Learning-based Robust Model Predictive Control for Sector-bounded Lur’e Systems

Seel, Katrine; Haring, Mark; Grøtli, Esten Ingar; Pettersen, Kristin Y.; Gravdahl, Jan Tommy

doi:10.1016/j.ifacol.2021.11.151

Cited by 3 publications

(8 citation statements)

References 7 publications

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“…So-called point-wise IQCs have been very recently considered, for example, in 20 and are inequalities of the form (IQC), but with the restriction 𝑍 = 0 which can be severe. Even for 𝑍 ≠ 0 and due to the vanishing initial condition of the filter in (5), it is immediate that (9) holds if (IQC) is satisfied; the converse does not hold, in general. Hence, demanding that Δ satisfies a point-wise IQC with storage is more restrictive than requiring it to satisfy a finite-horizon IQC with terminal cost and less than requiring it to satisfy a point-wise IQC 1 .…”

Section: Remark 1 Relation To Other Notions Of Iqcsmentioning

confidence: 99%

“…Moreover, we suppose that the map 𝑧  → 𝑧−𝐷𝑓 (𝑧) is bijective which means that the interconnection ( 11) is well-posed. Finally, we assume that the feedback operator satisfies (IQC) for some given stable LTI filter Ψ with realization as given in (5).…”

Section: Mpc Setupmentioning

confidence: 99%

“…In order to thoroughly debate the proposed MPC formulation synthesized with the IQC arguments, we compare it to the standard approach in the literature involving Lyapunov arguments to handle the nonlinearity using the sector condition, as done in 5,6,7 . Henceforth, we refer to this approach as traditional MPC and recall that the corresponding terminal ingredients are synthesized using Corollary 1 with  =  DG (see Remark 3).…”

Section: Numerical Examplementioning

confidence: 99%

“…Regarding the control of Lur'e systems, which are addressed in this work, the usual approach in the MPC literature (e.g. 3,4,5,6,7 ) is to replace the nonlinear interconnection equation constraint by sector conditions applied over the interconnection signals, e.g. 8,9 .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stabilizing Model Predictive Control Synthesis using Integral Quadratic Constraints and Full-Block Multipliers*

Morato

Holicki

Scherer

2023

Preprint

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In this paper, we discuss how to synthesize stabilizing Model Predictive Control (MPC) algorithms based on convexly parameterized Integral Quadratic Constraints (IQCs), with the aid of general multipliers. Specifically, we consider Lur’e systems subject to sector-bounded and slope-restricted nonlinearities. As the main novelty, we introduce point-wise IQCs with storage in order to accordingly generate the MPC terminal ingredients, thus enabling closed-loop stability, strict dissipativity with regard to the nonlinear feedback, and recursive feasibility of the optimization. Specifically, we consider formulations involving both static and dynamic multipliers, and provide corresponding algorithms for the synthesis procedures. The major benefit of the proposed approach resides in the flexibility of the IQC framework, which is capable to deal with many classes of uncertainties and nonlinearities. Moreover, for the considered class of nonlinearities, our method yields larger regions of attraction of the synthesized predictive controllers (with reduced conservatism) if compared to the standard approach to deal with sector constraints from the literature.

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Section: Remark 1 Relation To Other Notions Of Iqcsmentioning

confidence: 99%

Section: Mpc Setupmentioning

confidence: 99%

Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stabilizing Model Predictive Control Synthesis using Integral Quadratic Constraints and Full-Block Multipliers*

Morato

Holicki

Scherer

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In order to thoroughly debate the proposed MPC formulation synthesized with the IQC arguments, we compare it to the standard approach in the literature involving Lyapunov arguments to handle the nonlinearity using the sector condition, as done in References 5‐7. Henceforth, we refer to this approach as traditional MPC and recall that the corresponding terminal ingredients are synthesized using Corollary 1 with

𝒩 = 𝒩_{DG}

(see Remark 3).…”

Section: Numerical Examplementioning

confidence: 99%

Stabilizing model predictive control synthesis using integral quadratic constraints and full‐block multipliers

Morato,

Holicki,

Scherer

2023

Intl J Robust & Nonlinear

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SummaryIn this paper, we discuss how to synthesize stabilizing model predictive control (MPC) algorithms based on convexly parameterized integral quadratic constraints (IQCs), with the aid of general multipliers. Specifically, we consider Lur'e systems subject to sector‐bounded and slope‐restricted nonlinearities. As the main novelty, we introduce point‐wise IQCs with storage in order to accordingly generate the MPC terminal ingredients, thus enabling closed‐loop stability, strict dissipativity with regard to the nonlinear feedback, and recursive feasibility of the optimization. Specifically, we consider formulations involving both static and dynamic multipliers, and provide corresponding algorithms for the synthesis procedures. The major benefit of the proposed approach resides in the flexibility of the IQC framework, which is capable to deal with many classes of uncertainties and nonlinearities. Moreover, for the considered class of nonlinearities, our method yields larger regions of attraction of the synthesized predictive controllers (with reduced conservatism) if compared to the standard approach to deal with sector constraints from the literature.

show abstract

Distributionally Robust Optimization with Unscented Transform for Learning-Based Motion Control in Dynamic Environments

Hakobyan

Yang

2023

2023 IEEE International Conference on Robotics and Automation (ICRA)

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Learning-based Robust Model Predictive Control for Sector-bounded Lur’e Systems

Cited by 3 publications

References 7 publications

Stabilizing Model Predictive Control Synthesis using Integral Quadratic Constraints and Full-Block Multipliers*

Stabilizing Model Predictive Control Synthesis using Integral Quadratic Constraints and Full-Block Multipliers*

Stabilizing model predictive control synthesis using integral quadratic constraints and full‐block multipliers

Distributionally Robust Optimization with Unscented Transform for Learning-Based Motion Control in Dynamic Environments

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