{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T12:42:45Z","timestamp":1784032965713,"version":"3.55.0"},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2010,1,6]],"date-time":"2010-01-06T00:00:00Z","timestamp":1262736000000},"content-version":"vor","delay-in-days":370,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>This paper considers the problem of controlling the solution of an initial boundary\u2010value problem for a wave equation with time\u2010dependent sound speed. The control problem is to determine the optimal sound speed function which damps the vibration of the system by minimizing a given energy performance measure. The minimization of the energy performance measure over sound speed is subjected to the equation of motion of the system with imposed initial and boundary conditions. Using the modal space technique, the optimal control of distributed parameter systems is simplified into the optimal control of bilinear time\u2010invariant lumped\u2010parameter systems. A wavelet\u2010based method for evaluating the modal optimal control and trajectory of the bilinear system is proposed. The method employs finite CAS wavelets to approximate modal control and state variables. Numerical examples are presented to demonstrate the effectiveness of the method in reducing the energy of the system.<\/jats:p>","DOI":"10.1155\/2009\/636271","type":"journal-article","created":{"date-parts":[[2010,1,6]],"date-time":"2010-01-06T15:30:54Z","timestamp":1262791854000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Optimal Control Systems by Time\u2010Dependent Coefficients Using CAS Wavelets"],"prefix":"10.1155","volume":"2009","author":[{"given":"Taher","family":"Abualrub","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ibrahim","family":"Sadek","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marwan","family":"Abukhaled","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2010,1,6]]},"reference":[{"key":"e_1_2_8_1_2","series-title":"Series on Advances in Mathematics for Applied Sciences","doi-asserted-by":"crossref","DOI":"10.1142\/3439","volume-title":"Homogenization","author":"Berdichersky V.","year":"1999"},{"key":"e_1_2_8_2_2","series-title":"Series on Advances in Mathematics for Applied Sciences","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1142\/9789812812919_0011","volume-title":"Homogenization","author":"Lurie K. 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