Real-time computation of feedback controls for constrained optimal control problems. Part 2: A correction method based on multiple shooting

On the basis of Part 1 of this paper, a numerical method is developed for the real-time computation of neighbouring optimal feedback controls for constrained optimal control problems. We use the idea of multiple shooting to develop a numerical method which has the following properties: 1. The method is applicable to optimal control problems with constraints (differential equations, boundary conditions, inequality constraints, problems with discontinuities, etc.). 2. The control variables and the switching points are computed for the remaining time interval of the process. 3. All constraints are checked. 4. The method is appropriate for real-time computations on onboard computers of space vehicles. 5. The scheme is robust in that controllable deviations from a precalculated flight path are much larger than deviations typical for perturbations occuring in space vehicles. The re-entry of a space vehicle is investigated as an example. One problem contains a control variable inequality constraint with a large variety of different switching structures, including problems with a corner. A second problem contains a state variable inequality constraint with one or two boundary points or one boundary arc. The different switching structures depend on the tightness of the constraints.