Learning an Approximate Model Predictive Controller With Guarantees

Hertneck, Michael; Köhler, Johannes; Trimpe, Sebastian; Allgöwer, Frank

doi:10.1109/lcsys.2018.2843682

Cited by 196 publications

(113 citation statements)

References 24 publications

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“…Proof. The proof is analogous to [19], except for the satisfaction of the terminal constraint, which is guaranteed by Assumption 4, compare also [48,Thm. 7].…”

Section: ) Robust Tracking Mpcmentioning

confidence: 97%

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A Nonlinear Model Predictive Control Framework Using Reference Generic Terminal Ingredients

Köhler

Müller

Allgöwer

2020

IEEE Trans. Automat. Contr.

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In this paper, we present a quasi infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi infinite horizon terminal cost. As a result we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. As a corollary, the terminal cost can also be used to design nonlinear MPC schemes that reliably operate under online changing conditions, including unreachable reference signals. The practicality of this approach is demonstrated with a benchmark example.

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“…Proof. The proof is analogous to [19], except for the satisfaction of the terminal constraint, which is guaranteed by Assumption 4, compare also [48,Thm. 7].…”

Section: ) Robust Tracking Mpcmentioning

confidence: 97%

“…In [19] the robust constraint tightening is considered for an MPC scheme without terminal constraints, compare Remark 4. Some details regarding the extension/modification of the robust MPC scheme to a setting with terminal constraints are based on [48].…”

Section: ) Terminal Ingredientsmentioning

confidence: 99%

A Nonlinear Model Predictive Control Framework Using Reference Generic Terminal Ingredients

Köhler

Müller

Allgöwer

2020

IEEE Trans. Automat. Contr.

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“…However, it is possible to make statistical statements about π approx using Hoeffding's inequality [21]. For the statistical guarantees, we adopt the approach from [13] and use our improved validation criterion as introduced in Proposition 2.…”

Section: Proposition 2 Let Assumption 1 Hold Suppose the Model Mismmentioning

confidence: 99%

“…3) Algorithm: The overall procedure for the AMPC is summarized in Algorithm 3, based on Hertneck et al in [13].…”

Section: Proposition 2 Let Assumption 1 Hold Suppose the Model Mismmentioning

confidence: 99%

Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control

Nubert

Köhler

Berenz

et al. 2020

IEEE Robot. Autom. Lett.

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136

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Fast feedback control and safety guarantees are essential in modern robotics. We present an approach that achieves both by combining novel robust model predictive control (MPC) with function approximation via (deep) neural networks (NNs). The result is a new approach for complex tasks with nonlinear, uncertain, and constrained dynamics as are common in robotics. Specifically, we leverage recent results in MPC research to propose a new robust setpoint tracking MPC algorithm, which achieves reliable and safe tracking of a dynamic setpoint while guaranteeing stability and constraint satisfaction. The presented robust MPC scheme constitutes a one-layer approach that unifies the often separated planning and control layers, by directly computing the control command based on a reference and possibly obstacle positions. As a separate contribution, we show how the computation time of the MPC can be drastically reduced by approximating the MPC law with a NN controller. The NN is trained and validated from offline samples of the MPC, yielding statistical guarantees, and used in lieu thereof at run time. Our experiments on a state-of-the-art robot manipulator are the first to show that both the proposed robust and approximate MPC schemes scale to real-world robotic systems.

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“…Although there are some novel results in the research on guarantees, e.g. [11], [12], the problem is still open.…”

Section: Introductionmentioning

confidence: 99%

Performance Guarantees on Machine-Learning-based Overtaking Strategies for Autonomous Vehicles

Németh

Hegedüs

Gáspár

2020

2020 European Control Conference (ECC)

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The control of autonomous vehicles in overtaking scenarios is an important challenge, in which an autonomous vehicle in a multiple vehicle environment must be safely driven. Due to the complexity of vehicle scenarios, several machinelearning-based design strategies have been developed, which provide outstanding results. However, in most of these methods it is difficult to provide a theoretical guarantee on the most important performance of the overtaking strategy, i.e., the avoidance of collisions with the surrounding vehicles. This paper proposes a design architecture with which this performance can be guaranteed. The method is based on the robust control framework and it is independent from the structure of the machine-learning-based agent. The effectiveness of the method is illustrated through simulation examples.

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Learning an Approximate Model Predictive Controller With Guarantees

Cited by 196 publications

References 24 publications

A Nonlinear Model Predictive Control Framework Using Reference Generic Terminal Ingredients

A Nonlinear Model Predictive Control Framework Using Reference Generic Terminal Ingredients

Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control

Performance Guarantees on Machine-Learning-based Overtaking Strategies for Autonomous Vehicles

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