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1.
New optimal control problems for a conditionally correct system whose state is described by an elliptic quartic equation with conjugation conditions are considered. Efficient computation schemes for numerical determination of optimal controls are constructed, the admissible control sets being complete Hilbert spaces.The study was sponsored by the State Fund for Fundamental Research of the Ministry of Education and Science of Ukraine (contract No. F7/276-2001).__________Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 156–174, January–February 2005. 相似文献
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New optimal control problems for elliptic systems with contact conditions and nonsymmetric state operators are considered.
Existence theorems for optimal solutions are proved. High-accuracy schemes for approximating optimal controls are proposed
for the case where the set of admissible controls coincides with a complete Hilbert space.
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 67–85, November–December 2005. 相似文献
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New optimal control problems are constructed and considered for distributed systems whose states are described by Neumann boundary-value problems with conjugation conditions and non-unique solutions. The paper proposes accurate higher-order computation schemes for discretization of optimization problems for the case where a control set coincides with a full Hilbert space. 相似文献
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New optimal control problems for distributed systems described by initial boundary-value problems are considered in the paper for an elliptic-parabolic equation with conjugation conditions and quadratic cost functions. Theorems of existence of a unique optimal control are proved for all the considered cases. 相似文献
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《国际计算机数学杂志》2012,89(16):3553-3564
In this paper, a numerical method is developed to solve an N-carrier system with Neumann boundary conditions. First, we apply the compact finite difference scheme of fourth order for discretizing spatial derivatives at the interior points. Then, we develop a new combined compact finite difference scheme for the boundary, which also has fourth-order accuracy. Lastly, by using a Padé approximation method for the resulting linear system of ordinary differential equations, a new compact finite difference scheme is obtained. The present scheme has second-order accuracy in time direction and fourth-order accuracy in space direction. It is shown that the scheme is unconditionally stable. The present scheme is tested by two numerical examples, which show that the convergence rate with respect to the spatial variable from the new scheme is higher and the solution is much more accurate when compared with those obtained by using other previous methods. 相似文献
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New optimal control problems are considered for distributed systems described by elliptic equations with conjugate conditions and a quadratic minimized function. Highly accurate computational discretization schemes are constructed for the case where a feasible control set
coincides with the full Hilbert space
of controls. 相似文献
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New problems of optimal control of distributed systems described by a hyperbolic equation with conjugation conditions and a quadratic cost function are considered in the paper. Unique optimal control existence theorems are proved for all the analyzed cases. 相似文献
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A unified treatment of boundary conditions in least-square based finite-volume methods 总被引:1,自引:0,他引:1
We propose a unified treatment of internal and boundary vertex least-squares reconstructions in second-order accurate cell-centered finite-volume discretisation of 2-D steady diffusion problems. Dirichlet, Neumann, and Robin boundary conditions are taken into account in the same formulation by introducing suitable constraints in the least-squares minimization process. The method is discussed in its theoretical framework and a representative numerical experiment illustrates its capability in providing the second-order of accuracy. 相似文献
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Formal algorithms for complete asymptotic decompositions of solutions to optimal globally bounded control problems for elliptic equations with fast oscillating coefficients are constructed. If the kernel of a differential operator of the initial problem is nonzero, asymptotics of different orders may exist in the control system.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 84–95, September–October 2004. 相似文献
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Stevan Dubljevic 《国际强度与非线性控制杂志
》2009,19(2):135-150
》2009,19(2):135-150
Alternation of normal electrical activity in the myocardium is believed to be linked to the onset of life‐threatening ventricular arrhythmias and sudden cardiac death. In this paper, a spatially uniform unstable steady state of small amplitude of alternans described by parabolic partial differential equations (PDEs) is stabilized by boundary optimal control methods. A finite dimensional linear quadratic regulator (LQR) is utilized in both a full‐state‐feedback control structure and in a compensator design with the Luenberger observer, and it achieves global stabilization in a finite size tissue cable length. The ability to realize such control algorithm is analyzed based on the structure of the amplitude of alternans equation and the control methodology applied. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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New Dirichlet and Neumann boundary-value problems for elliptic equations with conjugation conditions are considered and existence and uniqueness of their solutions are studied. High-precision discretization algorithms are constucted based on the classes of discontinuous admissible functions. 相似文献
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A compact alternating direction implicit (ADI) finite difference method is proposed for two-dimensional time fractional sub-diffusion equations with nonhomogeneous Neumann boundary conditions. The unconditional stability and convergence of the method is proved. The error estimates in the weighted - and -norms are obtained. The proposed method has the fourth-order spatial accuracy and the temporal accuracy of order , where is the order of the fractional derivative. In order to further improve the temporal accuracy, two Richardson extrapolation algorithms are presented. Numerical results demonstrate the accuracy of the compact ADI method and the high efficiency of the extrapolation algorithms. 相似文献
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《国际计算机数学杂志》2012,89(8-9):685-694
A numerical technique for solving a second-order nonlinear Neumann problem is presented. The authors’ approach is based on semi-orthogonal B-spline wavelets. Two test problems are presented and numerical results are tabulated to show the efficiency of the proposed technique for the studied problem. 相似文献
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New multicomponent soil media ecology problems and respective optimal control problems are considered in the paper. Existence theorems for the unique optimal control are proved for all the cases considered. Computation algorithms of high-accuracy discretization are constructed for some new classes of problems with discontinuous solutions. 相似文献
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This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller. 相似文献