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This paper attempts to present a numerical method for solving optimal control problems. The method is based upon constructing the $n$-th degree Jacobi polynomials to approximate the control vector and use differentiation matrix to approximate derivative term in the state system. The system dynamics are then converted into system of algebraic equations and hence the optimal control problem is reduced to constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.
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A. H. Bhrawy / 2010 / Jacobi spectral Galerkin method for the integrated forms of second-order differential equations / Applied Mathematics and Computation 217 : 2684 ~ 2697
D. Gottlieb / 1977 / Numerical Analysis of Spectral Methods: Theory and Applications / CBMS-NSF Regional Conference Series in Applied Mathematics
E. H. Doha / 2003 / Efficient spectral-Galerkin algorithms for direct solution of second-order equations using ultraspherical polynomials / SIAM J. Sci. Comput 24 (2) : 548 ~
E. H. Doha / 2004 / On the construction of recurrence relations for the expansion and connec- tion coefficients in series of Jacobi polynomials / J. Phys. A 37 (3) : 657 ~ 67
A. H. Bhrawy / 2010 / Jacobi spectral Galerkin method for the integrated forms of second-order differential equations / Applied Mathematics and Computation 217 : 2684 ~ 2697
D. Gottlieb / 1977 / Numerical Analysis of Spectral Methods: Theory and Applications / CBMS-NSF Regional Conference Series in Applied Mathematics
E. H. Doha / 2003 / Efficient spectral-Galerkin algorithms for direct solution of second-order equations using ultraspherical polynomials / SIAM J. Sci. Comput 24 (2) : 548 ~
E. H. Doha / 2004 / On the construction of recurrence relations for the expansion and connec- tion coefficients in series of Jacobi polynomials / J. Phys. A 37 (3) : 657 ~ 67
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