Optimal control of a parabolic distributed parameter system via radial basis functions |
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| Institution: | 1. Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran 19839, Iran;2. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran;3. Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran 19839, Iran;1. Dpto. Matemática Aplicada and IUMA, Universidad de Zaragoza, Pedro Cerbuna, 12, Zaragoza E-50009, Spain;2. Centro Universitario de la Defensa, Academia General Militar, Ctra. Huesca s/n, Zaragoza E-50090, Spain;1. Department of Electrical Engineering, Guilin College of Aerospace Technology, Guilin 541002, PR China;2. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541003, PR China;3. School of Mathematical Sciences, Fudan University, Shanghai 200433, PR China;1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, People’s Republic of China;2. Jiangxi University of Science and Technology, Ganzhou 341000, People’s Republic of China;3. Wuhan Center for Magnetic Resonance, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, People’s Republic of China |
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| Abstract: | This paper attempts to present a meshless method to find the optimal control of a parabolic distributed parameter system with a quadratic cost functional. The method is based on radial basis functions to approximate the solution of the optimal control problem using collocation method. In this regard, different applications of RBFs are used. To this end, the numerical solutions are obtained without any mesh generation into the domain of the problems. The proposed technique is easy to implement, efficient and yields accurate results. Numerical examples are included and a comparison is made with an existing result. |
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