Stabilizing non‐linear model predictive control using linear parameter‐varying embeddings and tubes

Abstract This paper proposes a model predictive control (MPC) approach for non‐linear systems where the non‐linear dynamics are embedded inside a linear parameter‐varying (LPV) representation. The non‐linear MPC problem is therefore replaced by an LPV MPC problem, without using linearization. Compared to general non‐linear MPC, advantages of this approach are that it allows for the tractable construction of a terminal set and cost, and that only a single convex program must be solved online. The key idea that enables proving recursive feasibility and stability, is to restrict the state evolution of the non‐linear system to a time‐varying sequence of state constraint sets. Because in LPV embeddings, there exists a relationship between the scheduling and state variables, these state constraints are used to construct a corresponding future scheduling tube. Compared to non‐time‐varying state constraints, tighter bounds on the future scheduling trajectories are obtained. Computing a scheduling tube in this setting requires applying a non‐linear function to the sequence of constraint sets. Outer approximations of this non‐linear projection‐based scheduling tube can be found, e.g., via interval analysis. The computational properties of the approach are demonstrated on numerical examples.