Jacobi Discrete Approximation for Solving Optimal Control Problems

Abstract

Abstract. 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.

A Jacobi collocation approximation for nonlinear coupled viscous Burgers’ equation

“…There are several particular cases of them such as Legendre polynomials, all kinds of Chebyshev polynomials and Gegenbauer polynomials [30]. Also, the Jacobi polynomials have been used in a variety of applications due to their ability to approximate general classes of functions, some of which are the resolution of the Gibbs' phenomenon [31], electrocardiogram data compression [32] and the solution to differential equations [33,34].…”

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

“…The problem now is how to deal with the two non-local boundary conditions (37). For this purpose, let us also develop a collocation treatment for the two non-local conservation conditions.…”

“…There are several particular cases of them such as Legendre, the four kinds of Chebyshev and Gegenbauer polynomials [33]. Also, the Jacobi polynomials have been used in a variety of applications due to their ability to approximate general classes of functions, some of which are the resolution of the Gibbs' phenomenon [34], electrocardiogram data compression [35] and the solution to differential equations [36,37]. For the interval [0 L], we may use shifted Jacobi polynomials.…”