Decentralized Impulse Control for Multiagent Space Systems

For nonlinear systems that admit continuous-time stabilizing controllers, we propose a Lyapunov-based technique to map this continuous-time control input into a sequence of discrete impulses while guaranteeing the desired performance of the closed-loop system. Specifically, a numerical algorithm, running in real-time, determines the instants of control impulse injections into the system based on comparison of a Lyapunov function value predicated on continuous-time control and on impulse control. No control input is applied to the system throughout the operation except for these occasional impulsive control injections. The main advantage of the proposed technique is two-fold: first, it allows to significantly reduce control effort while still achieving the desired control objective and secondly, our method takes into account the control saturation limits as part of the underlying design. We apply this technique to design decentralized cooperative control for the formation flying of multiple satellites and spacecraft distributed along the orbit. These vehicles typically use discrete burns to reduce fuel consumption, and hence, the proposed technique is well-suited for such application. We demonstrate its efficacy through numerical simulations.