Behavioral theory for stochastic systems? A data-driven journey from Willems to Wiener and back again

Faulwasser, Timm; Ou, Ruchuan; Pan, Guanru; Schmitz, Philipp; Worthmann, Karl

doi:10.1016/j.arcontrol.2023.03.005

Cited by 18 publications

(10 citation statements)

References 87 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, using the generalized square root of the covariance, we obtain a linear parametrization of W K , which in turn simplifies the data-driven uncertainty propagation. Furthermore, for all W k collecting the normalized random variables ξ k , k ∈ I [0,N −1] in the basis (7), we obtain the coefficient dynamics (8). These dynamics are structurally similar to the original dynamics in random variables (1).…”

Section: B Pce Representation Of Disturbancesmentioning

confidence: 97%

“…would render it more difficult to work with data-driven system descriptions. We refer to [7] for a more detailed comparison of moment propagation and PCE.…”

Section: B Pce Representation Of Disturbancesmentioning

confidence: 99%

“…Proposition 1 (PCEs for DRO chance constraints): Consider a random variable V ∈ L 2 (Ω, F, µ; R nv ) with its PCE V (ξ) = L−1 j=0 v j ϕ j (ξ) regarding the basis (7). For a ∈ R nv , the distributionally robust chance constraint…”

Section: B Distributionally Robust Data-driven Ocpmentioning

confidence: 99%

“…□ Proof: The proof relies on that the PCE reformulation of all random variables in the basis (7) is exact and the omission of the basis from OCP (4) to OCP ( 16) is without loss of information. Due to Assumption 1 the system is observable and the measurements of (u, w, y) are exact.…”

Section: B Distributionally Robust Data-driven Ocpmentioning

confidence: 99%

“…The authors gratefully acknowledge funding by the German Research Foundation (Deutsche Forschungs-gemeinschaft DFG) under project number 499435839. GP and TF are with the Institute for Energy Systems, Energy Efficiency and Energy Economics, TU Dortmund University, Dortmund, Germany guanru.pan@tu-dortmund.de and timm.faulwasser@ieee.org the data-driven description of stochastic linear systems based on Polynomial Chaos Expansion (PCE) from [6], [7] towards uncertainty surrounding the disturbance distribution.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On a Stochastic Fundamental Lemma and Its Use for Data-Driven Optimal Control

Pan

Faulwasser

2023

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability measures or distributions. Typically, stochastic optimal control requires knowledge of underlying dynamics and is as such challenging. Relying on a stochastic fundamental lemma from data-driven control and on the framework of polynomial chaos expansions, we propose an approach to reformulate distributionally robust optimal control problems with ambiguity sets as uncertain conic programs in a finite-dimensional vector space. We show how to construct these programs from previously recorded data and how to relax the uncertain conic program to numerically tractable convex programs via appropriate sampling of the underlying distributions. The efficacy of our method is illustrated via a numerical example.

show abstract

Section: B Pce Representation Of Disturbancesmentioning

confidence: 97%

“…would render it more difficult to work with data-driven system descriptions. We refer to [7] for a more detailed comparison of moment propagation and PCE.…”

Section: B Pce Representation Of Disturbancesmentioning

confidence: 99%

Section: B Distributionally Robust Data-driven Ocpmentioning

confidence: 99%

Section: B Distributionally Robust Data-driven Ocpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On a Stochastic Fundamental Lemma and Its Use for Data-Driven Optimal Control

Pan

Faulwasser

2023

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

show abstract

Towards data‐driven stochastic predictive control

Pan

Faulwasser

2023

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

SummaryData‐driven predictive control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, little has been done on data‐driven stochastic control. In this paper, we propose a data‐driven stochastic predictive control scheme for LTI systems subject to possibly unbounded additive process disturbances. Based on a stochastic extension of the fundamental lemma and leveraging polynomial chaos expansions, we construct a data‐driven surrogate optimal control problem (OCP). Moreover, combined with an online selection strategy of the initial condition of the OCP, we provide sufficient conditions for recursive feasibility and for stability of the proposed data‐driven predictive control scheme. Finally, two numerical examples illustrate the efficacy and closed‐loop properties of the proposed scheme for process disturbances governed by different distributions.

show abstract