Control of a class of nonlinear uncertain systems by combining state observers and parameter estimators

Adaptive control and orbit determination for elliptical rendezvous

“…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.…”

“…According to the performance analysis of ESO given in [24] and [25], we can get the boundedness of the state signals {x,ẋ, y,ẏ, z,ż} and the estimation errors {x 3 ,z 3 }. To be specific, define a compact region…”

“…Then, from [24] and [25], we know that the state trajectories of the closed loop system can not go beyond the set Ω by taking the gains ε 1 and ε 2 small enough. Furthermore, we also have that there exist t xz > 0 and small positive numbers δ x and δ z , such that |x 3 …”

“…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 .…”

Control of uncertain nonlinear systems based on observers and estimators

“…Therefore, it is of great significance, both theoretically and practically, to investigate this problem. To solve it, Huang and Guo (2012) proposed to estimate the uncertainties by combining observers and estimators for the output feedback control of a class of nonlinear systems with the integrators in series structure. Furthermore, in Scheinker and Krstić (2013), a state feedback based on the extremum seeking (ES) design has been developed for semi-global stabilization of unstable and time-varying systems, where the control direction is unknown and is allowed to persistently change signs.…”