Wavelet based approximations in the optimal control of parabolic problems

作     者：Taher ABUALRUB Ibrahim SADEK Farah EL NACHAR 

作者机构：Department of Mathematics and Statistics American University of Sharjah 

出 版 物：《控制理论与应用（英文版）》 (Journal of Control Theory and Applications)

年 卷 期：2013年第11卷第1期

页      面：103-107页

核心收录：

学科分类：0711[理学-系统科学] 0808[工学-电气工程] 07[理学] 08[工学] 0802[工学-机械工程] 0835[工学-软件工程] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 071102[理学-系统分析与集成] 081103[工学-系统工程] 

主　　题：Bilinear system Parabolic equation Optimal control CAS wavelets 

摘      要：We consider optimal control of a bilinear parabolic equation. The determination of such control requires to minimize a given energy performance measure. The performance measure of the system is taken as a combination of its modified total energy and the penalty term describing the approach used in the control process. Using an appropriate transformation modal expansion, the optimal control of a distributed parameter system （DPS） is simplified into the optimal control of a bilinear time-varying lumped parameter system （LPS）. A computational efficient formulation to evaluate the optimal trajectory and control of the system is determined. It is based on the parametrization of the state and control variables by using finite wavelets. Numerical examples are provided to demonstrate the applicability and the efficiency of the proposed method and the results are quite satisfactory.