Karimi, H. R.; Jabedar Maralani, P.; Moshiri, B.; Lohmann, B. Numerically efficient approximations to the optimal control of linear singularly perturbed systems based on Haar wavelets. (English) Zbl 1070.65052 Int. J. Comput. Math. 82, No. 4, 495-507 (2005). Summary: We present an implementation of the Haar wavelet to the optimal control of linear singularly perturbed systems. The approximated composite control and the slow and fast trajectories with respect to a quadratic cost function are calculated by solving only the linear algebraic equations. The results are illustrated by a simple example. Cited in 16 Documents MSC: 65K10 Numerical optimization and variational techniques 49J15 Existence theories for optimal control problems involving ordinary differential equations 65T60 Numerical methods for wavelets 49M15 Newton-type methods Keywords:numerical example; singular perturbation; Haar wavelet; optimal control PDFBibTeX XMLCite \textit{H. R. Karimi} et al., Int. J. Comput. Math. 82, No. 4, 495--507 (2005; Zbl 1070.65052) Full Text: DOI References: [1] DOI: 10.1080/00207727508941868 · Zbl 0311.93015 · doi:10.1080/00207727508941868 [2] DOI: 10.1007/BFb0041228 · doi:10.1007/BFb0041228 [3] Krueger K, Automatisierungstechnik 38 pp 343– (1990) [4] DOI: 10.1109/TAC.1979.1102023 · Zbl 0399.49002 · doi:10.1109/TAC.1979.1102023 [5] Hwang C, Int. J. Control 34 pp 557– (1981) [6] DOI: 10.1080/00207178408933269 · Zbl 0539.93028 · doi:10.1080/00207178408933269 [7] Burrus CS, Introduction to Wavelets and Wavelet Transforms (1998) [8] DOI: 10.1109/TCS.1986.1086019 · Zbl 0613.65072 · doi:10.1109/TCS.1986.1086019 [9] DOI: 10.1080/00207160211932 · Zbl 0995.65145 · doi:10.1080/00207160211932 [10] Xie Xin, Arizona State University (2002) [11] DOI: 10.1080/03057920412331272225 · Zbl 1068.65088 · doi:10.1080/03057920412331272225 [12] Kokotovic PV, Singular Perturbation Methods in Control: Analysis Design (1986) [13] DOI: 10.1016/0005-1098(84)90044-X · Zbl 0532.93002 · doi:10.1016/0005-1098(84)90044-X [14] DOI: 10.1007/BF01456326 · JFM 41.0469.03 · doi:10.1007/BF01456326 [15] DOI: 10.1109/81.828579 · doi:10.1109/81.828579 [16] DOI: 10.1049/ip-cta:19970702 · Zbl 0880.93014 · doi:10.1049/ip-cta:19970702 [17] DOI: 10.1080/00207160410001712323 · Zbl 1059.65058 · doi:10.1080/00207160410001712323 [18] Athans M, Optimal Control (1966) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.