Homothetic tube MPC for constrained linear difference inclusions

Raković, Sas̆a V.; Cheng, Qifeng

doi:10.1109/ccdc.2013.6561023

Cited by 17 publications

(33 citation statements)

References 13 publications

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“…Furthermore, the more flexible parameterization reduces the conservatism at the expense of more decision variables. In [11], a homothetic tube [5], [29] is used, where online optimized matrices Λ j k|t characterize the tube propagation as follows…”

Section: Remark 2 (Complexity and Conservatism Of Robust Mpc Methods)mentioning

confidence: 99%

“…In the considered scenario, the tube size computed using the formula (30) is equivalent to the proposed approach (28), which implies that the conservatism of using d ≥ d i is negligible in this example. The simplified formula (29) is significantly more conservative, resulting in approximately 3-times the tube size s.…”

Section: Complexity Robust Mpcmentioning

confidence: 99%

“…These trade-offs between complexity and conservatism are, however, very problem specific. In this example the uncertainty is mainly due to the parametric uncertainty, which is why (28) and (30) are approximately equivalent and (29), which overapproximates the effect of the parametric uncertainty, is so conservative.…”

Section: Complexity Robust Mpcmentioning

confidence: 99%

“…Since the functionw η satisfies the same properties, we can also use this function to reduce the computational demand. The tube propagation (29) can be implemented using…”

Section: A Polytopic Tubementioning

confidence: 99%

“…This implementation uses r(1 + 2 pB ) linear inequality constraints and an additional auxiliary variable g. Thus, in case p B << p, this can lead to a significant reduction in the computational complexity. Furthermore, for p B = 0, the auxiliary variable g is not necessary and the constraint can be directly implemented using (29) with r linear inequality constraints. Compared to (28) this formulation can be significantly more conservative, compare numerical example.…”

Section: A Polytopic Tubementioning

confidence: 99%

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Linear robust adaptive model predictive control: Computational complexity and conservatism

Köhler

Andina

Soloperto

et al. 2019

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

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In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with theoretical guarantees (constraint satisfaction and stability), while allowing for reduced conservatism and improved performance due to online parameter adaptation. A moving window parameter set identification is used to compute a fixed complexity parameter set based on past data. Robust constraint satisfaction is achieved by using a computationally efficient tube based robust MPC method. The predicted cost function is based on a least mean squares point estimate, which ensures finite-gain L2 stability of the closed loop. The overall algorithm has a fixed (user specified) computational complexity. We illustrate the applicability of the approach and the trade-off between conservatism and computational complexity using a numerical example.

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Section: Remark 2 (Complexity and Conservatism Of Robust Mpc Methods)mentioning

confidence: 99%

Section: Complexity Robust Mpcmentioning

confidence: 99%

Section: Complexity Robust Mpcmentioning

confidence: 99%

“…Since the functionw η satisfies the same properties, we can also use this function to reduce the computational demand. The tube propagation (29) can be implemented using…”

Section: A Polytopic Tubementioning

confidence: 99%

Section: A Polytopic Tubementioning

confidence: 99%

See 3 more Smart Citations

Linear robust adaptive model predictive control: Computational complexity and conservatism

Köhler

Andina

Soloperto

et al. 2019

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

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Robust adaptive tube tracking model predictive control for piece‐wise constant reference signals

Peschke¹,

Görges²

2023

Intl J Robust & Nonlinear

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Robust tracking of piece‐wise constant reference signals for constrained systems with parametric plant uncertainty and additive disturbances is addressed in this paper. The parametric uncertainty is decreased online by set‐membership estimation and a nominal model is updated for improving set‐point tracking. The online estimated parametric uncertainty is used for an online‐determined terminal set which enlarges the set of reachable references close to the system constraints when compared to an offline worst‐case consideration. An artificial target state is introduced which can deviate from the nominal target state. This new target state is used to ensure recursive feasibility for unreachable references and changes in the reference signal. Moreover, a novel “recovery mode” is specified which is deployed in case the new nominal model yields an infeasible control problem. Control algorithms are developed for time‐invariant systems and systems with arbitrarily fast changing plants but known relative bounds. Constraint satisfaction and ‐stability are guaranteed for the proposed algorithms. Controlling the engine load of a self‐propelled work machine is used as a practical example.

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