Parameterized nonlinear suboptimal control for tracking and rendezvous with a non-cooperative target

A specific parameterized nonlinear suboptimal control technique is proposed to control the relative position of a spacecraft in order to track a rotating target. The technique consists of using power series expansion to parameterize an SDRE (State-Dependent Riccati Equation) with an algebraic expression. One of the major contributions of this technique is the avoidance of online solution of algebraic Riccati and Lyapunov equations that will be much faster than the standard SDRE and θ−D control. Meanwhile, parameterized nonlinear suboptimal control is extended to adaptive form to verify robustness to unknown disturbances. Finally, we show two benchmark examples using this parameterized technique to construct controllers. Specifically, we also apply this technique to design the nonlinear control of a chaser spacecraft to track and rendezvous with a rotating non-cooperative target accompanied by an unknown translational maneuver. Numerical results demonstrate that the computational efficiency and tracking performance accuracy are superior to existing methods and an adaptive form is capable of offsetting unknown parameters.