Real - Time Computation of Feedback

Based on the rst part of this paper 17 , a numerical method is developed for the real-time computation of neighboring optimal feedback controls for constrained optimal control problems. Using the idea of multiple shooting, a numerical method is developed which has the following properties: 1. The method is applicable to optimal control problems with constraints (diierential 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 ight path are much larger than deviations typical for perturbations occurring in space vehicles. The reentry of a space vehicle is investigated as an example. One problem contains a control variable inequality constraint with a large variety of diierent 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 diier-ent switching structures depend on the tightness of the constraints.