Research on nature-inspired metaheuristics for optimal control of
fractional differential equation
Abstract
This study offers a general formulation for a class of fractional
optimal control problems (FOCPs) where the performance index is
expressed as a function of both control and state variables and the
dynamic control system depends on Caputo fractional derivatives. The
operational matrices of fractional Riemann-Liouville integration for
Bernoulli polynomials and properties of Bernoulli polynomials are
utilized to reduce the given optimization problems to the nonlinear
programming problem (NLP) by solving of which we can approximate the
optimal solution of FOCP. By implementing three metaheuristic approaches
called multi-verse optimizer (MVO), moth-flame optimization (MFO), and
whale optimization algorithm (WOA), the NLP is solved and the best
approximation solution of FOCP is obtained. A survey on the superiority
and the efficiency between these methods are considered by applying
three numerical examples. Comprehensive analysis reveals that the MFO
considerably solves these examples. Moreover, the profits and advantages
of preference with its precision are demonstrated numerically.
Simulation results obviously show that the objective functional value
obtained by MFO effectively decreased on three illustrative examples in
comparison with MVO and WOA.