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

• Published in: Journal of applied and computational mechanics Vol. 7; no. 2; pp. 970 - 976
• Main Authors: Fikret Aliev, Nihan Aliev, Nargiz Safarova, Yegana Mamedova
• Format: Journal Article
• Language: English
• Published: Shahid Chamran University of Ahvaz 01-03-2021
• Subjects: analytical construction of controllers; euler-lagrange equation; fractional derivative; fundamental matrix; hamiltonian matrix; mittag-leffler function
• ISSN: 2383-4536; 2383-4536
• DOI: 10.22055/jacm.2021.35130.2572

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.