Interval Arithmetic in Robust Nonlinear MPC

This paper shows how interval arithmetic can be used to design stabilizing robust MPC controllers. Interval arithmetic provides a suitable framework to obtain a tractable procedure to calculate an outer bound of the range of a given nonlinear function. This can be used to calculate a guaranteed outer bound on the predicted sequence of reachable sets. This allows us to consider the effect of the uncertainties in the prediction and to formulate robust dual-mode MPC controllers with ensured admissibility and convergence. Interval arithmetic can also be used to estimate the state when only outputs are measurable. This method provides a guaranteed outer bound on the set of states consistent with the output measurements. Generalizing the controllers based on reachable sets, a novel robust output feedback MPC controller is also proposed.