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Solving Fixed Final Time Fractional Optimal Control Problems Using the Parametric Optimization Method
Author(s) -
Idiri Ghania,
Djennoune Saïd,
Bettayeb Maamar
Publication year - 2016
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1247
Subject(s) - parameterized complexity , optimal control , mathematics , fractional calculus , nonlinear system , mathematical optimization , optimization problem , parametric statistics , control variable , state variable , expression (computer science) , control theory (sociology) , control (management) , computer science , algorithm , statistics , physics , quantum mechanics , artificial intelligence , thermodynamics , programming language
In this paper, the parametric optimization method is used to find optimal control laws for fractional systems. The proposed approach is based on the use for the fractional variational iteration method to convert the original optimal control problem into a nonlinear optimization one. The control variable is parameterized by unknown parameters to be determined, then its expression is substituted into the system state‐space model. The resulting fractional ordinary differential equations are solved by the fractional variational iteration method, which provides an approximate analytical expression of the closed‐form solution of the state equations. This solution is a function of time and the unknown parameters of the control law. By substituting this solution into the performance index, the original fractional optimal control problem reduces to a nonlinear optimization problem where the unknown parameters, introduced in the parameterization procedure, are the optimization variables. To solve the nonlinear optimization problem and find the optimal values of the control parameters, the Alienor global optimization method is used to achieve the global optimal values of the control law parameters. The proposed approach is illustrated by two application examples taken from the literature.