scholarly journals A Domain Decomposition Method for the Helmholtz Equation and Related Optimal Control Problems

1997 ◽  
Vol 136 (1) ◽  
pp. 68-82 ◽  
Author(s):  
Jean-David Benamou ◽  
Bruno Desprès
Keyword(s):  
Optimal Control ◽  
Helmholtz Equation ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Optimal Control Problems ◽  
Domain Decomposition Method ◽  
Control Problems

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.

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.

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