Neural Koopman Lyapunov control

Zinage, Vrushabh; Bakolas, Efstathios

doi:10.1016/j.neucom.2023.01.029

Cited by 9 publications

(2 citation statements)

References 38 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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“…We have found the most application to be the minimum-fuel orbital rendezvous. One approach employed Koopman Map Inversion to obtain a linearized model for optimal control [66], while another approach demonstrated Neural Koopman Lyapunov Control for linearizing a generalized affine system [76]. Minimization of the Frobenius norm was performed on a similarly affine thrust-vectoring application using the pseudo-inverse to directly solve for the Koopman operator [32].…”

Section: Space Systemsmentioning

confidence: 99%

Vehicular Applications of Koopman Operator Theory—A Survey

2023

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Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering purposes. The introduction of a recent computationally efficient method in the context of fluid dynamics, which is based on the system dynamics decomposition to a set of normal modes in descending order, has overcome this long-lasting computational obstacle. The purely data-driven nature of Koopman operators holds the promise of capturing unknown and complex dynamics for reduced-order model generation and system identification, through which the rich machinery of linear control techniques can be utilized. Given the ongoing development of this research area and the many existing open problems in the fields of smart mobility and vehicle engineering, a survey of techniques and open challenges of applying Koopman operator theory to this vibrant area is warranted. This review focuses on the various solutions of the Koopman operator which have emerged in recent years, particularly those focusing on mobility applications, ranging from characterization and component-level control operations to vehicle performance and fleet management. Moreover, this comprehensive review of over 100 research papers highlights the breadth of ways Koopman operator theory has been applied to various vehicular applications with a detailed categorization of the applied Koopman operator-based algorithm type. Furthermore, this review paper discusses theoretical aspects of Koopman operator theory that have been largely neglected by the smart mobility and vehicle engineering community and yet have large potential for contributing to solving open problems in these areas.

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