A robust adaptive model predictive control framework for nonlinear uncertain systems

In this paper, 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...

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Published in:arXiv.org
Main Authors: Köhler, Johannes, Kötting, Peter, Soloperto, Raffaele, Allgöwer, Frank, Müller, Matthias A
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 20.10.2020
Subjects:
Adaptive control
Algorithms
Constraint modelling
Disturbances
Feasibility
Liapunov functions
Nonlinear control
Nonlinear systems
Parameter estimation
Predictive control
Robust control
Robustness (mathematics)
Uncertainty
ISSN:2331-8422
Online Access:Get full text
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Summary:In this paper, 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 to 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 \(\mathcal{L}_2\) stability w.r.t. additive disturbances. As a first contribution we derive suitable monotonicity and non-increasing 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 paper, 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 to state of the art approaches.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
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ISSN:2331-8422
DOI:10.48550/arxiv.1911.02899