Multi-objective and reliable control for trajectory-tracking of rendezvous via parameter-dependent Lyapunov functions

Adaptive control and orbit determination for elliptical rendezvous

“…Up to now, we have obtained the estimated parameterŵ 0 (t) = kθ 3/2 by (15), and the estimated extended statesx 3 andẑ 3 by (21) and (25). Then, what we need to do is to find an estimation method for the other three parameters {θ ,θ ,θ 2 } from the estimatesx 3 andẑ 3 .…”

“…Theorem 1: Consider the relative motion system for rendezvous given by (1), the control laws given by (17), (22) and (24) with the parameter and state estimation components given by (15), (21) and (25). Then, the estimation errors {w 0 (t),x 3 (t),z 3 (t)} and the tracking errors {E y (t), E x (t), E z (t)} are ultimately bounded.…”

“…So far, the four time-varying parameters w 0 (t), w 1 (t), w 2 (t), and w 3 (t) have been estimated by (15) and (36). Then, with the analysis (3)-(9) given in subsection 2.3, we can get the orbital elements as…”

“…Moreover, in most previous work about elliptical rendezvous, the target orbital elements are considered as priori knowledge and the chaser spacecraft is able to receive real-time orbital information by communication with the target spacecraft or ground stations. In this way, the authors in [12,13,14,15] design feedback controllers to directly compensate the terms of the relative motion equations with time-varying parameters by using the known orbital information. For some non-cooperative targets, such as damaged spacecraft, space debris, and asteroid, the accurate relative motion of the space rendezvous is usually difficult to obtain since the orbital information of the target orbit is unknown.…”

Observer-Based Robust Mixed H 2 /H ∞ Control for Autonomous Spacecraft Rendezvous

“…This paper uses C-W equations which contain the non-circle uncertainty (NCU) to build the model of system, The trust of chasing spacecraft is divided into three categories, impulsive trust, continuous trust and variable trust [7,8]. The robust controller for rendezvous was studied in [3,9,10]. However, in fact, the velocity states cannot be observed for state feedback, so the state-observer theory is applied to spacecraft rendezvous control [11][12][13].…”