Numerical solution of optimal control problems using multiple-interval integral Gegenbauer pseudospectral methods

• Multiple-interval integral Gegenbauer pseudospectral methods are developed.
• Costate and constraint multiplier estimates for the proposed methods are provided.
• Efficient computation of mesh pseudospectral integration matrices is presented.

The main purpose of this work is to provide multiple-interval integral Gegenbauer pseudospectral methods for solving optimal control problems. The latest developed single-interval integral Gauss/(flipped Radau) pseudospectral methods can be viewed as special cases of the proposed methods. We present an exact and efficient approach to compute the mesh pseudospectral integration matrices for the Gegenbauer–Gauss and flipped Gegenbauer–Gauss–Radau points. Numerical results on benchmark optimal control problems confirm the ability of the proposed methods to obtain highly accurate solutions.