Tractable robust MPC design based on nominal predictions. (March 2022) - Alvarado, Ignacio; Krupa, Pablo; Limon, Daniel; Alamo, Teodoro
Abstract: Many popular approaches in the field of robust model predictive control (MPC) are based on nominal predictions. This paper presents a novel formulation of this class of controller with proven input-to-state stability and robust constraint satisfaction. Its advantages are: (i) the design of its main ingredients are tractable for medium to large-sized systems, (ii) the terminal set does not need to be robust with respect to all the possible system uncertainties, but only for a reduced set that can be made arbitrarily small, thus facilitating its design and implementation, (iii) under certain conditions the terminal set can be taken as a positive invariant set of the nominal system, allowing us to use a terminal equality constraint, which facilitates its application to large-scale systems, and (iv) the complexity of its optimization problem is comparable to the non-robust MPC variant. We show numerical closed-loop results of its application to a multivariable chemical plant and compare it against other robust MPC formulations. Highlights: We present a robust MPC with nominal predictions with tightened constraints. The terminal set needs only to be robust for an arbitrarily small uncertainty set. The ingredients of the formulation are tractable for medium to large-sized systems. Performance and constraint tightening are decoupled. Design procedures for the ingredients of the formulation are provided.