Efficient computation of RPI sets for tube-based robust MPC

Darup, Moritz Schulze; Teichrib, Dieter

doi:10.23919/ecc.2019.8796265

Cited by 4 publications

(17 citation statements)

References 14 publications

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“…A. Darup and Teichrib, [9] This work combines the advantages of both [10] and [11] to yield an algorithm that is more efficient than [11] and can generate RPI sets that are less conservative than [10]. This is accomplished by first using the techniques presented in [11] to compute, for the user defined ≥ 0, the value k * such that…”

Section: Proposed Rpi Set Computation Methodsmentioning

confidence: 99%

“…In (9) the symmetric, positive definite cost matrices Q and R are chosen to be the same as in (4). Additional design variables for the problem include the terminal cost matrix P , the terminal set X N , and the constraint sets Z and Ū.…”

Section: Online Optimization Problemmentioning

confidence: 99%

“…However this can easily be fixed by enlarging ∆ by an arbitrarily small amount as needed. Finally, we also make an assumption (see [9], [10]) that the minimal RPI set for (12) satisfies ER ∞ ⊆ Φ o where Φ o denotes the interior of Φ.…”

Section: G Computing Rmentioning

confidence: 99%

“…The method in [11] could be employed to obtain a small RPI set, but this would require computationally expensive Minkowski additions. One computationally viable option that could yield a small R is given by [9], however in this work we choose to use a novel method that is described in Section V which is an extension to [9] and [12].…”

Section: G Computing Rmentioning

confidence: 99%

“…The Minkowski sum of two sets A and B is defined as A ⊕ B := {a + b | a ∈ A, b ∈ B}, and is known to be a computationally expensive operation that scales poorly with the dimension and complexity of the sets. To overcome this challenge, we leverage the work in [9] where an approach for the efficient computation of RPI sets is developed based on a clever combination of the methods in [10] and [11]. We also take advantage of the work by [12], who proposes a method for computing RPI sets requires only a single linear program.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Simple and Efficient Tube-based Robust Output Feedback Model Predictive Control Scheme

Lorenzetti¹,

Pavone²

2019

Preprint

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The control of constrained systems using model predictive control (MPC) becomes more challenging when full state information is not available and when the nominal system model and measurements are corrupted by noise. Since these conditions are often seen in practical scenarios, techniques such as robust output feedback MPC have been developed to address them. However, existing approaches to robust output feedback MPC are still challenged by increased complexity of the online optimization problem, increased computational requirements for controller synthesis, or both. In this work we present a simple and efficient methodology for synthesizing a tube-based robust output feedback MPC scheme for linear, discrete, timeinvariant systems subject to bounded, additive disturbances. Specifically, we completely avoid the use of Minkowski addition during controller synthesis and the online optimization problem has the same complexity as in the nominal full state feedback MPC problem, enabling our approach to scale with system dimension more effectively than previously proposed schemes.

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Section: Proposed Rpi Set Computation Methodsmentioning

confidence: 99%

Section: Online Optimization Problemmentioning

confidence: 99%

Section: G Computing Rmentioning

confidence: 99%

Section: G Computing Rmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Simple and Efficient Tube-based Robust Output Feedback Model Predictive Control Scheme

Lorenzetti¹,

Pavone²

2019

Preprint

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Nonlinear learning‐based model predictive control supporting state and input dependent model uncertainty estimates

Wabersich

Zeilinger

2021

Intl J Robust & Nonlinear

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While model predictive control (MPC) methods have proven their efficacy when applied to systems with safety specifications and physical limitations, their performance heavily relies on an accurate prediction model. As a consequence, a significant effort in the design of MPC controllers is dedicated to the modeling part and often requires advanced physical expertise. In order to facilitate the controller design, we present an MPC scheme supporting nonlinear learning-based prediction models, that is, data-driven models with probabilistic parameter uncertainties. A tube-based MPC formulation in combination with an additional implicit state and input constraint forces the closed-loop system to be operated in domains of sufficient model confidence, thereby ensuring asymptotic stability and constraint satisfaction at a prespecified level of probability. Furthermore, by relying on tube-based MPC concepts, the proposed learning-based MPC formulation offers a general framework for addressing different problem classes, such as economic MPC, while providing a general interface to probabilistic prediction models based, for example, on Bayesian regression or Gaussian processes.A design procedure is proposed for approximately linear systems and the efficiency of the method is illustrated using numerical examples.

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Distributed Economic MPC for Dynamically Coupled Systems With Stochastic Disturbances

Zhou,

Dai,

et al. 2023

IEEE Trans. Circuits Syst. I

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Efficient computation of RPI sets for tube-based robust MPC

Cited by 4 publications

References 14 publications

A Simple and Efficient Tube-based Robust Output Feedback Model Predictive Control Scheme

A Simple and Efficient Tube-based Robust Output Feedback Model Predictive Control Scheme

Nonlinear learning‐based model predictive control supporting state and input dependent model uncertainty estimates

Distributed Economic MPC for Dynamically Coupled Systems With Stochastic Disturbances

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