Nonlinear model predictive control with polytopic invariant sets. (English) Zbl 1033.93022
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.
Reviewer: Ingmar Randvee (Tallinn)
MSC:
| 93B51 | Design techniques (robust design, computer-aided design, etc.) |
| 93C10 | Nonlinear systems in control theory |
| 90C05 | Linear programming |
Keywords:
polytopic invariant sets; nonlinear model predictive control; ellipsoidal invariant sets; linear feedback; linear programs; polytopic target setsReferences:
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