Constrained MPC using feedback linearization on SISO bilinear systems with unstable inverse dynamics. (English) Zbl 1094.93010
Expressions for maximal partially invariant sets are derived, and an algorithm for significant enlargement of maximal PIF (partially invariant and feasible) sets are developed. The derivation is based on the concept of partial invariance in order to identify regions in state space where OIOFL (optimal input-output feedback linearization) applied to SISO bilinear systems steers the state to the kernel of the output map even in the presence of non-minimum phase characteristics. The enlarged PIF sets (in fact, suitably inscribed polytopes) are used as terminal sets in the dual prediction mode paradigm of MPC (model predictive control). The second order bilinear system whose OIOFL has one stable and one unstable equilibrium point is used to illustrate the benefits (in terms of PIF enlargement) of the proposed algorithm in dual prediction mode MPC.
Reviewer: Ingmar Randvee (Tallinn)
MSC:
| 93B40 | Computational methods in systems theory (MSC2010) |
| 93B51 | Design techniques (robust design, computer-aided design, etc.) |
| 93C10 | Nonlinear systems in control theory |
Keywords:
predictive control; bilinear systems; feedback linearization; invariant sets; terminal setsReferences:
| [1] | Bacic M, IEEE Transactions on Automatic Control 48 pp pp. 1443–1447– (2003) |
| [2] | DOI: 10.1016/0005-1098(71)90066-5 · Zbl 0215.21801 · doi:10.1016/0005-1098(71)90066-5 |
| [3] | Blanchini F, Automatica 35 pp pp. 1747–1767– (1999) |
| [4] | Chen H, University of Stutgart (1997) |
| [5] | Doyle FJ, Proc. Amer. Control Conf pp pp. 2571–2575– (1992) |
| [6] | Doyle FJ, IEEE Transactions on Automatic Control 41 pp pp. 305–309– (2003) |
| [7] | DOI: 10.1109/9.871769 · Zbl 0988.93022 · doi:10.1109/9.871769 |
| [8] | DOI: 10.1016/S0005-1098(99)00214-9 · Zbl 0949.93003 · doi:10.1016/S0005-1098(99)00214-9 |
| [9] | Niemiec M, Non-linear Predictive Control – Theory and Practice pp pp. 107–130– (2001) |
| [10] | DOI: 10.1080/00207179608921835 · Zbl 0849.93026 · doi:10.1080/00207179608921835 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
