| 11. |
- Berbyuk, Viktor, 1953, et al.
(författare)
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Mathematical design of gantry robots for automating assembly processes
- 1989
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Ingår i: Soviet journal of computer and systems sciences. - 0882-4002. ; 27:2, s. 1-8
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Tidskriftsartikel (refereegranskat)abstract
- A methodology for an automatic selection of the structural schema and the parameters of an assembly robot based on an optimization procedure is described. A finite collection of so-called test positions for the operating element which are determined by the robot purpose and by its characteristic movements is specified. The dynamic, strength, etc. characteristics are computed at these test positions for each structural schema and the constraints for the optimization problem are formulated. The procedure for selecting the structural schema of the robot and its technical parameters consists of minimizing some functional for the indicated constraints. An example of computing the parameters of a gantry robot is given.
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| 12. |
- Berbyuk, Viktor, 1953
(författare)
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On the controlled rotation of a system of two rigid bodies with elastic elements
- 1984
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Ingår i: Journal of Applied Mathematics and Mechanics, Elsevier Science Ltd.. - : Elsevier BV. - 0021-8928. ; 48:2, s. 164-170
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Tidskriftsartikel (refereegranskat)abstract
- The problem of controlling the plane rotational motions of two rigid bodies connected by an elastic rod is studied. One end of the rod is attached to the support by a hinge with a spring, the latter modelling the elastic compliance of the fastening, and the other end is rigidly joined to the load. The Hamilton principle is used to obtain the integrodifferential equations and boundary conditions describing the motion of the system support — spring — rod — load. The following problem is posed: it is required to rotate the system by a given angle by means of the controlling force moment, with quenching of the relative oscillations of the load elements which appear as a result of the deformability of the rod and of the elastic torsion of the spring. Similar problem arise in the study of the dynamics and control of the motion of devices used in transporting loads through space (robots, manipulators, load lifting machines, etc.). In computing their control modes a significant part is played not only by the deformability of the elements, but also by the elastic compliance of the connecting joints. Asymptotic methods are used to botain a solution of the control problem in question for two limiting cases: 1) the mass of the load carried is much greater than the mass of the rod and support, and 2) the rod has high flexural rigidity.
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| 13. |
- Berbyuk, Viktor, 1953
(författare)
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The use of first integrals in problems of synthesizing optimal control systems
- 1986
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Ingår i: Journal of Applied Mathematics and Mechanics (English translation of Prikladnaya Matematika i Mekhanika). - 0021-8928. ; 50:1, s. 11-16
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Tidskriftsartikel (refereegranskat)abstract
- The problem of synthesizing optimal control of the motion of a non-linear unsteady system is considered. The control quality is evaluated by a functional of mixed type (a Boltz functional). A method of synthesizing optimal control systems is worked out for systems of variational problems with a fixed time and a free right end, based on the use of first integrals of the equations of a free uncontrolled object. The effectiveness of the proposed method is illustrated by examples.
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| 14. |
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| 15. |
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| 16. |
- Burdakov, Oleg, 1953-
(författare)
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Conjugate direction methods for solving systems of equations and finding saddle points. Part 1
- 1982
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Ingår i: Engineering Cybernetics. - 0013-788X. ; 20:3, s. 13-19
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Tidskriftsartikel (refereegranskat)abstract
- This article is devoted to the development of methods of pseudo-orthogonal directions for solving systems of nonlinear equations in which the mapping is uniformly monotonic. Rapidly convergent methods that do not involve evaluation of derivatives are constructed. They constitute a generalization of such methods of unconditional minimization as the method of parallel displacements, Zangwill's method, and Powell's method. The methods developed can be applied, in particular, to finding saddle points of uniformly convex-concave functions.
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| 17. |
- Burdakov, Oleg, 1953-
(författare)
-
Conjugate direction methods for solving systems of equations and finding saddle points. Part 2
- 1982
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Ingår i: Engineering Cybernetics. - 0013-788X. ; 20:4, s. 23-31
-
Tidskriftsartikel (refereegranskat)abstract
- This article is the second part of a paper devoted to the development of methods of pseudo-orthogonal directions for solving systems of nonlinear equations (for part I see Eng. Cybern. 1982, Vol. 20, No. 3, p. 13-19). An approach is developed for studying the reate of convergence of such methods. Local quadratic convergence of the proposed methods to the solution of the system of equations is proven. This implies the quadratic convergence of some methods of unconstrained minimization: the method of parallel displacements, Zangull's method, and Powell's method.
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| 18. |
- Burdakov, Oleg, 1953-
(författare)
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Methods of the secant type for systems of equations with symmetric Jacobian matrix
- 1983
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Ingår i: Numerical Functional Analysis and Optimization. - : Taylor & Francis. - 0163-0563 .- 1532-2467. ; 6:2, s. 183-195
-
Tidskriftsartikel (refereegranskat)abstract
- Symmetric methods (SS methods) of the secant type are proposed for systems of equations with symmetric Jacobian matrix. The SSI and SS2 methods generate sequences of symmetric matrices J and H which approximate the Jacobian matrix and inverse one, respectively. Rank-two quasi-Newton formulas for updating J and H are derived. The structure of the approximations J and H is better than the structure of the corresponding approximations in the traditional secant method because the SS methods take into account symmetry of the Jacobian matrix. Furthermore, the new methods retain the main properties of the traditional secant method, namely, J and H-1are consistent approximations to the Jacobian matrix; the SS methods converge superlinearly; the sequential (n + 1)-point SS methods have the R-order at least equal to the positive root of tn+1-tn-1=0.
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| 19. |
- Burdakov, Oleg, 1953-
(författare)
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On Superlinear Convergence of Some Stable Variants of the Secant Method
- 1986
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Ingår i: Zeitschrift für angewandte Mathematik und Mechanik. - : Wiley. - 0044-2267 .- 1521-4001. ; 66:2, s. 615-622
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Tidskriftsartikel (refereegranskat)abstract
- In a recent author's paper four classes of methods of the secant type for solving systems of nonlinear equations were proposed. They are stable with respect to linear dependence of the search directions. If the Jacobian matrix is symmetric, then two of them take into account this property. It is proved here that some four special methods from the classes converge superlinearly.
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| 20. |
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