Safe approaching control for spacecraft rendezvous with disturbances: A positive system approach

Abstract

This paper concerns about the safe approaching in rendezvous with spherical envelops of spacecraft. Based on the nonnegative characteristic of positive systems, a novel strategy of controlling the relative distance positive and convergent is proposed to guarantee no‐collision approaching. The dynamics of the relative distance is decoupled from that of the relative angles. A nonlinear disturbance observer is designed, and two anti‐disturbance controllers are constructed to reject the effect of disturbances for the subsystems of relative distance and angles. Under the controllers, the closed‐loop subsystem of relative distance is a positive and stable system, while that of relative angles is a general stable system satisfying the given time‐varying constraints. Particularly, a theorem is proposed to present the conditions of controllers to ensure the system positivity under a class of external inputs without nonnegativity default. Finally, simulation results are presented to illustrate the effectiveness of proposed methods.

Stability and stabilization of periodic piecewise positive systems: A time segmentation approach

“…A and p i,j 7 ! p j ; one can find that inequalities (7a) and (7b) are the same as ( 8) and (9). For periodic piecewise positive systems, the subsystem may be unstable and matrix A i needs not be Hurwitz.…”

“…Positive systems, whose state is always in the nonnegative orthant, have drawn increasing attention in recent decades. Due to the positivity of the state, the systems feature a couple of advantages in theoretical research, including decrease of the complexity of stability conditions [1, 2], simplification of the characterization for some input–output gains, like ‐ and ‐gains, which were first considered in Briat [3], and reduction of conservativeness of conditions for stability and input–output gain analysis for some kinds of positive systems [4, 5] and therefore have a wide range of applications in engineering fields, including disease transmission [6], population dynamics [7], networked fluid flow [8], and spacecraft rendezvous process [9].…”

Dynamic observer‐based fault estimation and fault‐tolerant control for switched stochastic systems with multiple faults

“…The disturbances in (1) are listed separately, through the different matrices of known coefficients B i , and D i indicates that faults and disturbances enter the system through different channels. Moreover, the possible disturbances in (2) are no longer listed separately, but are included in 𝑓 s (t). The injection of stochastic noise makes the whole system more realistic.…”

“…When fault occurs in the system, fault diagnosis (FD) and FTC technologies can be considered to ensure that the system operation process can be carried out normally and achieve certain performance. At present, more and more people pay attention to FD and FTC, and related researches have also been extensively reported [1][2][3][4][5][6][7].…”

Refined Disturbance Rejection-Based Composite Control of Flexible Spacecrafts for Tracking a Tumbling Non-Cooperative Target

“…However, only one type of disturbance is considered in the above-mentioned control methods. In practical engineering, multiple disturbances with different characteristics are present, which motivates the studies of CHADC methods [14], [15]. In the framework of CHADC, an enhanced anti-disturbance control law is proposed for the attitude control system of flexible spacecrafts [16].…”