Development of Metaheuristic Interval Minimization Methods for Optimal Program Control Design

2019 ◽  
Vol 80 (2) ◽  
pp. 334-347
Author(s):  
A. V. Panteleev ◽  
V. N. Panovskiy
Keyword(s):  
Control Design ◽  
Program Control ◽  
Optimal Program ◽  
Minimization Methods

Comparison of the Direct Method and the Maximum Principle in the Problem of the Aircraft Program Control Design

2019 ◽  
Vol 20 (6) ◽  
pp. 367-375
Author(s):  
O. N. Korsun ◽  
A. V. Stulovskii
Keyword(s):  
Optimal Control ◽  
Boundary Value Problem ◽  
Direct Method ◽  
Boundary Value ◽  
Control Design ◽  
Population Based ◽  
Program Control ◽  
Point Boundary ◽  
Hamilton Function

The article deals with the problem of program control design for a dynamic object defined by a nonlinear system of differential equations. Known methods of optimal control require the two-point boundary value problem solution, which in general is coupled with fundamental difficulties. Therefore, this paper proposes a technique that uses the direct method, in which the functional is minimized directly using a population-based algorithm. The use of direct methods is based on the assumption that control signals may be defined by a finite set of parameters. Then a scalar functional is formed, the numerical value of which measures the quality of the obtained solutions. In this case, the search for optimal control is reduced to the problem of single-criterion multi-parameter optimization. The practical importance of this approach is that it eliminates the need to solve a two-point boundary value problem. However, this results in another difficulty, since the approximation of control, in general, requires a large number of parameters. It is known that in this case, the effectiveness of conventional gradient numerical optimization methods decreases markedly. Therefore, it is proposed to take the next step and apply genetic or population-based optimization algorithms that have confirmed their performance in solving this class of problems. For this purpose the paper uses one of the modifications of the particle swarm algorithm. The technique is applied to a test problem describing the spatial movement of a maneuverable aircraft. The direct method is compared with two classical solutions based on the condition that the partial control derivatives of the Hamilton function are equal to zero and with the condition of Hamilton function maximum over controls (Pontryagin’s maximum principle). The presented results show the high degree of similarity between obtained controls for all considered methods of selecting the target functional. At the same time, the accuracy of classical algorithms turns out to be slightly worse, and they show a higher sensitivity to the quality of the initial approximation. Thus, the obtained results confirm the approximate equivalence of the direct method and the classical methods of program control design, at least for the class of problems under consideration. The practical significance of this research is that the use of the direct method is much simpler than solving a two-point boundary value problem necessary for classical algorithms.

FINDING OF THE OPTIMAL PROGRAM CONTROL OF THE METHOD OF VARIATIONS

2015 ◽  
Vol 2 (1) ◽  
pp. 254-257 ◽  
Author(s):  
Григорьев ◽  
I. Grigorev ◽  
Мустафина ◽  
S. Mustafina
Keyword(s):  
Optimal Control ◽  
Numerical Solution ◽  
Optimal Control Problems ◽  
Control Area ◽  
Program Control ◽  
Control Problems ◽  
Optimal Program ◽  
Basic Concepts

The article outlines the basic concepts of the numerical solution of optimal control problems based on the method of variations in the control area

AREA OF INITIAL POSITIONS OF A UAV (UNMANNED AERIAL APPARATUS) IN THREEDIMENSIONAL SPACE

2018 ◽  
pp. 24-29
Author(s):  
I. O. Makhonin
Keyword(s):  
Necessary Conditions ◽  
Auxiliary Problem ◽  
Program Control ◽  
Boundary Values ◽  
Optimal Program ◽  
The Maximum Principle ◽  
Phase Coordinates ◽  
Aerial Vehicle ◽  
The Moment ◽  
Computational Solution

When landing an unmanned aerial vehicle (UAV) on a ship, it is required to perform the specified boundary values of the state vector at the moment of approach to the hook equipment. The article considers the solution of the problem of calculating the points of the area of initial positions of UAV. It is mean, that each point provide hitting for the UAV to a predetermined aiming area at a given time in the vicinity of the hitch. In this case, the phase coordinates of the UAV at the time of approach to the hook device have to defined. To calculate the points located on the boundary of the area of initial positions, auxiliary problems of optimal program control have been solved. To solve it, the necessary conditions for the maximum principle of L. S. Pontryagin were used. The article considers the algorithm of the computational solution of the auxiliary problem of optimal program control and the results of calculating points thats located at the far boundary of the area of initial positions, that is mean, that points located at the maximum distance from the aiming point (the location of the hook device).

PENGARUH MODEL PEMBELAJARAN QUANTUM LEARNING BERNUANSA MUSIK KLASIK TERHADAP HASIL BELAJAR IPA KELAS VI DI SDN 58 DAN SDN 82 PEKANBARU

2019 ◽  
Vol 3 (4) ◽  
Author(s):  
Neni Hermita ◽  
Zufriady Zufriady
Keyword(s):  
Control Design ◽  
Quantum Learning

Penelitian ini dilatarbelakangi oleh belum optimalnya hasil belajar IPA kelas VI di SD Pekanbaru, melalui hasil wawancara langsung dengan beberapa siswa kelas VI SD, diketahui bahwa sebagian besar siswa lebih mudah belajar sambil mendengarkan audio dari pada visual, maupun kinestetik. Penelitian ini bertujuan untuk mengetahui: (1) pengaruh model pembelajaran quantum learning bernuansa musik Mozart terhadap hasil belajar IPA kelas VIb SD Negeri 82 Pekanbaru; dan (2) pengaruh model pembelajaran quantum learning bernuansa musik Beathoven terhadap hasil belajar IPA kelas VI SD Negeri 58 Pekanbaru. Penelitian ini adalah penelitian eksperimen dengan desain true-experimental, yaitu posttest only control design. Hasil penelitian menunjukkan bahwa: (1) terdapat pengaruh model pembelajaran quantum learning bernuansa musik Mozart terhadap hasil belajar IPA kelas VIb SD Negeri 82 Pekanbaru. Diketahui dari nilai nilai thitung > nilai ttabel (3,037 > 2,064). Dengan demikian, hipotesis penelitian yang berbunyi diduga terdapat pengaruh model pembelajaran quantum learning bernuansa musik Mozart terhadap hasil belajar IPA kelas VIb SD Negeri 82 Pekanbaru, diterima; dan (2) terdapat pengaruh model pembelajaran quantum learning bernuansa musik Beathoven terhadap hasil belajar IPA kelas VIa SD Negeri 58 Pekanbaru Diketahui dari nilai nilai thitung > nilai ttabel (2,834 > 2,093). Namun, setelah dibandingkan kedua hasil belajar kelompok eksperimen tersebut, diketahui tidak adanya perbedaan, karena thitung < nilai ttabel (0,509 < 2,014). Dengan demikian, hipotesis penelitian yang berbunyi diduga terdapat pengaruh model pembelajaran quantum learning bernuansa musik Beathoven terhadap hasil belajar IPA kelas VIa SD Negeri 58 Pekanbaru, diterima.

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