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Efficient Chebyshev collocation methods for solving optimal control problems governed by Volterra integral equations

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  • Tang, Xiaojun

Abstract

The main purpose of this work is to provide efficient Chebyshev collocation methods for solving optimal control problems (OCPs) governed by Volterra integral equations. The basic principle of our approach is to approximate the state and control using the Chebyshev polynomials and collocate the dynamic constraints at the Chebyshev-type points. Furthermore, we present an exact, efficient, and stable approach for computing the associated Chebyshev integration matrices. Numerical results on benchmark OCPs demonstrate the spectral rate of convergence for the proposed methods.

Suggested Citation

  • Tang, Xiaojun, 2015. "Efficient Chebyshev collocation methods for solving optimal control problems governed by Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 118-128.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:118-128
    DOI: 10.1016/j.amc.2015.07.055
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    References listed on IDEAS

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    1. J. Frédéric Bonnans & Constanza Vega & Xavier Dupuis, 2013. "First- and Second-Order Optimality Conditions for Optimal Control Problems of State Constrained Integral Equations," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 1-40, October.
    2. C. De La Vega, 2006. "Necessary Conditions for Optimal Terminal Time Control Problems Governed by a Volterra Integral Equation," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 79-93, July.
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