fractional optimal control of systems using Bernoulli wavelets

Abstract

In order to provide a new method for partial optimal control of systems, this work uses Bernoulli wavelets and uses Caputo's formula to solve partial optimal control problems (FOCPs) with inequality constraints. For the new optimization technique, the work uses partial order Bernoulli wave functions (F-BWFs) as basic functions. The answer using this method is expressed in terms of F-BWF where the coefficients have not yet been found. To simplify FOCPs in a system of nonlinear algebraic equations the procedure entails transforming inequality constraints into equality requirements by using operational matrices of fractional integration and F-BWFs and using the multipliers technique Lagrange. Numerical examples confirm the validity of the proposed strategy and demonstrate its correctness and efficiency when compared to the analytical or approximate answers provided by other methods.