Details
| Original language | English |
|---|---|
| Pages (from-to) | 8725-8749 |
| Number of pages | 25 |
| Journal | International Journal of Robust and Nonlinear Control |
| Volume | 31 |
| Issue number | 18 |
| Early online date | 24 Aug 2020 |
| Publication status | Published - 18 Nov 2021 |
Abstract
In this article, we present a tube-based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set-membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared with robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean-squared point estimate in the objective function the framework ensures finite-gain (Formula presented.) stability w.r.t. additive disturbances. As a first contribution we derive suitable monotonicity and nonincreasing properties on general parameter estimation algorithms and tube/set-based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this article, we provide similar conditions for a tube-based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared with state of the art approaches.
Keywords
- adaptive control, constrained control, nonlinear model predictive control, uncertain systems
ASJC Scopus subject areas
- Engineering(all)
- Mechanical Engineering
- Engineering(all)
- Aerospace Engineering
- Chemical Engineering(all)
- Engineering(all)
- Electrical and Electronic Engineering
- Engineering(all)
- Control and Systems Engineering
- Engineering(all)
- Industrial and Manufacturing Engineering
- Engineering(all)
- Biomedical Engineering
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: International Journal of Robust and Nonlinear Control, Vol. 31, No. 18, 18.11.2021, p. 8725-8749.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A robust adaptive model predictive control framework for nonlinear uncertain systems
AU - Köhler, Johannes
AU - Kötting, Peter
AU - Soloperto, Raffaele
AU - Allgöwer, Frank
AU - Müller, Matthias A.
N1 - Funding Information: information Deutsche Forschungsgemeinschaft, AL 316/12-2; GRK 2198/1; MU 3929/1-2; International Max Planck Research School for Intelligent Systems (IMPRS-IS)This work was supported by the German Research Foundation under Grants GRK 2198/1-277536708, AL 316/12-2, and MU 3929/1-2-279734922. The authors thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting R.S.
PY - 2021/11/18
Y1 - 2021/11/18
N2 - In this article, we present a tube-based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set-membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared with robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean-squared point estimate in the objective function the framework ensures finite-gain (Formula presented.) stability w.r.t. additive disturbances. As a first contribution we derive suitable monotonicity and nonincreasing properties on general parameter estimation algorithms and tube/set-based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this article, we provide similar conditions for a tube-based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared with state of the art approaches.
AB - In this article, we present a tube-based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set-membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared with robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean-squared point estimate in the objective function the framework ensures finite-gain (Formula presented.) stability w.r.t. additive disturbances. As a first contribution we derive suitable monotonicity and nonincreasing properties on general parameter estimation algorithms and tube/set-based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this article, we provide similar conditions for a tube-based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared with state of the art approaches.
KW - adaptive control
KW - constrained control
KW - nonlinear model predictive control
KW - uncertain systems
UR - http://www.scopus.com/inward/record.url?scp=85089675183&partnerID=8YFLogxK
U2 - 10.1002/rnc.5147
DO - 10.1002/rnc.5147
M3 - Article
VL - 31
SP - 8725
EP - 8749
JO - International Journal of Robust and Nonlinear Control
JF - International Journal of Robust and Nonlinear Control
SN - 1049-8923
IS - 18
ER -