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Using B‐spline functions (BSFs) of various degrees to obtain a powerful method for numerical solution for a special class of optimal control problems (OCPs)
Author(s) -
Kafash Behzad,
Alavizadeh Seyed Rouhollah
Publication year - 2019
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2687
Subject(s) - convergence (economics) , spline (mechanical) , state variable , state (computer science) , reliability (semiconductor) , mathematical optimization , variable (mathematics) , control variable , control theory (sociology) , mathematics , class (philosophy) , series (stratigraphy) , optimal control , optimization problem , control (management) , computer science , engineering , algorithm , mathematical analysis , paleontology , power (physics) , statistics , physics , structural engineering , quantum mechanics , artificial intelligence , economics , thermodynamics , economic growth , biology
In this paper, the optimal control problems (OCPs) are converted into a constrained optimization problem based on state parameterization via the B‐spline functions (BSFs). In fact, the state variable can be considered as a series of the BSFs with unknown coefficients, and the OCPs are transformed into a constrained optimization problem. With the proposed method, the control and state variables also the performance index can be obtained approximately. Also, the convergence theorem of the presented approach is proved in details, some illustrative examples are reported. Also, an example, which has analytic noncontinuous state and control variable, is presented to show the efficiency and reliability of the purposed method, compared with other existing methods.