Robust reference governor for input-constrained model predictive control to enforce state constraints at low computational cost

In the setting of discrete-time linear systems with unmeasured set-bounded disturbances, this paper proposes a control scheme that combines a disturbance free input-constrained Model Predictive Control (uMPC) policy and a reference governor (RG) which modifies the reference command to enforce constraints that are not enforced by the uMPC policy. Such a scheme, referred to as the robust RGMPC, can handle (possibly nonlinear) state and input constraints and only requires solving an optimisation problem for MPC with polytopic input constraints, for which fast algorithms exist. Conditions are given which ensure recursive feasibility of the robust RGMPC scheme, finite-time convergence of the modified reference command to the desired reference command and asymptotic convergence of the state to an invariant neighbourhood of the associated set-point. Simulation results for a constrained spacecraft rendezvous manoeuvre demonstrate that the rRGMPC scheme has lower average computational time than several robust state and input-constrained MPC controllers.