scholarly journals SOLUTION OF INFINITE HORIZON NONLINEAR OPTIMAL CONTROL PROBLEMS BY PIECEWISE ADOMIAN DECOMPOSITION METHOD

2013 ◽  
Vol 18 (4) ◽  
pp. 543-560 ◽  
Author(s):  
Hassan Saberi Nik ◽  
Paulo Rebelo ◽  
Moosarreza Shamsyeh Zahedi
Keyword(s):  
Optimal Control ◽  
Decomposition Method ◽  
Optimal Control Problems ◽  
Infinite Horizon ◽  
Adomian Decomposition Method ◽  
Nonlinear Optimal Control ◽  
Suboptimal Control ◽  
Control Problems ◽  
Time Step ◽  
Adomian Decomposition

In this paper, a Piecewise Adomian Decomposition Method (PADM) is used to obtain the analytical approximate solution for a class of infinite horizon nonlinear optimal control problems (OCPs). The method is a new modification of the standard ADM, in which it is treated as an algorithm in a sequence of small intervals (i.e. with small time step) for finding accurate approximate solutions to the corresponding OCPs. Applying the PADM, the nonlinear two-point boundary value problem (TPBVP), derived from the application of Pontryagin's maximum principle (PMP), is transformed into a sequence of linear time-invariant TPBVP's. Through the finite iterations of algorithm, a suboptimal control law is obtained for the nonlinear optimal control problem. Comparing the methodology with some known techniques shows that the present approach is powerful and reliable. It is remarkable accuracy properties are finally demonstrated by two examples.

Modified Adomian decomposition method for solving fractional optimal control problems

2017 ◽  
Vol 40 (6) ◽  
pp. 2054-2061 ◽  
Author(s):  
Ali Alizadeh ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Decomposition Method ◽  
Optimal Control Problems ◽  
Adomian Decomposition Method ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Fractional Optimal Control Problems

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.

Numerical Schemes for Fractional Optimal Control Problems

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Ali Alizadeh ◽  
Sohrab Effati ◽  
Aghileh Heydari
Keyword(s):  
Optimal Control ◽  
Decomposition Method ◽  
Optimal Control Problems ◽  
Adomian Decomposition Method ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Variational Iteration ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Fractional Optimal Control Problems

In the present study, variational iteration and Adomian decomposition methods (ADMs) are applied for solving a class of fractional optimal control problems (FOCPs). Also, a comparative study between these two methods is presented. The fractional derivative (FD) in these problems is in the Caputo sense. To solve the problem, first the necessary optimality conditions of FOCP are achieved for a linear tracking fractional optimal control problem, and then, these two methods are used to solve the resulting fractional differential equations (FDEs). It is shown that the modified Adomian decomposition method and variational iteration method (VIM) use the same iterative formula for solving linear and nonlinear FOCPs. The convergence of the modified Adomian decomposition method is analytically studied and to illustrate the validity and applicability of the methods, some examples are provided.

scholarly journals Approximated Solutions of Linear Quadratic Fractional Optimal Control Problems

2016 ◽  
Vol 12 (2) ◽  
pp. 83-94
Author(s):  
S. Soradi Zeid ◽  
M. Yousefi ◽  
M. Yousefi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Adomian Decomposition Method ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Linear Quadratic ◽  
Fractional Optimal Control ◽  
Adomian Decomposition ◽  
Fractional Optimal Control Problems ◽  
The Cost

Abstract In this study we apply the Adomian decomposition method (ADM) to approximate the solution of fractional optimal control problems (FOCPs) where the dynamic of system is a linear control system with constant coefficient and the cost functional is defined in a quadratic form. First we stated the necessary optimality conditions in a form of fractional two point boundary value problem (TPBVP), then the ADM is used to solve the resulting fractional differential equations (FDEs). Some examples are provided to demonstrate the validity and applicability of the proposed method.

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