Optimal Terminal Rendezvous as a Stochastic Differential Game Problem

The optimal terminal rendezvous of two satellites in orbit about the Earth is studied using a stochastic model and formulating the rendezvous as a game problem. Each satellite has noise-corrupted output measurements and uses a Kalman filter to generate the best estimate of the states describing the rendezvous. The optimal control for the satellites is determined. A comparison is made in terms of dimensionality and complexity to a deterministic solution of the rendezvous problem.     

An Approach to Optimization of Terminal Rendezvous

The optimal solution is presented to a cooperative game which is described by a common quadratic cost functional subject to linear ordinary differential equation constraints. The optimal feedback controller is constructed for both players when all components of the state vector can be measured. For the case that only some components of the state vector are available, the optimal feedback controller is designed using a dynamic observer. As a specific application, the approach is used in determining the optimal feedback controllers for two satellites which are performing a rendezvous on a circular orbit. Simulation results are presented to illustrate the applicability of the approach.