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

Received: 2 February 2015/Accepted: 18 August 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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*Corresponding author; email: waleeda_um@yahoo.com

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