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Legendre–Galerkin spectral methods for optimal control problems with integral constraint for state in one dimension

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  • Jianwei Zhou
  • Danping Yang

Abstract

In this paper, we investigate the optimal control problems governed by elliptic equations with integral constraint for state variable in one dimension by Legendre–Galerkin spectral methods. We deduce optimal conditions of the optimal control problems. Meanwhile, we obtain an a priori error estimate and a posteriori error estimator. Furthermore, we obtain an explicit formula of the a posteriori error estimator by orthogonal properties of Legendre polynomials. Finally, we present numerical examples to confirm our analytical results. Copyright Springer Science+Business Media New York 2015

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  • Jianwei Zhou & Danping Yang, 2015. "Legendre–Galerkin spectral methods for optimal control problems with integral constraint for state in one dimension," Computational Optimization and Applications, Springer, vol. 61(1), pages 135-158, May.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:1:p:135-158
    DOI: 10.1007/s10589-014-9700-x
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    References listed on IDEAS

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    1. Olaf Benedix & Boris Vexler, 2009. "A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints," Computational Optimization and Applications, Springer, vol. 44(1), pages 3-25, October.
    2. R. Hoppe & M. Kieweg, 2010. "Adaptive finite element methods for mixed control-state constrained optimal control problems for elliptic boundary value problems," Computational Optimization and Applications, Springer, vol. 46(3), pages 511-533, July.
    3. Jaddu, Hussein, 2002. "Spectral method for constrained linear–quadratic optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(2), pages 159-169.
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