Practical Implementation Aspects of Large-Scale Optimal Control Solvers

The direct transcription methods of optimal control problems lead to large-scale nonlinear programming problems. One suitable framework for the solution of this type of optimization problems is sequential quadratic programming, which is described in Chap. 2. But it is crucial for large-scale applications, that the SQP-algorithm takes into account the particular properties and structure of the objective and constraint functions. The Karush–Kuhn–Tucker matrices, which occur in the subproblems, must be sparse, so that the linear equation systems can be efficiently solved. To accomplish this task for general problems the structure of the matrix must be determined, the derivatives have to be calculated, and a sparse Quasi-Newton update has to be implemented.