Enlargement of polytopic terminal region in NMPC by interpolation and partial invariance

Polytopic invariant sets have significant advantages over ellipsoidal invariant sets in the design of constrained control laws due to their potential for greater flexibility in shape. This paper uses the concept of partial invariance to derive a sequence of linear programs in order to maximize offline the volume of an invariant polytopic set with an arbitrary predefined number of vertices subject to a bound on closed-loop performance. Interpolation techniques are used to determine a nonlinear control law which is optimal with respect to a closed-loop cost bound through the online solution of a linear program. The invariant polytope is used to define a receding horizon control law through an appropriate terminal constraint and cost.