On the design of Robust tube-based MPC for tracking

Limón, Daniel; Alvarado, I.; Álamo, T.; Camacho, Eduardo F.

doi:10.3182/20080706-5-kr-1001.02593

Cited by 34 publications

(47 citation statements)

References 8 publications

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“…The optimization problem then becomes the minimization described in (3 [31,32], Limon et al [3,33], and Mayne et al [27,28,34,35] expanding the concept into robust output-feedback, tracking, and nonlinear problems.…”

Section: Incorporating Input and State Constraintsmentioning

confidence: 99%

“…A further difficulty is introduced if the target point is arbitrarily shifted off of the origin, which requires the terminal set to be re-computed for each new steady state in order to ensure feasibility. The work by Alvarado et al [31,32] and Limon et al [3,4,33] developed a Tube-based robust model predictive controller for tracking which moves this determination online and introduced an artificial steady state as an additional optimization problem decision variable. The tracking offset is limited by an additional penalizing term in the optimization problem and the terminal set re-computation is avoided using an invariant set for tracking [32].…”

Section: The State-feedback Tube-based Robust Mpc For Trackingmentioning

confidence: 99%

“…The state-feedback case for tracking will be outlined in this section, following from [2][3][4][31][32][33]. A practical implementation is conducted for a sample problem in the next chapter to describe how this theory is put to use.…”

Section: The State-feedback Tube-based Robust Mpc For Trackingmentioning

confidence: 99%

“…where the vector ∈ ℝ is a parameter vector characterizing any solution and and are suitably chosen matrices. In [2,33], it is advocated that and be defined using the singular value decomposition (SVD)…”

Section: Set Point Characterizationmentioning

confidence: 99%

“…Selecting a larger Ω results in a larger domain of attraction, and thereby a larger invariant set for tracking. It is common to choose Ω to be the LQR gain [33].…”

Section: The Invariant Set For Trackingmentioning

confidence: 99%

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Tube-Based Model Predictive Control for the Approach Maneuver of a Spacecraft to a Free-Tumbling Target Satellite

Buckner

Lampariello

2018

2018 Annual American Control Conference (ACC)

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I would also like to thank my family. Nik, Rufus, Sophie, and Anni, have provided me with a constant environment of love and support, stayed up the long nights with me, and, kept me in coffee and chocolate. Thank you for doing this with me. This would not have been possible without you. To my parents, my brothers, and Hartmut and Heidi, thank you for your constant support, in its various forms, and interest in my work. I love you all.

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Section: Incorporating Input and State Constraintsmentioning

confidence: 99%

Section: The State-feedback Tube-based Robust Mpc For Trackingmentioning

confidence: 99%

Section: The State-feedback Tube-based Robust Mpc For Trackingmentioning

confidence: 99%

Section: Set Point Characterizationmentioning

confidence: 99%

“…Selecting a larger Ω results in a larger domain of attraction, and thereby a larger invariant set for tracking. It is common to choose Ω to be the LQR gain [33].…”

Section: The Invariant Set For Trackingmentioning

confidence: 99%

See 3 more Smart Citations

Tube-Based Model Predictive Control for the Approach Maneuver of a Spacecraft to a Free-Tumbling Target Satellite

Buckner

Lampariello

2018

2018 Annual American Control Conference (ACC)

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Robust MPC for linear systems with bounded disturbances based on admissible equilibria sets

Santos

Cunha

2021

Intl J Robust & Nonlinear

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This article presents a robust model predictive control (MPC) for piecewise constant reference tracking based on a constrained linear model and a terminal constraint defined from the admissible equilibria set. The new robust MPC algorithm based on nominal predictions ensures recursive feasibility and convergence to an optimal target, but the terminal constraint is derived from an admissible equilibria set with a suitable disturbance translation. The computation of the proposed terminal constraint is simple because no subset verification is required and the number of half-spaces of the proposed terminal constraint is fixed a priori. A zonotope disturbance bound description is used to simplify the computation of the admissible equilibria. Furthermore, it is shown that the proposed strategy can be directly extended to other MPC algorithms based on artificial targets, as a stochastic MPC based on the individual chance constraints, for instance. Two case studies are used to illustrate the usefulness of the proposed robust MPC for piecewise constant set-point tracking based on nominal predictions.

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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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On the design of Robust tube-based MPC for tracking

Cited by 34 publications

References 8 publications

Tube-Based Model Predictive Control for the Approach Maneuver of a Spacecraft to a Free-Tumbling Target Satellite

Tube-Based Model Predictive Control for the Approach Maneuver of a Spacecraft to a Free-Tumbling Target Satellite

Robust MPC for linear systems with bounded disturbances based on admissible equilibria sets

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

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