Learning Contraction Policies From Offline Data

Rezazadeh, Navid; Maxwell, Kolarich,; Kia, Solmaz S.; Mehr, Negar

doi:10.1109/lra.2022.3145100

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…A principled approach, however, that guarantees some form of stability is largely lacking. Progress has been made when it comes to handling side-information [AEK20], obtaining statistical stability guarantees [Bof+21], in the context of input-state stability under CTRNN modelling assumptions [Yan+22], in the context of input-output stability by exploiting the Hamilton-Jacobi inequality [OK22], by exploiting contraction theory [Rez+22] and by exploiting Koopman operator theory [ZB22], to name a few. As these methods are data-driven, errors inevitably slip in and great care must be taken when one aims to mimic CLF-based controllers, i.e., if L g V (x) = 0 =⇒ L f V (x) < 0 holds for the estimated system, does it hold for the real system and what happens if it does not?…”

Section: Stabilitymentioning

confidence: 99%

On continuation and convex Lyapunov functions

Jongeneel¹,

Schwan²

2023

Preprint

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Given any two continuous dynamical systems on Euclidean space such that the origin is globally asymptotically stable and assume that both systems come equipped with-possibly different-convex smooth Lyapunov functions asserting the origin is indeed globally asymptotically stable. We show that this implies those two dynamical systems are homotopic through qualitatively equivalent dynamical systems. It turns out that relaxing the assumption on the origin to any compact convex set or relaxing the convexity assumption to geodesic convexity does not alter the conclusion. Imposing the same convexity assumptions on control Lyapunov functions leads to a Hautus-like stabilizability test. These results ought to find applications in optimal control and reinforcement learning.

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Section: Stabilitymentioning

confidence: 99%

On continuation and convex Lyapunov functions

Jongeneel¹,

Schwan²

2023

Preprint

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“…Remark 1: While it is not possible to obtain deterministic Lipschitz constant bounds from finite amount of data, estimation of Lipschitz constants is an active research area [25], [26]. For instance, given A, B, ψ and a data set D, if D xu is independent and identically distributed, statistical methods such as scenario approach or extreme value theory can be used to obtain an estimate [24], [27]. The same statistical techniques can also be applied to directly estimate a bound on E A,B from data.…”

Section: A Computing Koopman Over-approximationsmentioning

confidence: 99%

Koopman-Inspired Implicit Backward Reachable Sets for Unknown Nonlinear Systems

Balim,

Aspeel,

Liu

et al. 2023

IEEE Control Syst. Lett.

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Koopman liftings have been successfully used to learn high dimensional linear approximations for autonomous systems for prediction purposes, or for control systems for leveraging linear control techniques to control nonlinear dynamics. In this paper, we show how learned Koopman approximations can be used for state-feedback correct-by-construction control. To this end, we introduce the Koopman over-approximation, a (possibly hybrid) lifted representation that has a simulation-like relation with the underlying dynamics. Then, we prove how successive application of controlled predecessor operation in the lifted space leads to an implicit backward reachable set for the actual dynamics. Finally, we demonstrate the approach on two nonlinear control examples with unknown dynamics.

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Learning Contraction Policies From Offline Data

Cited by 2 publications

References 22 publications

On continuation and convex Lyapunov functions

On continuation and convex Lyapunov functions

Koopman-Inspired Implicit Backward Reachable Sets for Unknown Nonlinear Systems

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