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Article information
2015 , Volume 20, ¹ 3, p.58-74
Rybakov K.A.
Construction of admissible controls in spectral form of mathematical description
One of the methods for solution of problems arising in the control theory is the spectral method based on the representation of functions by orthogonal series (spectral form of the mathematical description). Its main advantage is that we can do all computations only with series coefficients. Thus, a problem that can be described, for example, by differential or integral equations is reduced to the solution of algebraic equations. In the spectral form of the mathematical description the functions are represented by column matrices, linear operators are represented by square matrices, and linear functionals are represented by row matrices. They are called the spectral characteristics of functions, the spectral characteristics of operators, and the spectral characteristics of linear functionals, respectively. Constraints on admissible controls are introduced for problems on the most optimal control. It is advisable to construct an analogue for the set of admissible controls as a set of respective spectral characteristics. In this case the admissibility check of the controls is simpler. This paper proposes a general method for constructing the set of admissible controls when the mathematical description is represented in the spectral form. This method prevents a typical transition from the spectral characteristics to the functions defined by them. We consider geometric constraints for admissible controls. The proposed method can be used in direct methods for optimization of dynamic systems. Some examples for the set of admissible controls in spectral form of mathematical description are given for Legendre polynomials and trigonometric functions. An exact description for the set of admissible controls and an example of finding the optimal control for second order dynamical system are given for Walsh functions.
[full text]
Keywords: admissible controls, spectral characteristic, spectral method
Author(s):
Rybakov Konstantin Alexandrovich
PhD. , Associate Professor
Position: Associate Professor
Office: Moscow Aviation Institute
Address: 125993, Russia, Moscow, GSP-3, A-80, Volokolamskoe shosse, 4
Phone Office: (499) 158-48-11
E-mail: rkoffice@mail.ru
SPIN-code: 2215-1921 References:
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Bibliography link:
Rybakov K.A. Construction of admissible controls in spectral form of mathematical description // Computational technologies. 2015. V. 20. ¹ 3. P. 58-74
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