A non-Lyapunov approach to control design with application to spacecraft docking

Abstract

In this paper, we present a novel control design framework for nonlinear dynamical systems that is not based on traditional Lyapunov approach. Specifically, the Iterative Control Framework (ICF) is designed to guarantee the convergence of the closed-loop system state to zero without a priori verification of Lyapunov-like conditions. The approach is based on a numerical routine that reconfigures the control input vector at each iteration in such a way that when the control input is applied to the system, the system trajectory reaches closer to the desired state. This allows the control of real-world systems regardless of complexity in model nonlinearities or system dimensionality. Here we apply this framework to spacecraft control during the final stage of its rendezvous with another space vehicle, that is, docking. Since spacecrafts are controlled by impulsive thrusters with very short activation time, this application presents an ideal case study for ICF. We show that all states of the dynamical model are driven to the desired equilibrium and run Monte Carlo simulations to demonstrate the robustness of the approach.