Circular orbital rendezvous with actuator saturation and delay: A parametric Lyapunov equation approach

This study concerns circular orbital rendezvous by using saturated and delayed controls. By identifying the linearised relative motion, known as Clohessy-Wiltshire equations that are asymptotically null controllable by bounded controls, linear feedback laws are designed to semi-globally stabilise the system in the presence of both actuator saturation and delay, namely, the initial condition of the system can be as large as desired as long as it is bounded. To design these controllers, only solutions to a class of parametric Lyapunov equations are required and whose solution can be obtained explicitly. Numerical example is worked out to show the effectiveness of the proposed methodology.