Controlled Process of Crystallization in Weld Pool

2021 ◽  
Vol 1037 ◽  
pp. 258-263
Author(s):  
Valery Melyukov ◽  
Evgeny A. Marinin
Keyword(s):  
Optimal Control ◽  
Weld Pool ◽  
Optimal Control Problems ◽  
Continuous Functions ◽  
Smooth Functions ◽  
Piecewise Constant ◽  
Rear Part ◽  
Piecewise Continuous ◽  
Submerged Arc ◽  
Electron Beam Plasma

In this report the problem of control of solidification crack formation in welded plates is considered. In this problem the welding source is determined in dependence on the preset configuration and curvature of the rear part weld pool. A double ellipsoid model of weld pool with preset semi-axes may be used for the first approximation of preset weld pool configuration. It is an inverse problem which may be more efficiently solved as optimal control problem. The Function of welding source as a controlling function obtained in the result of solution is determined in a class of piecewise continuous functions which is more common class and the continuous-smooth functions are special partial case of common class. Recent methods of optimal control which use for solution of optimal control problems require to present the controlling functions in class of piecewise constant functions. Laser influence, electron beam, plasma, arc and submerged arc are the welding sources with high concentrated energy. A mathematical models of these welding sources may be introduced in class of piecewise continuous function with an efficient accuracy.

Computation of Approximately Optimal Control Signals for Systems With Time Delays

1974 ◽  
Vol 96 (3) ◽  
pp. 269-276
Author(s):  
L. B. Horwitz
Keyword(s):  
Optimal Control ◽  
Time Delays ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Control Signal ◽  
Control Problems ◽  
Piecewise Constant ◽  
Switching Times ◽  
Control Signals ◽  
Approximate Nature

A computational algorithm is presented for a class of optimal control problems involving time delays. The approach is to restrict the control signal to a class of piecewise constant time functions with a prescribed number of switching times, compute the optimal member of this class, and then repeat with a larger number of switching times. By allowing the number of switching times to increase beyond bound a sequence of restricted optimal control signals is developed whose limit approaches the unrestricted optimal control signal. In practice the computations are terminated after a finite number of repeats, thus leading to the approximate nature of the solution. The results of two examples are included to illustrate the technique.

scholarly journals Sufficiency for Purely Essentially Bounded Optimal Controls

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 238
Author(s):  
Gerardo Sánchez Licea
Keyword(s):  
Nonlinear Dynamics ◽  
Optimal Control ◽  
Optimal Control Problems ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Optimal Controls ◽  
Embedding Theorems ◽  
State Control ◽  
Discontinuous Solutions ◽  
Piecewise Continuous

For optimal control problems of Bolza with variable and free end-points, nonlinear dynamics, nonlinear isoperimetric inequality and equality restrictions, and nonlinear pointwise mixed time-state-control inequality and equality constraints, sufficient conditions for strong minima are derived. The algorithm used to prove the main theorem of the paper includes a crucial symmetric inequality, making this technique an independent self-contained method of classical concepts such as embedding theorems from ordinary differential equations, Mayer fields, Riccati equations, or Hamilton–Jacobi theory. Moreover, the sufficiency theory given in this article is able to detect discontinuous solutions, that is, solutions which need to be neither continuous nor piecewise continuous but only essentially bounded.

scholarly journals On solving optimal control problems by means of splines

1987 ◽  
pp. 10
Author(s):  
V.V. Gusar ◽  
A.A. Ligun
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Piecewise Smooth ◽  
Control Problems ◽  
Smooth Functions ◽  
Piecewise Smooth Functions ◽  
Automatic Search ◽  
Points Of Discontinuity

We consider spline-methods of solving problems, in which piecewise-smooth functions can be the sought solution. We provide and ground the algorithm of approximation of piecewise-smooth functions by splines with automatic search for points of discontinuity of the function and its derivatives. On the base of this algorithm, we describe methods to determine the spline-solution for some optimal control problems.

scholarly journals Numerical solution to optimal control problems of oscillatory processes

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kamil Aida-Zade ◽  
Jamila Asadova
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Dissipation Factor ◽  
Numerical Approach ◽  
Resistance Coefficient ◽  
Continuous Functions ◽  
Control Problems ◽  
Control Actions ◽  
Analytical Formulas ◽  
Oscillatory Processes

<p style='text-indent:20px;'>A numerical approach to the investigation of optimal control problems of oscillatory processes with boundary and intermediate concentrated (lumped) control actions has been proposed in this paper. The corresponding analytical formulas for the components of the target functional gradient with respect to control actions considered on the class of piecewise continuous functions are obtained. The results of numerical experiments on the examples of solving model problems of optimal control of oscillatory processes with boundary and intermediate concentrated controls are provided. These results illustrate the dependence of the minimum settling time of oscillatory processes on the number and locations of concentrated control actions, on the process parameters, on the resistance coefficient of the medium (dissipation factor), and other factors.</p>

scholarly journals The control parameterization enhancing transform for constrained optimal control problems

1999 ◽  
Vol 40 (3) ◽  
pp. 314-335 ◽  
Author(s):  
K. L. Teo ◽  
L. S. Jennings ◽  
H. W. J. Lee ◽  
V. Rehbock
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Piecewise Linear ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Piecewise Constant ◽  
Control Parameterization ◽  
Switching Times ◽  
Control Functions ◽  
Decision Variables

AbstractConsider a general class of constrained optimal control problems in canonical form. Using the classical control parameterization technique, the time (planning) horizon is partitioned into several subintervals. The control functions are approximated by piecewise constant or piecewise linear functions with pre-fixed switching times. However, if the optimal control functions to be obtained are piecewise continuous, the accuracy of this approximation process greatly depends on how fine the partition is. On the other hand, the performance of any optimization algorithm used is limited by the number of decision variables of the problem. Thus, the time horizon cannot be partitioned into arbitrarily many subintervals to reach the desired accuracy. To overcome this difficulty, the switching points should also be taken as decision variables. This is the main motivation of the paper. A novel transform, to be referred to as the control parameterization enhancing transform, is introduced to convert approximate optimal control problems with variable switching times into equivalent standard optimal control problems involving piecewise constant or piecewise linear control functions with pre-fixed switching times. The transformed problems are essentially optimal parameter selection problems and hence are solvable by various existing algorithms. For illustration, two non-trivial numerical examples are solved using the proposed method.

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