New adapted spectral method for solving stochastic optimal control problem
- سال انتشار: 1403
- محل انتشار: مجله آنالیز غیر خطی و کاربردها، دوره: 15، شماره: 11
- کد COI اختصاصی: JR_IJNAA-15-11_001
- زبان مقاله: انگلیسی
- تعداد مشاهده: 147
نویسندگان
Mathematical Analysis and Applications Laboratory, Departement of Mathematics, Faculty of Mathematics and Informatics, Mohamed El Bachir El Ibrahimi university of Bordj Bou Arreridj, El Anasser, ۳۴۰۳۰, Algeria
Mathematical Analysis and Applications Laboratory, Departement of Mathematics, Faculty of Mathematics and Informatics, Mohamed El Bachir El Ibrahimi university of Bordj Bou Arreridj, El Anasser, ۳۴۰۳۰, Algeria
چکیده
Optimal control theory is a branch of mathematics. It is developed to find optimal ways to control a dynamic system. In ۱۹۵۷, R.Bellman applied dynamic programming to solve optimal control of discrete-time systems. His procedure resulted in closed-loop, generally nonlinear, and feedback schemes. Optimal control problems which will be tackled involve the minimization of a cost function subject to constraints on the state vector and the control. Lagrange multipliers provide a method of converting a constrained minimization problem into an unconstrained minimization problem of higher order. The necessary condition for optimality can be obtained as the solution of the unconstrained optimization problem of the Lagrange function and the bordered Hessian matrix is used for the second-derivative test. A spectral method for solving optimal control problems is presented. The method is based on Bernoulli polynomials approximation. By using the Bernoulli operational matrix of integration and the Lagrangian function, stochastic optimal control is transformed into an optimisation problem, where the unknown Bernoulli coefficients are determined by using Newton's iterative method. The convergence analysis of the proposed method is given. The simulation results based on the Monte-Carlo technique prove the performance of the proposed method. Some error estimations are provided and illustrative examples are also included to demonstrate the efficiency and applicability of the proposed method.کلیدواژه ها
Bernoulli polynomial, Open loop, feedback, Optimal control problem, Operational matrix, Brownian motionاطلاعات بیشتر در مورد COI
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