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Jacobi discrete approximation for solving optimal control problems. (English) Zbl 1236.65072
Summary: 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 the differentiation matrix to approximate the derivative term in the state system. The system dynamics are then converted into a system of algebraic equations and hence the optimal control problem is reduced to a constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.

65K10 Numerical optimization and variational techniques
49J15 Existence theories for optimal control problems involving ordinary differential equations
49M25 Discrete approximations in optimal control
Ipopt; OPTRAGEN; Matlab
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