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

摘要

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.