Robust Optimal Onboard Reentry Guidance of a Space Shuttle: Dynamic Game Approach and Guidance Synthesis via Neural Networks

Robust optimal control problems for dynamic systems must be solved ifmodeling inaccuracies cannot be avoided and/or unpredictable andunmeasurable influences are present. Here, the return of a future Europeanspace shuttle to Earth is considered. Four path constraints have to beobeyed to limit heating, dynamic pressure, load factor, and flight pathangle at high velocities. For the air density associated with theaerodynamic forces and the constraints, only an altitude-dependent rangecan be predicted. The worst-case air density is analyzed via an antagonisticnoncooperative two-person dynamic game. A closed-form solution of the gameprovides a robust optimal guidance scheme against all possible air densityfluctuations. The value function solves the Isaacs nonlinear first-orderpartial differential equation with suitable interior and boundaryconditions. The equation is solved with the method of characteristics in therelevant parts of the state space. A bundle of neighboring characteristictrajectories yields a large input/output data set and enables a guidancescheme synthesis with three-layer perceptrons. The difficult andcomputationally expensive perceptron training is done efficiently with thenew SQP-training method FAUN. Simulations show the real-time capability androbustness of the reentry guidance scheme finally chosen.