Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation

Toyoğlu, Fatma; Yagubov, Gabil

doi:10.11648/j.acm.20150402.11

Cited by 3 publications

(1 citation statement)

References 10 publications

(8 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 Therefore, finding the optimal solution for these systems is interesting to many researchers. [2][3][4][5][6][7][8][9][10] Although the optimal control problem for linear systems without delays was solved in the 1960s, 11 the optimal control problem for linear systems with delays is still open, depending on the delay type, specific system equation, criterion, etc. 12 Kharatishvili extended the Pontryagin maximum principle to time-delay systems and obtained conditions for optimality.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of linear time‐delay systems by a hybrid of block‐pulse functions and biorthogonal cubic Hermite spline multiwavelets

Mohammadzadeh

Lakestani

2017

Optim Control Appl Methods

View full text Add to dashboard Cite

SummaryThis paper proposes a new numerical approach for finding the solution of linear time-delay control systems with a quadratic performance index using new hybrid functions. This method is based on a hybrid of block-pulse functions and biorthogonal multiwavelets that consist of cubic Hermite splines on the primal side. The excellent properties of the hybrid functions together with the operational matrices of integration, product, and delay are presented. Using these matrices, the solution of the optimal control of delay systems is reduced to the solution of algebraic equations. Because of the sparsity nature of these matrices, this method is computationally very attractive and reduces CPU time and computer memory. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. The effectiveness of the method and the accuracy of the solution are shown in comparison with some other methods by illustrative examples.

show abstract