Robust MPC via min–max differential inequalities

Villanueva, Mario E.; Quirynen, Rien; Diehl, Moritz; Chachuat, Benoît; Houska, Boris

doi:10.1016/j.automatica.2016.11.022

Cited by 93 publications

(65 citation statements)

References 37 publications

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“…In [21], the tube is parametrized with online optimized matrices P t ∈ R n×n , i.e., X t = {x| x t − x 2 Pt ≤ 1}, where (6c) is ensured using min-max differential inequalities.…”

Section: Setup and General Theorymentioning

confidence: 99%

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

123

133

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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 L2 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.

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“…In [21], the tube is parametrized with online optimized matrices P t ∈ R n×n , i.e., X t = {x| x t − x 2 Pt ≤ 1}, where (6c) is ensured using min-max differential inequalities.…”

Section: Setup and General Theorymentioning

confidence: 99%

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

123

133

View full text Add to dashboard Cite

show abstract

“…3 Vincent Berenz is with the Autonomous Motion Department at the Max Planck Institute for Intelligent Systems, 72076 Tübingen, Germany (vberenz@tuebingen.mpg.de). 4 Sebastian Trimpe is with the Intelligent Control Systems Group, Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany (trimpe@is.mpg.de).…”

Section: Introductionmentioning

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.

134

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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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“…During the past two decades, there have been many suggestions on how to increase the robustness of nominal model predictive control schemes by taking external disturbance models into account [20]. An in-depth review of the numerous approaches, for example, based on min-max robust dynamic programming [3], scenario-tree MPC [28], [5], semidefinite programming reformulations [15], uncertainty-affine feedback parameterizations [8], as well as modern Tube MPC formulations [22], [29] would certainly go beyond the scope of this paper. However, we refer to [22] and [12] for review articles of existing robust MPC approaches.…”

Section: Introductionmentioning

confidence: 99%

Parallel Explicit Tube Model Predictive Control

Wang

Jiang

Oravec

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This paper is about a parallel algorithm for tube-based model predictive control. The proposed control algorithm solves robust model predictive control problems suboptimally, while exploiting their structure. This is achieved by implementing a real-time algorithm that iterates between the evaluation of piecewise affine functions, corresponding to the parametric solution of small-scale robust MPC problems, and the online solution of structured equality constrained QPs. The performance of the associated real-time robust MPC controllers is illustrated by a numerical case study.

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Robust MPC via min–max differential inequalities

Cited by 93 publications

References 37 publications

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

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

Parallel Explicit Tube Model Predictive Control

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