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 -