Solution of the Problem of Analytical Construction of Optimal ‎Regulators for a Fractional Order Oscillatory System in the ‎General Case

• Main Authors: Fikret Aliev, Nihan Aliev, Nargiz Safarova, Yegana Mamedova
• Format: Article
• Language: English
• Published: Shahid Chamran University of Ahvaz 2021-04-01
• Series: Journal of Applied and Computational Mechanics
• Subjects: fractional derivative; analytical construction of controllers; hamiltonian matrix; fundamental matrix; mittag-leffler function; ‎euler-lagrange equation‎
• Online Access: https://jacm.scu.ac.ir/article_16462_7b8d482401be8a8a0685cd87afcbbc01.pdf
• ISSN: 2383-4536; 2383-4536

An algorithm is proposed for solving the problem of analytical constructing of an optimal fractional-order regulator (OFOR) in the general case. By inscribing the extended functional, the corresponding fractional order Euler-Lagrange equation is determined. Then, using the Mittag-Leffler function, a fundamental solution to the corresponding Hamiltonian system is constructed. It is shown that to obtain an analogue of the analytical construction of AM Letov's regulators, the order of the fractional derivatives must be a rational number, the denominator and numerator of which are odd numbers. Numerical illustrative examples are provided.