相关论文: Towards Data-driven LQR with Koopmanizing Flows
Koopman operator theory yields powerful tools for modeling, analysis, and control of nonlinear dynamical systems. Prominently, linear time-invariant (LTI) Koopman representations have been proposed to enable the application of linear…
System representations inspired by the infinite-dimensional Koopman operator (generator) are increasingly considered for predictive modeling. Due to the operator's linearity, a range of nonlinear systems admit linear predictor…
The Koopman framework proposes a linear representation of finite-dimensional nonlinear systems through a generally infinite-dimensional globally linear embedding. Originally, the Koopman formalism has been derived for autonomous systems. In…
A popular technique used to obtain linear representations of nonlinear systems is the so-called Koopman approach, where the nonlinear dynamics are lifted to a (possibly infinite dimensional) linear space through nonlinear functions called…
Sparked by the Willems' fundamental lemma, a class of data-driven control methods has been developed for LTI systems. At the same time, the Koopman operator theory attempts to cast a nonlinear control problem into a standard linear one…
Quadrotor systems are common and beneficial for many fields, but their intricate behavior often makes it challenging to design effective and optimal control strategies. Some traditional approaches to nonlinear control often rely on local…
In this work, we introduce a novel data-driven formulation, the Koopman-Linearly-Time-Invariant (Koopman-LTI) analysis, for analyzing Fluid-Structure Interactions (FSI). An implementation of the Koopman-LTI on a subcritical free-shear flow…
Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…
This work proposes a Linear-Time-Invariance (LTI) notion to the Koopman analysis, finding an invariant subspace on which Koopman modes are consistent and physically meaningful. It also develops the Koopman-LTI architecture -- a systematic…
This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…
The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have been useful in…
In the reinforcement learning literature, strong theoretical guarantees have been obtained for algorithms applicable to LTI systems. However, in the nonlinear case only weaker results have been obtained for algorithms that mostly rely on…
Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…
Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…
This paper addresses a learning problem for nonlinear dynamical systems with incorporating any specified dissipativity property. The nonlinear systems are described by the Koopman operator, which is a linear operator defined on the…
This serial work presents a Linear-Time-Invariance (LTI) notion to the Koopman analysis, finding consistent and physically meaningful Koopman modes and addressing a long-standing problem of fluid-structure interactions: deterministically…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…