Neural Koopman Lyapunov Control
- URL: http://arxiv.org/abs/2201.05098v1
- Date: Thu, 13 Jan 2022 17:38:09 GMT
- Title: Neural Koopman Lyapunov Control
- Authors: Vrushabh Zinage, Efstathios Bakolas
- Abstract summary: We propose a framework to identify and construct stabilizable bilinear control systems and its associated observables from data.
Our proposed approach provides provable guarantees of global stability for the nonlinear control systems with unknown dynamics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Learning and synthesizing stabilizing controllers for unknown nonlinear
systems is a challenging problem for real-world and industrial applications.
Koopman operator theory allow one to analyze nonlinear systems through the lens
of linear systems and nonlinear control systems through the lens of bilinear
control systems. The key idea of these methods, lies in the transformation of
the coordinates of the nonlinear system into the Koopman observables, which are
coordinates that allow the representation of the original system (control
system) as a higher dimensional linear (bilinear control) system. However, for
nonlinear control systems, the bilinear control model obtained by applying
Koopman operator based learning methods is not necessarily stabilizable and
therefore, the existence of a stabilizing feedback control is not guaranteed
which is crucial for many real world applications. Simultaneous identification
of these stabilizable Koopman based bilinear control systems as well as the
associated Koopman observables is still an open problem. In this paper, we
propose a framework to identify and construct these stabilizable bilinear
models and its associated observables from data by simultaneously learning a
bilinear Koopman embedding for the underlying unknown nonlinear control system
as well as a Control Lyapunov Function (CLF) for the Koopman based bilinear
model using a learner and falsifier. Our proposed approach thereby provides
provable guarantees of global asymptotic stability for the nonlinear control
systems with unknown dynamics. Numerical simulations are provided to validate
the efficacy of our proposed class of stabilizing feedback controllers for
unknown nonlinear systems.
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