Dynamic Tube Model Predictive Control for Powered-Descent Guidance

Abstract

In this paper, a dynamic tube nonlinear model predictive control (NMPC) scheme is developed to solve the powered-descent guidance (PDG) problem in the presence of bounded disturbances and no-fly zones. First, owing to its simplicity and robustness, time-varying boundary layer sliding mode control (SMC) is used as an ancillary controller to compensate for external disturbances. Consequently, the tube geometry dynamics can be established as first-order differential equations to calculate the robust control invariant tube. Hence, the nominal trajectory and tube geometry are optimized simultaneously to improve the control performance by augmenting the tube geometry dynamics in open-loop MPC optimization. Moreover, the tube can be shrunk to reduce the conservativeness and enhance optimization feasibility by exploiting the tube geometry and tracking error dynamics. In addition, a constraint-tightening method is employed to ensure that the PDG problem satisfies all the constraints while accounting for the uncertainty caused by the disturbance. Finally, numerical case studies and Monte Carlo simulations validate the effectiveness and performance of the proposed strategy.