Spectral Analogs of Admissible Controls for Finite Basis
Author(s):
Konstantin A. Rybakov
Moscow aviation institute (national research university),
Mathematical cybernetics department, associate professor
associate professor, candidate of physico-mathematical sciences
rkoffice@mail.ru
Abstract:
The spectral analogs of admissible scalar controls
with geometric constraints for dynamical systems are described.
The spectral analog is a set of Fourier coefficients for admissible controls.
The existing results for orthonormal functions are generalized
for biorthonormal functions. Schoenberg and Leontiev splines are used
to build these sets. Also, local polynomial splines and arbitrary
finite functions are used to build a cube as the spectral analog
of admissible scalar controls. An optimal control problem for
the two-dimensional dynamical system with constrained controls is solved.
Keywords
- biorthonormal basis
- finite functions
- geometric constraints
- optimal control
- spectral method
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