Robust model predictive control under uncontrollable sampling intervals

This paper proposes a robust model predictive control (RMPC) framework under uncontrollable sampling intervals, i.e. only a known bound on the sampling interval, designed for incrementally stabilizable nonlinear systems with general state and input-dependent disturbances. We begin by establishing a tube that sets an upper limit for an offline incremental Lyapunov function, defining the permissible range for the actual state deviation from the optimal state at each prediction step due to disturbances. This tube construction employs piecewise dynamics, considering the input trajectory to be optimized and an incrementally stabilizing feedback, leading to a piecewise growth rate of tube size. The varying growth rate in tube size poses a challenge to recursive feasibility, which we address by imposing constraints on the predicted uncertainty variations within the optimization process. Additionally, a reconstructed tube, derived from the initial one, is presented. This tube considers all potential open-loop behaviors before the next actual state value is available. It is used to tighten the nominal state and input constraints, ensuring the robust satisfaction of physical constraints. This framework achieves recursive feasibility and stability despite the presence of unpredictable sampling intervals and state and input-dependent disturbances.