A nearly optimal control for spacecraft rendezvous with constrained controls

Abstract

A neural network Hamilton–Jacobi–Bellman (HJB) approach is introduced to deal with the spacecraft rendezvous problem with target spacecraft in arbitrary elliptical orbit. The Lawden equations are utilized to describe the relative motion of two spacecrafts. A generalized non-quadratic functional is introduced to describe constrained control. An approximate solution to the value function of the HJB equation corresponding to constrained controls is obtained by solving for a sequence of cost functions satisfying a sequence of Lyapunov equations. An inverse optimal controller is introduced to design the initial stabilizing admissible control for successive approximation. Furthermore, an optimal control law is obtained to stabilize the closed-loop system under constrained controls, and the spacecraft rendezvous mission can be accomplished with the nearly optimal controller. In comparison with the existing quadratic-regulation-based approaches used to deal with the rendezvous problem, which requires the value function of the nonlinear differential equations, the optimization factor and constrained control are taken into consideration simultaneously, and an approximate optimal constrained state feedback controller has been tuned a priori off-line. Stability analysis as well as simulation results are provided to illustrate the effectiveness of the presented approach.