Generalized Lagrange Function and Generalized Weak Saddle Points for a Class of Multiobjective Fractional Optimal Control Problems

2012 ◽  
Vol 154 (2) ◽  
pp. 370-381 ◽  
Author(s):  
Haijun Liu ◽  
Neng Fan ◽  
Panos M. Pardalos
2017 ◽  
Vol 40 (6) ◽  
pp. 2054-2061 ◽  
Author(s):  
Ali Alizadeh ◽  
Sohrab Effati

In this study, we use the modified Adomian decomposition method to solve a class of fractional optimal control problems. The performance index of a fractional optimal control problem is considered as a function of both the state and the control variables, and the dynamical system is expressed in terms of a Caputo type fractional derivative. Some properties of fractional derivatives and integrals are used to obtain Euler–Lagrange equations for a linear tracking fractional control problem and then, the modified Adomian decomposition method is used to solve the resulting fractional differential equations. This technique rapidly provides convergent successive approximations of the exact solution to a linear tracking fractional optimal control problem. We compare the proposed technique with some numerical methods to demonstrate the accuracy and efficiency of the modified Adomian decomposition method by examining several illustrative test problems.


2019 ◽  
Vol 25 (15) ◽  
pp. 2143-2150 ◽  
Author(s):  
M Abdelhakem ◽  
H Moussa ◽  
D Baleanu ◽  
M El-Kady

Two schemes to find approximated solutions of optimal control problems of fractional order (FOCPs) are investigated. Integration and differentiation matrices were used in these schemes. These schemes used Chebyshev polynomials in the shifted case as a functional approximation. The target of the presented schemes is to convert such problems to optimization problems (OPs). Numerical examples are included, showing the strength of the schemes.


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