Generalized B-spline functions method for solving optimal control problems
نویسندگان
چکیده
In this paper we introduce a numerical approach that solves optimal control problems (OCPs) using collocation methods. This approach is based upon B-spline functions. The derivative matrices between any two families of B-spline functions are utilized to reduce the solution of OCPs to the solution of nonlinear optimization problems. Numerical experiments confirm our theoretical findings.
منابع مشابه
Generalized B-spline functions method for solving optimal control problems
In this paper we introduce a numerical approach that solves optimal control problems (OCPs) using collocation methods. This approach is based upon B-spline functions. The derivative matrices between any two families of B-spline functions are utilized to reduce the solution of OCPs to the solution of nonlinear optimization problems. Numerical experiments confirm our heoretical findings.
متن کاملSolving optimal control problems with integral equations or integral equations - differential with the help of cubic B-spline scaling functions and wavelets
In this paper, a numerical method based on cubic B-spline scaling functions and wavelets for solving optimal control problems with the dynamical system of the integral equation or the differential-integral equation is discussed. The Operational matrices of derivative and integration of the product of two cubic B-spline wavelet vectors, collocation method and Gauss-Legendre integration rule for ...
متن کاملAn ${cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems
As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only ${cal O}(h^{2})$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The ${cal O}(h^{8})$ convergence analysis, mainly base...
متن کاملBiorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems
In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville in...
متن کاملB-Spline Solution of Boundary Value Problems of Fractional Order Based on Optimal Control Strategy
In this paper, boundary value problems of fractional order are converted into an optimal control problems. Then an approximate solution is constructed from translations and dilations of a B-spline function such that the exact boundary conditions are satisfied. The fractional differential operators are taken in the Riemann-Liouville and Caputo sense. Several example are given and the optimal err...
متن کامل