In this article, a novel variable-bandwidth extended state observer (VBESO) is proposed to estimate external disturbances for a class of $n$th-order nonlinear systems with measurement noise. Based on the feature of “high error, high bandwidth; low error, low bandwidth,” the bandwidth of the proposed observer is adjusted automatically with the output estimation error, achieving a tradeoff between the estimation accuracy and the robustness to measurement noise. Moreover, a designed filter is introduced into the observer such that an arbitrarily small initial bandwidth can be set to alleviate the “peaking phenomenon,” and the convergence speed is improved by reducing the time constant of the filter. In addition, extensions to other kinds of observers are also established. Finally, the VBESO-based state-feedback control is presented and applied to the drag-free spacecraft hardware-in-loop experiment platform. Simulation and experiment results show that the proposed VBESO can improve the tolerance to the measurement noise and achieve a tradeoff between transient-state and steady-state performance.

In this paper, we investigate the cooperative pursuitevasion problem among on-orbit multiple spacecraft. The presented problem involves a dynamic pursuit process that gives rise to a multiple-to-one pursuit game, in which multiple pursuing spacecraft collaborate to collectively reduce the minimum distance between pursuers and evader. The main challenge lies in establishing the game amidst intricate mission intentions and ensuring efficient generation of game strategies, e.g., the Nash equilibrium strategy. To this end, we formulate the multiple spacecraft pursuit-evasion problem within the framework of a multi-player computational game. Subsequently, a one-step lookahead Nash equilibrium is introduced to facilitate the periodic modification of ideal trajectories during the dynamic game process. In addition, in order to enhance the solution efficiency, we integrate an action-reaction search procedure embedded with a dynamic pruning technique into the search for Nash equilibrium. Simulation results validate the effectiveness of the proposed scheme.

In this work, we investigate the measurement noise sensitivity and peaking problem of the extended state observer (ESO) under high-gain characteristics. For a class of n-order nonlinear systems with measurement noise, a new variable-order filter and the corresponding filtered ESO (FESO) are constructed to achieve arbitrary suppression ability of measurement noise. Such a salient feature lies in the establishment of the variable-order filter with independent parameters such that the observer poles and the order of the proposed filter can be set arbitrarily by the designer, thereby allowing the user to predefine the suppression strength in prior by adjusting parameters. In addition, a peaking-free FESO is further proposed to eliminate the undesired peaking phenomenon during the transient state. Finally, a comprehensive numerical comparison is presented, and the proposed peaking-free FESO is applied to the drag-free spacecraft hardware in-loop platform. The simulation results reveal the advantages of the proposed scheme in measurement noise suppression and peaking elimination.