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Sains Malaysiana 45(2)(2016): 305–313
Haar Wavelet Method for Constrained Nonlinear Optimal Control Problems with Application to Production Inventory Model (Kaedah Gelombang Kecil Haar untuk Masalah Kawalan Optimum
Kekangan tak Linear dengan Model Aplikasi untuk Inventori Pengeluaran)
Waleeda Swaidan12* & Amran Hussin1 1Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia 2Division of Basic Science, Faculty of Agriculture, University of Baghdad Diserahkan: 2 Februari 2015/Diterima:
18 Ogos 2015
ABSTRACT
A new numerical method was proposed in this paper
to address the nonlinear quadratic optimal control problems, with
state and control inequality constraints. This method used the quasilinearization
technique and Haar wavelet operational matrix to convert the nonlinear
optimal control problem into a sequence of quadratic programming
problems. The inequality constraints for trajectory variables were
transformed into quadratic programming constraints using the Haar
wavelet collocation method. The proposed method was applied to optimize
the control of the multi-item inventory model with linear demand
rates. By enhancing the resolution of the Haar wavelet, we can improve
the accuracy of the states, controls and cost. Simulation results
were also compared with other researchers' work. Keywords: Direct method; Haar wavelet
operational matrix; optimal control; quadratic programming problem
ABSTRAK
Kaedah berangka baru telah dicadangkan dalam
kertas ini untuk menangani masalah kawalan optimum quadratik tak linear dengan
kekangan keadaan serta kawalan ketidaksamaan. Kaedah ini menggunakan teknik
quasipelinearan dan matriks operasi gelombang kecil Haar untuk menukar masalah
kawalan optimum tak linear kepada suatu turutan masalah pengaturcaraan
quadratik. Kekangan ketidaksamaan bagi pemboleh ubah trajektori diubah menjadi
kekangan pengaturcaraan quadratik menggunakan kaedah kolokasi gelombang kecil
Haar. Kaedah cadangan telah digunakan untuk mengoptimumkan kawalan model
inventori item berbilang dengan kadar permintaan linear. Dengan
mempertingkatkan resolusi gelombang kecil Haar, ketepatan keadaan, kawalan
serta kos boleh ditambah baik. Keputusan simulasi juga dibandingkan dengan
hasil penyelidikan lain.
Kata kunci: Kawalan optimum; kaedah langsung; masalah
pengaturcaraan quadratik; matriks operasi gelombang kecil Haar
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*Pengarang untuk surat-menyurat; email: waleeda_um@yahoo.com
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