进化算法与确定性算法在优化控制问题中的收敛性对比

对比了进化算法(基因算法)与确定性算法(共轭梯度法)在优化控制问题中的优化效率．两种方法都与分散武优化策略-Nash对策进行了结合,并成功地应用于优化控制问题。计算模型采用绕NACA0012翼型的位流流场．区域分裂技术的引用使得全局流场被分裂为多个带有重叠区的子流场,使用4种不同的方法进行当地流场解的耦合,这些算法可以通过当地的流场解求得全局流场解。数值计算结果的对比表明．进化算法可以得到与共轭梯度法相同的计算结果．并且进化算法的不依赖梯度信息的特性使其在复杂问题及非线性问题中具有广泛的应用前景。     

Mixed thermoplasticity problem for open solids of revolution

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 6, pp. 3–9, June, 1988.     

Mixed problem of crack theory for antiplane deformation

The elastic equilibrium of an isotropic plane with one linear defect under conditions of longitudinal shear is considered. The strain field is constructed by the solution of a twodimensional boundary-value Riemann problem with variable coefficients. A special method that reduce the general two-dimensional problem to two one-dimensional problems is proposed. The strain field is described by three types of asymptotic relations: for the tups of the defect, for the tips of the reinforcing edge, and also at a distance from the closely spaced tips of the defect and the rib. The general form of asymptotic relations for strains with finite energy is deduced from analysis of the variational symmetries of the equations of longitudinal shear. A paradox of the primal mixed boundary-value problem for cracks is formulated and a method of solving the problem is proposed. Novosibirsk State Technical University, Novosibirsk 630092. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 163–172, May–June, 1998.     

Testing the quality of control algorithms for complex dynamic systems

A guaranteed approach to testing the quality of control algorithms for complex dynamic systems is considered. The worst perturbations are formed in the process of solving a special differential game problem. An objective quality index is calculated for the proposed control algorithm even in the case when this algorithm is considered as a “blackbox”.     

Optimal synthesis in the problem of uniaxial stabilization for a satellite in the case of phase constraints

The optimal stabilization problem for the pitching oscillations of a satellite is considered. For the reduced system, an optimal control problem with phase constraints is formulated and a controllability domain is constructed. A necessary optimality condition (the maximum principle for the optimal control problem with phase constraints) is used to determine the optimal trajectories, the nature of interaction between a trajectory and the phase constraint boundary, and the number of boundary segments. An optimal synthesis is proposed in the constructed domain.     

Mixed boundary value problem of elasticity for a quarter space

We consider the static elasticity problem for a quarter space with zero displacements on one of its surfaces and with given stresses on the other. The method for solving this problem is based on the use of newunknown functions in the formof a linear combination of the desired displacements, which reduces the system of three Lamé equations to two equations to be solved simultaneously and one equation to be solved separately. The exact solution of this problem was obtained earlier by the same method [1]. But it was shown in [2] that such a solution is exact only under certain restrictions on the given functions. In the present paper, the solution of this problem is constructed without restrictions on the given functions, which necessitates solving a one-dimensional integro-differential equation; this can be done approximately by the orthogonal polynomial method. We present numerical results obtained on the basis of our solution.     

Mixed boundary value problem of heat conduction for infinite slab

Summary An axisymmetric steady state heat conduction boundary value problem having mixed boundary conditions on both faces of an infinite slab, is reduced to a pair of Fredholm integral equations of the second kind. For large values of h, the slab thickness, a solution correct to O(h ^–6) is obtained by expanding the kernels in power series.Presently at Imperial College, London.     

Mixed finite element method of hexahedral elements for Navier-Stokes problem

In this paper, we derive a new mixed element format of hexahedral elements for Navier-Stokes problem in three-dimensional space.     

Mixed problem of the theory of elasticity for a truncated paraboloid of revolution

KVIRTU PVO, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 5, pp. 27–32, May, 1991.     

Quality testing algorithms for the manual reentry guidance of the Soyuz-TMA spacecraft using a dynamic bench

The problem of developing the third level of the control system for a dynamic bench based on a CF-18 centrifuge is considered. The maximin testing procedure is used to check the stabilization accuracy of controlled objects. The first stage of this procedure is implemented by reducing the original dynamic game to a matrix game of large scale. When a saddle point does not exist, the problem is solved with the use of a mixed matrix game expansion by reducing it to a linear programming problem. An example of constructing the test perturbations used at the second stage of the maximin testing procedure is discussed.     

On the problem of stabilization of motion for a parametric family of nonlinear singularly perturbed systems

For nonlinear uncertain singularly perturbed systems, we construct a control guaranteeing their absolute parametric stability and estimate the set of values of the parameters for which this property of the system is preserved.     

Numerical solution to the problem of the complete stabilization of a supersonic boundary layer

A method is suggested for solving numerically the problem of the complete stabilization of a supersonic boundary layer. It is shown that when the surface is significantly cooled, the neutral stability curve splits into two branches. A calculation is given for the temperatures of complete stabilization for both neutral curves. A comparison of the results obtained with those derived from asymptotic calculations shows that above M = 2 (M is the Mach number) the asymptotic method gives incorrect results.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 39–43, March–April, 1972.     

Efficient augmented Lagrangian‐type preconditioning for the Oseen problem using Grad‐Div stabilization

Efficient preconditioning for Oseen‐type problems is an active research topic. We present a novel approach leveraging stabilization for inf‐sup stable discretizations. The Grad‐Div stabilization shares the algebraic properties with an augmented Lagrangian‐type term. Both simplify the approximation of the Schur complement, especially in the convection‐dominated case. We exploit this for the construction of the preconditioner. Solving the discretized Oseen problem with an iterative Krylov‐type method shows that the outer iteration numbers are retained independent of mesh size, viscosity, and finite element order. Thus, the preconditioner is very competitive. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical and asymptotic solution of the problem concerning the complete stabilization of a boundary layer

The numerical method given in [1] is used here for calculating the temperatures of complete stabilization for a supersonic boundary layer at a flat plate with the boundary condition (0) = 0, where denotes the amplitude of temperature perturbations. According to the results, the conclusion in [2] that there exist two regions of complete stabilization is wrong. The asymptotic method used in [2] is analyzed here. It is shown that two regions of complete stabilization appear to exist, because the equations used in [2] had been set up for the viscous case and, therefore, are not applicable at low surface temperatures. The results of this analysis are confirmed by direct numerical integration.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 60–64, May–June, 1972.The authors thank V. Ya. Levchenko for his continued interest in this study, and A. S. Dryzhova for her valuable comments.     

The influence of the stabilization parameter on the convergence factor of iterative methods for the solution of the discretized Stokes problem

This paper discusses the influence of the stabilization parameter on the convergence factor of various iterative methods for the solution of the Stokes problem discretized by the so-called locally stabilized Q1-P0 finite element. Our objective is to point out optimal parameters which ensure rapid convergence. The first part of the paper is concerned with the dual formulation of the problem. It gives the theoretical precision and practical developments of our stabilized context Uzawa-type algorithm. We assert that the convergence factor of such a method is majored independently of the mesh size by a function of the stabilization parameter. Moreover, we point out that there exists an optimal value of this parameter that minimizes this upper bound. This gives a theoretical justification of pre-existing numerical results. We show that the optimal parameter can be determined a priori. This is a key point when the method has to be implemented. Finally, we base an interpretation of the iterated penalty method numerical behaviour on some theoretical results about the minimum eigenvalue of the stabilized dual operator. This algorithm involves a penalty parameter and a stabilization parameter and we discuss a strategy for choosing optimal parameters. The mixed formulation of the problem is dealt with in the second part of the paper, which proposes several preconditioned conjugate-gradient-type methods. The indefinite character of the problem makes it intrinsically hard. However, if one chooses a suitable preconditioner, this difficulty is overcome, since the preconditioned operator becomes positive definite. We study the eigenvalue spectrum of the preconditioned operator and thereby the convergence factor of the algorithm. In contrast with the two previous formulations, we show that this convergence factor is majored independently of the stabilization parameter. More precisely, we point out convergence factors comparable with those obtained for Poisson-type problems. Finally, we present a variant of the latter method which uses our so-called macroblock-type preconditioner. A comparison with the simple case of diagonal preconditioning is addressed and the improved performance of the macroblock-type preconditioner is evidenced. Various 2D numerical experiments are given to corroborate the theories presented herein.