A Switching Strategy for Event-Trigger Control of Spacecraft Rendezvous

Abstract: This paper presents the design of a state-feedback control law for spacecraft rendezvous, formulated using the Hill-Clohessy-Wiltshire equations. The proposed method introduces an impulsive control strategy to regulate thruster operations. Specifically, a state-dependent switching framework is developed to determine both the control input magnitudes and the precise state conditions that trigger thruster activation. The nonlinear control law is derived using principles from automatic control theory, particularly Lyapunov stability analysis and the Linear Matrix Inequality framework. The resulting closed-loop system is proven to be stable, while simultaneously minimizing the total number of actuation events. The effectiveness of the proposed method is demonstrated through a numerical case study, which includes a comparative analysis with a standard Model Predictive Control scheme, highlighting the advantages and trade-offs of the developed control structure.