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.
Biography: Prof. William W. Hager is a Professor of Mathematics at the University of Florida, co-director of the Center for Applied Optimization, and a SIAM Fellow. He received his Ph.D. degree in Mathematics from MIT in 1974, in optimal control.
His research interests are in the areas of optimization, numerical methods in optimal control, and applications. In particular, he has developed a convergence analysis for discrete approximations to problems in optimal control as well as algorithms for solving large, sparse optimization problems with a particular focus on his Dual Active Set Method and the related sparse matrix techniques and theory involved in the implementation of active set methods.