Data-driven invariant subspace identification for black-box switched linear systems

Berger, Guillaume O.; Jungers, Raphaël M.; Wang, Zheming

doi:10.1109/cdc51059.2022.9993022

Cited by 3 publications

(9 citation statements)

References 24 publications

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“…This program is a data-driven version of the approximation of the CJSR with a quadratic Lyapunov function, as described in (8), and using l-product liftings, as shown in Equation (11). In addition to generalizing data-driven programs expressed in [17,18] to the constrained case, our formulation takes into account noise, as one can see in constraints (13c).…”

Section: Resultsmentioning

confidence: 99%

“…(i) One can see that program (13) is the sampled form of a quasi-linear program, as defined in [18]. Indeed, c is strongly convex, the admissible set for the variables is X |U | , which is compact, and ω N is a finite subset of ∆.…”

Section: Proposition 3 Consider An Unknown Csls S(g A)mentioning

confidence: 99%

“…For these reasons, novel data-driven techniques have been recently developed for switching linear systems, but where the switching rule is supposed to be arbitrary. Some of them provide chance-constrained bounds on the joint spectral radius [17][18][19], using scenario optimization as their main tool [20]. Other methods extend classical tools from machine learning such as k-means clustering [21].…”

Section: Introductionmentioning

confidence: 99%

“…Contributions In this paper, we provide a data-driven method to assess the quality of approximation of the CJSR of a CSLS based on a finite set of observations of trajectories, thereby generalizing [17][18][19] to the constrained case and therefore taking into account hybrid state-spaces, which consists in a supplementary technical challenge. We investigate several different types of problems, depending on the information available on the trajectories.…”

Section: Introductionmentioning

confidence: 99%

“…On top of providing complete proofs our contribution is threefold compared with the latter references. First, we present a unified framework for the different types of bounds, using chanceconstrained results on quasi-linear programs [18]. Second, we extend our methods to multiple steps and noisy observations, whereas 1-step observations are assumed in [23], and noise-free observations are assumed in [23,24].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Black-box stability analysis of hybrid systems with sample-based multiple Lyapunov functions

Banse

Raphael

Jungers

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is constrained by labeled graphs, namely constrained switching linear systems. In order to do so, we provide chance-constrained bounds on stability guarantees, that can be obtained from a finite number of noisy observations.We first present a method providing stability guarantees from sampled trajectories in the hybrid state-space of the system. We then study the harder situation where one only observes the continuous part of the hybrid states. We show that in this case, one may still obtain formal chance-constrained stability guarantees. For this latter result we provide a new upper bound of general interest, also for model-based stability analysis.

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