Model predictive control for linear uncertain systems using integral quadratic constraints

Schwenkel, Lukas; Köhler, Johannes; Müller, Matthias A.; Allgöwer, Frank

doi:10.48550/arxiv.2104.05444

Cited by 3 publications

(4 citation statements)

References 29 publications

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“…Less conservative/tight reachability bounds for state space models with parametric uncertainty require more sophisticated robust control tools, e.g., integral quadratic constraints. However, exploiting such tools in MPC is part of ongoing research [13].…”

Section: Discussionmentioning

confidence: 99%

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State space models vs. multi-step predictors in predictive control: Are state space models complicating safe data-driven designs?

Köhler¹,

Wabersich²,

Berberich³

et al. 2022

Preprint

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This paper contrasts recursive state space models and direct multi-step predictors for linear predictive control. We provide a tutorial exposition for both model structures to solve the following problems: 1. stochastic optimal control; 2. system identification; 3. stochastic optimal control based on the estimated model. Throughout the paper, we provide detailed discussions of the benefits and limitations of these two model parametrizations for predictive control and highlight the relation to existing works. Additionally, we derive a novel (partially tight) constraint tightening for stochastic predictive control with parametric uncertainty in the multi-step predictor.

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Section: Discussionmentioning

confidence: 99%

“…A variety of results are available to ensure robustness w.r.t. parametric uncertainty in state space models by using tube-based approaches [7]- [13]. More recently, a number of predictive control approaches have been proposed that directly exploit multi-step predictors, as also done in early MPC approaches [2]- [4]:…”

Section: Introductionmentioning

confidence: 99%

State space models vs. multi-step predictors in predictive control: Are state space models complicating safe data-driven designs?

Köhler¹,

Wabersich²,

Berberich³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A library of frequency-domain ρ-IQCs is provided in (Boczar et al 2017) for various types of perturbations. As shown in (Schwenkel et al 2021), a general class of frequency-domain ρ-IQCs can be translated into time-domain ρ-hard IQC by a multiplier factorization.…”

Section: Partially Observed Nonlinear Systems With Uncertaintymentioning

confidence: 99%

Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems

Yin

Ghaoui

et al. 2022

AAAI

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Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many cases, requires controllers to retain and process long-term memories of the past. We consider the important class of recurrent neural networks (RNN) as dynamic controllers for nonlinear uncertain partially-observed systems, and derive convex stability conditions based on integral quadratic constraints, S-lemma and sequential convexification. To ensure stability during the learning and control process, we propose a projected policy gradient method that iteratively enforces the stability conditions in the reparametrized space taking advantage of mild additional information on system dynamics. Numerical experiments show that our method learns stabilizing controllers with fewer samples and achieves higher final performance compared with policy gradient.

show abstract

“…A library of frequency-domain ρ-IQCs is provided in(Boczar et al 2017) for various types of perturbations. As shown in(Schwenkel et al 2021), a general class of frequency-domain ρ-IQCs can be translated into time-domain ρ-hard IQC by a multiplier factorization.…”

mentioning

confidence: 99%

Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems

Gu¹,

Yin²,

Ghaoui³

et al. 2021

Preprint

View full text Add to dashboard Cite

Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many cases, requires controllers to retain and process long-term memories of the past. We consider the important class of recurrent neural networks (RNN) as dynamic controllers for nonlinear uncertain partially-observed systems, and derive convex stability conditions based on integral quadratic constraints, S-lemma and sequential convexification. To ensure stability during the learning and control process, we propose a projected policy gradient method that iteratively enforces the stability conditions in the reparametrized space taking advantage of mild additional information on system dynamics. Numerical experiments show that our method learns stabilizing controllers while using fewer samples and achieving higher final performance compared with policy gradient.

show abstract

Model predictive control for linear uncertain systems using integral quadratic constraints

Cited by 3 publications

References 29 publications

State space models vs. multi-step predictors in predictive control: Are state space models complicating safe data-driven designs?

State space models vs. multi-step predictors in predictive control: Are state space models complicating safe data-driven designs?

Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems

Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems

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