficial influence on the theoretical and numerical complexity of the problem, since only one algebraic Riccati equation is to be solved here, as compared to two algebraic Riccati equations needed in known techniques concerning theH
-optimization problem with dynamic measurement feedback.The work described in this paper has been partially funded by the General Secretariat for Research and Technology of the Greek Ministry of Industry, Research, and Technology and by the Heracles General Cement Company of Greece. 相似文献
7.
Zbigniew Leyk 《Numerische Mathematik》1986,49(1):39-53
Summary A method of a collocation type based onC
0-piecewise polynomial spaces is presented for a two-point boundary value problem of the second order. The method has an optimal order of convergence under smoothness requirements on the exact solution which are weaker than forC
1-collocation methods. If the differential operator is symmetric, a modification of this method leads to a symmetric system of linear equations. It is shown that if the collocation solution is a piecewise polynomial of degree not greater thanr, the method is stable and convergent with orderh
r
inH
1-norm. A similar symmetric modification forC
0-colloction-finite element method [7] is also obtained. Superconvergence at the nodes is established. 相似文献
8.
Kalle M. Mikkola 《Integral Equations and Operator Theory》2006,55(2):249-271
A finite-dimensional linear time-invariant system is output-stabilizable if and only if it satisfies the finite cost condition, i.e., if for each initial state there exists at least one L2 input that produces an L2 output. It is exponentially stabilizable if and only if for each initial state there exists at least one L2 input that produces an L2 state trajectory. We extend these results to well-posed linear systems with infinite-dimensional input, state and output
spaces. Our main contribution is the fact that the stabilizing state feedback is well posed, i.e., the map from an exogenous input (or disturbance) to the feedback, state and output signals is continuous in Lloc2 in both open-loop and closed-loop settings. The state feedback can be chosen in such a way that it also stabilizes the I/O
map and induces a (quasi) right coprime factorization of the original transfer function. The solution of the LQR problem has
these properties. 相似文献
9.
We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization
is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called
Isaacs' equation. Links between supersolutions and epicontingent solutions to Isaacs' equation are studied. Finally, we derive
(possibly discontinuous) disturbance attenuation feedback of the H
∞
problem from contingent formulation of Isaacs' equation.
Accepted 20 January 1998 相似文献
10.
M. I. Comodi 《Numerische Mathematik》1985,47(3):435-458
Summary We study a variational formulation of the unilaterally supported bent plate problem and we analyze the approximation of the problem by a mixed finite element method. We proveO(h) andO(h|lnh|1/2) error bounds respectively for the moments and the displacement.Work partially supported by M.P.I., by G.N.I.M. of C.N.R. and by I.A.N. of C.N.R. of Pavia 相似文献
11.
M. Dryja 《Numerische Mathematik》1982,39(1):51-64
Summary An efficient algorithm for the solution of linear equations arising in a finite element method for the Dirichlet problem is given. The cost of the algorithm is proportional toN
2log2
N (N=1/h) where the cost of solving the capacitance matrix equations isNlog2
N on regular grids andN
3/2log2
N on irregular ones. 相似文献
12.
The Picard variety Pic0(?
n
) of a complex n-dimensional torus?
n
is the group of all holomorphic equivalence classes of topologically trivial holomorphic (principal) line bundles on ?
n
. The total space of a topologically trivial holomorphic (principal) line bundle on a compact K?hler manifold is weakly pseudoconvex.
Thus we can regard Pic0(?
n
) as a family of weakly pseudoconvex K?hler manifolds. We consider a problem whether the Kodaira's -Lemma holds on a total space of holomorphic line bundle belonging to Pic0(?
n
). We get a criterion for this problem using a dynamical system of translations on Pic0(?
n
). We also discuss the problem whether the -Lemma holds on
strongly pseudoconvex K?hler manifolds or not. Using the result of ColColţoiu, we find a 1-convex complete K?hler manifold
on which the -Lemma does not hold.
Received: 11 June 1999 / Revised version: 22 November 1999 相似文献
13.
Karl Scherer 《Numerische Mathematik》1980,36(2):151-176
Summary In the second section a general method of obtaining optimal global error bounds by scaling local error estimates is developed. It is reduced to the solution of a fixpoint problem. In Sect. 3 we show more concrete error estimates reflecting a singularity of order . It is shown that under general circumstances an optimal global error bound is achieved by an (asymptotically) geometric mesh for the local error estimates. In the fourth section we specialize this to the best approximation ofg(x)x
by piecewise polynomials with variable knots and degrees having a total numberN of parameters. This generalizes the result of R. DeVore and the author forg(x)=1. In the last section this problem is studied for the functione
–x on (0, ). The exact asymptotic behaviour of the approximation withN parameters is determined toe
qoN
, whereq
o=0.895486 .... 相似文献
14.
15.
16.
In this paper we define a new condition number ?(A) for the following problem: given a m by n matrix A, find x∈ℝ
n
, s.t. Ax<0. We characterize this condition number in terms of distance to ill-posedness and we compare it with existing condition
numbers for the same problem.
Received: November 5, 1999 / Accepted: November 2000?Published online September 17, 2001 相似文献
17.
Giuseppina Vannella 《Annali di Matematica Pura ed Applicata》2002,180(4):429-440
We consider a Neumann problem of the type -εΔu+F
′(u(x))=0 in an open bounded subset Ω of R
n
, where F is a real function which has exactly k maximum points.
Using Morse theory we find that, for ε suitably small, there are at least 2k nontrivial solutions of the problem and we give some qualitative information about them.
Received: October 30, 1999 Published online: December 19, 2001 相似文献
18.
G. Mühlbach 《Numerische Mathematik》1985,46(3):339-349
Summary This note is concerned with the following problem: Given a systemA·x=b of linear equations and knowing that certains of its subsystemsA
1·x
1=b
1, ...,A
m
·x
m
=b
m
can be solved uniquely what can be said about the regularity ofA and how to find the solutionx fromx
1, ...,x
m
? This question is of particular interest for establishing methods computing certain linear or quasilinear sequence transformations recursively [7, 13, 15].Work performed under NATO Research Grant 027-81 相似文献
19.
Model selection for regression on a fixed design 总被引:1,自引:0,他引:1
Yannick Baraud 《Probability Theory and Related Fields》2000,117(4):467-493
We deal with the problem of estimating some unknown regression function involved in a regression framework with deterministic
design points. For this end, we consider some collection of finite dimensional linear spaces (models) and the least-squares
estimator built on a data driven selected model among this collection. This data driven choice is performed via the minimization
of some penalized model selection criterion that generalizes on Mallows' C
p
. We provide non asymptotic risk bounds for the so-defined estimator from which we deduce adaptivity properties. Our results
hold under mild moment conditions on the errors. The statement and the use of a new moment inequality for empirical processes
is at the heart of the techniques involved in our approach.
Received: 2 July 1997 / Revised version: 20 September 1999 / Published online: 6 July 2000 相似文献
20.
Koichi Niijima 《Numerische Mathematik》1985,46(4):521-539
Summary A difference scheme of exponential type for solving a nonlinear singular perturbation problem is analysed. Although this scheme is not of monotone type, aL
1 convergence result is obtained. Relations between this scheme and Engquist-Osher scheme are also discussed. 相似文献