An approximate solution of bivariate nonlinear Fredholm integral equations using hybrid block-pulse functions with Chebyshev polynomials

Mohammadi, Mahnaz; Zakeri, Ali; Karami, M.

doi:10.1007/s40096-020-00336-7

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2022

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“…16 More recently, an extensive use of hybrid functions could be noticed in literature. Indeed, many researchers are actually proposing solution to some classes of Fredholm integro-differential equations by associating Legendre, 17 Chebychev, 18 or Bernstein polynomials 19 to BPFs basis. On the contrary, several mathematical problems related to fractional nonlinear differential equations had been tackled by the mean of Taylor series 20,21 or LPs 22 combined to the piecewise orthogonal basis.…”

Section: Introductionmentioning

confidence: 99%

Suboptimal control synthesis for state and input delayed quadratic systems

Bouafoura

Braïek

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this article a suboptimal linear-state feedback controller for multi-delay quadratic system is investigated. Optimal state and input coefficients resulting from the expansion over a hybrid basis of block pulse and Legendre polynomials are first obtained by formulating a nonlinear programming problem. Afterwards, suboptimal control gains are found by solving a least square problem constructed with optimal coefficients of the open loop study. A sufficient condition for the exponential stability of the closed loop is obtained from generalized Grönwall–Bellman lemma. The Van de Vusse chemical reactor case is handled allowing to validate the proposed technique.

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