Optimal control problems are often too complex to solve analytically. Computational methods usually replace the continuous infinite dimensional problem by a finite dimensional discrete approximation. The talk will survey classical discretization techniques based on a Runge-Kutta approximation to the differential equations (an h-method) and then introduce recent approximations based on collocation at the roots of orthogonal polynomials (a p-method). The best approximations are often achieved using an hp-framework that combines the best features of both approaches. Numerical results using the GPOPS-II (General Pseudospectral Optimal Control Software package) will be presented.
Organizers: Jia-Jie Zhu