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A numerical method based on Cardan polynomials for solving optimal control problems. (English) Zbl 1424.49002

Summary: This paper presents an iterative numerical scheme for solving a class of optimal control problems. The solution is based on the state parametrization such that, the state variable can be considered as a linear combination of Cardan polynomials with the unknown coefficients. This converts the optimal control problem to a non-linear polynomial optimization problem. Illustrative examples are included to demonstrate the efficiency of the proposed method.

MSC:

49J15 Existence theories for optimal control problems involving ordinary differential equations
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems
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