@MISC{LPT-pre-2010-14,
AUTHOR = {R. Hannemann and W. Marquardt},
TITLE = {{Combining Direct and Indirect Methods for Optimal Control - a Case Study}},
LPTKey = {LPT-pre-2010-14},
}

Combining Direct and Indirect Methods for Optimal Control - a Case Study

Abstract:
Adaptive control vector parameterization for the solution of optimal control problems approximates the original infinite-dimensional optimal control problem by a set of finite-dimensional nonlinear programs (NLPs) whose control grids are iteratively refined. The refinement is stopped by a heuristic stopping criterion. The Hessians of the Lagrangian of these NLPs can be efficiently computed by the technique of composite adjoints as recently proposed by the authors. By means of a case study, namely the optimal control of the Williams-Otto semi-batch reactor, we show how to interpret composite adjoints as estimates for the continuous adjoints referred to by Pontryagin's Minimum Principle. Thus, these composite adjoints can be used to (i) construct a novel and mathematical sound stopping criterion for the iterative refinement of the control grid and to (ii) setup an indirect multiple shooting method the solution of which verifies and improves the approximate solution to the exact one.

Keywords:
optimal control, direct single shooting, indirect multiple shooting, multipoint boundary value problem, Pontryagin, adjoints