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Hermite series approach to optimal control. (English) Zbl 0636.93036
Summary: A general expression for the operational matrix of integration, $${\mathbb{P}}$$, in the case of Hermite polynomials is derived. The structure of $${\mathbb{P}}$$ is simple and it is therefore computationally attractive. Using this $${\mathbb{P}}$$, the optimal control with quadratic index problem and the singularly perturbed optimal control problem are studied. Some numerical examples are also included.

##### MSC:
 93C05 Linear systems in control theory 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 44A45 Classical operational calculus 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 34E15 Singular perturbations, general theory for ordinary differential equations 93C15 Control/observation systems governed by ordinary differential equations
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