Details
| Original language | English |
|---|---|
| Pages (from-to) | 4987-5001 |
| Number of pages | 15 |
| Journal | International Journal of Robust and Nonlinear Control |
| Volume | 29 |
| Issue number | 15 |
| Early online date | 5 Sept 2017 |
| Publication status | Published - 1 Oct 2019 |
| Externally published | Yes |
Abstract
Sufficient conditions for the stability of stochastic model predictive control without terminal cost and terminal constraints are derived. Analogous to stability proofs in the nominal setup, we first provide results for the case of optimization over general feedback laws and exact propagation of the probability density functions of the predicted states. We highlight why these results, being based on the principle of optimality, do not directly extend to currently used computationally tractable approximations such as optimization over parameterized feedback laws and relaxation of the chance constraints. Based thereon, for both cases, stability results are derived under stronger assumptions. A third approach is presented for linear systems where propagation of the mean value and the covariance matrix of the states instead of the complete distribution is sufficient, and hence, the principle of optimality can be used again. The main results are presented for nonlinear systems along with examples and computational simplifications for linear systems.
Keywords
- constrained control, MPC without terminal constraints, nonlinear systems, stochastic model predictive control
ASJC Scopus subject areas
- Engineering(all)
- Mechanical Engineering
- Engineering(all)
- Aerospace Engineering
- Chemical Engineering(all)
- General Chemical Engineering
- Engineering(all)
- Electrical and Electronic Engineering
- Engineering(all)
- Control and Systems Engineering
- Engineering(all)
- Industrial and Manufacturing Engineering
- Engineering(all)
- Biomedical Engineering
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In: International Journal of Robust and Nonlinear Control, Vol. 29, No. 15, 01.10.2019, p. 4987-5001.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stochastic model predictive control without terminal constraints
AU - Lorenzen, Matthias
AU - Müller, Matthias A.
AU - Allgöwer, Frank
N1 - Funding information: Financial support of the project by the German Research Foundation (DFG) through the research grants MU3929/1-1 and AL316/12-1, as well as within the Cluster of Excellence in Simulation Technology (EXC 310/2) at the University of Stuttgart is gratefully acknowledged. Matthias A. Müller is indebted to the Baden-Württemberg Stiftung for financial support of this research project by the Eliteprogramme for Postdocs.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - Sufficient conditions for the stability of stochastic model predictive control without terminal cost and terminal constraints are derived. Analogous to stability proofs in the nominal setup, we first provide results for the case of optimization over general feedback laws and exact propagation of the probability density functions of the predicted states. We highlight why these results, being based on the principle of optimality, do not directly extend to currently used computationally tractable approximations such as optimization over parameterized feedback laws and relaxation of the chance constraints. Based thereon, for both cases, stability results are derived under stronger assumptions. A third approach is presented for linear systems where propagation of the mean value and the covariance matrix of the states instead of the complete distribution is sufficient, and hence, the principle of optimality can be used again. The main results are presented for nonlinear systems along with examples and computational simplifications for linear systems.
AB - Sufficient conditions for the stability of stochastic model predictive control without terminal cost and terminal constraints are derived. Analogous to stability proofs in the nominal setup, we first provide results for the case of optimization over general feedback laws and exact propagation of the probability density functions of the predicted states. We highlight why these results, being based on the principle of optimality, do not directly extend to currently used computationally tractable approximations such as optimization over parameterized feedback laws and relaxation of the chance constraints. Based thereon, for both cases, stability results are derived under stronger assumptions. A third approach is presented for linear systems where propagation of the mean value and the covariance matrix of the states instead of the complete distribution is sufficient, and hence, the principle of optimality can be used again. The main results are presented for nonlinear systems along with examples and computational simplifications for linear systems.
KW - constrained control
KW - MPC without terminal constraints
KW - nonlinear systems
KW - stochastic model predictive control
UR - http://www.scopus.com/inward/record.url?scp=85028769089&partnerID=8YFLogxK
U2 - 10.1002/rnc.3912
DO - 10.1002/rnc.3912
M3 - Article
VL - 29
SP - 4987
EP - 5001
JO - International Journal of Robust and Nonlinear Control
JF - International Journal of Robust and Nonlinear Control
SN - 1049-8923
IS - 15
ER -