Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended version

Köhler, Johannes; Andina, Elisa; Soloperto, Raffaele; Müller, Matthias A.; Allgöwer, Frank

doi:10.48550/arxiv.1909.01813

Cited by 7 publications

(56 citation statements)

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“…This is a common problem setup used in robust adaptive model predictive control frameworks, see e.g. [12], [13] and [14]. The uncertain parameters θ are assumed to enter the dynamics (1) affinely as follows:…”

Section: A Problem Descriptionmentioning

confidence: 99%

“…Ellipsoidal RPI sets for linear feedback controllers can be computed through semi-definite programming, see e.g. [19] and [14,Appendix].…”

Section: A Adaptive Model Predictive Safety Certification Algorithmmentioning

confidence: 99%

“…Due to the uncertain model, the computation of the re-quired backup trajectory can be conservative, motivating the use of recent advances in robust adaptive MPC schemes [12], [13], [14] and [15]. At every time step k, we compute a tube in the state space starting from the current state measurement x k , which is guaranteed to contain the future states for any disturbances in W and uncertain parameters in Θ k through the use of a tube control law κ : R n × R nv → R m with n v parameters.…”

Section: A Adaptive Model Predictive Safety Certification Algorithmmentioning

confidence: 99%

“…Under Assumption 3, recursive feasibility of (4) can be shown. Note that this generalised assumption contains specific robust adaptive MPC formulation such as [12], [13], [14] and [15] as special cases.…”

Section: A Recursively Feasible Mpsc Schemementioning

confidence: 99%

“…The proposed scheme allows to augment any learning-based controller such that state and input constraint satisfaction properties are ensured for all future time steps. Instead of performing episodic model learning updates, we leverage recent results from adaptive MPC literature, see [12], [13], [14] and [15], to estimate uncertain parameters in the system dynamics online. By using setmembership estimation, implausible model parametrisations are recursively eliminated, see [16].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Model Predictive Safety Certification for Learning-based Control -- Extended Version

Didier,

Wabersich,

Zeilinger

2021

Preprint

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We propose an adaptive Model Predictive Safety Certification (MPSC) scheme for learning-based control of linear systems with bounded disturbances and uncertain parameters with known bounds. An MPSC is a modular framework, which can be used in combination with any learning-based controller to ensure state and input constraint satisfaction of a dynamical system by solving an online optimisation problem. By continuously connecting the current system state with a safe terminal set using a robust tube, safety can be ensured. Thereby, the main sources of conservative safety interventions are model uncertainties and short planning horizons. We develop an adaptive mechanism to improve the system model, which leverages set-membership estimation to guarantee recursively feasible and non-decreasing safety performance improvements. In order to accommodate short prediction horizons, iterative safe set enlargements using previously computed robust backup plans are proposed. Finally, we illustrate the increase of the safety performance through the parameter and safe set adaptation for numerical examples with up to 16 state dimensions.

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Section: A Problem Descriptionmentioning

confidence: 99%

“…Ellipsoidal RPI sets for linear feedback controllers can be computed through semi-definite programming, see e.g. [19] and [14,Appendix].…”

Section: A Adaptive Model Predictive Safety Certification Algorithmmentioning

confidence: 99%

Section: A Adaptive Model Predictive Safety Certification Algorithmmentioning

confidence: 99%

Section: A Recursively Feasible Mpsc Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive Model Predictive Safety Certification for Learning-based Control -- Extended Version

Didier,

Wabersich,

Zeilinger

2021

Preprint

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A robust adaptive model predictive control framework for nonlinear uncertain systems

Köhler

Kötting

Soloperto

et al. 2020

Intl J Robust & Nonlinear

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Summary 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 ℒ2 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.

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Adaptive Robust Model Predictive Control for Bilateral Teleoperation

Almasalmah,

Omran,

Liu

et al. 2023

2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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In this work, we use recent developments in the field of adaptive robust Model Predictive Control (MPC) to build a controller for bilateral teleoperation systems. To guarantee robust constraint satisfaction, we incorporate polytopic tube controllers in the MPC design. In addition, we use online learning methods to learn the environment model. Namely, we use set membership learning to learn the parametric uncertainty bounds and reduce the conservatism of the robust controller, and we combine it with least mean square method to learn a point estimate of the model parameters, which enhances the controller performance. Our simulation demonstrates the effectiveness of the proposed approach in maintaining robust constraint satisfaction and enhancing performance by learning during teleoperation tasks.

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Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended version

Cited by 7 publications

References 0 publications

Adaptive Model Predictive Safety Certification for Learning-based Control -- Extended Version

Adaptive Model Predictive Safety Certification for Learning-based Control -- Extended Version

A robust adaptive model predictive control framework for nonlinear uncertain systems

Adaptive Robust Model Predictive Control for Bilateral Teleoperation

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