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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.

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