Nonlinear model predictive control with polytopic invariant sets. (Q1410381)

A nonlinear model predictive control (NMPC) method in which low complexity polytopic invariant sets are used in place of ellipsoidal invariant sets is proposed. It is shown that (i) low-complexity polytopic invariant sets have larger volume than invariant ellipsoidal sets; (ii) the systematic design of maximum volume low-complexity invariant polytopes and linear feedback laws satisfying given performance bounds can be performed through the sequential off-line solution of a number of simple linear programs; and (iii) low-complexity invariant polytopic sets can be effectively used in NMPC of fast-sampling input-affine nonlinear systems. The advantages of feasible invariant polytopic sets over ellipsoidal sets are illustrated through the numerical examples. Also, the closed-loop performance of NMPC based on polytopic target sets is compared to NMPC based on ellipsoidal target sets.