Predictive control of constrained nonlinear systems via LPV linear embeddings

This paper analyzes the applicability of convex MPC schemes, synthesized for LPV polytopic systems, to nonlinear plants. The nonlinear systems under consideration are those whose trajectories can be embedded within those of a polytopic LPV discrete‐time system. It is postulated that the latter belongs to a polytopic family of linear systems, each member of which is parameterized by the value that a parameter vector assumes in the unit simplex. Such a parameter can be measured on‐line and exploited for feedback while a bound on its rate of change is known and exploited for predictions. Different customizations and improvements of a recently introduced MPC scheme for LPV systems are presented and contrasted in terms of their numerical burdens and control performance. The proposed predictive controllers are proved to quadratically stabilize LPV polytopic systems, as well as any other embedded non‐linear system, in the presence of input and state constraints.