Related papers: Koopman Form of Nonlinear Systems with Inputs
We devise a novel formulation and propose the concept of modal participation factors to nonlinear dynamical systems. The original definition of modal participation factors (or simply participation factors) provides a simple yet effective…
Reinforcement Learning (RL) has made significant strides in various domains, and policy gradient methods like Proximal Policy Optimization (PPO) have gained popularity due to their balance in performance, training stability, and…
To avoid complex constraints of the traditional nonlinear method for tethered space robot (TSR) deployment, this paper proposes a data-driven optimal control framework with an improved deep learning based Koopman operator that could be…
This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…
Koopman spectral analysis has attracted attention for nonlinear dynamical systems since we can analyze nonlinear dynamics with a linear regime by embedding data into a Koopman space by a nonlinear function. For the analysis, we need to find…
When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric…
Modeling of nonlinear behaviors with physical-based models poses challenges. However, Koopman operator maps the original nonlinear system into an infinite-dimensional linear space to achieve global linearization of the nonlinear system…
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…
Reachability analysis of nonlinear dynamical systems is a challenging and computationally expensive task. Computing the reachable states for linear systems, in contrast, can often be done efficiently in high dimensions. In this paper, we…
This paper introduces a systematic approach to synthesize linear parameter-varying (LPV) representations of nonlinear (NL) systems which are described by input affine state-space (SS) representations. The conversion approach results in…
Approximating nonlinear systems as linear ones is a common workaround to apply control tools tailored for linear systems. This motivates our present work where we developed a data-driven model predictive controller (MPC) based on the…
The dynamic complexity of robots and mechatronic systems often pertains to the hybrid nature of dynamics, where governing equations consist of heterogenous equations that are switched depending on the state of the system. Legged robots and…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
For every non-autonomous system, there is the related family of Koopman operators $\mathcal{K}^{(t,t_0)}$, parameterized by the time pair $(t,t_0)$. In this paper we are investigating the time dependency of the spectral properties of the…
Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…
Unlike for Linear Time-Invariant (LTI) systems, for nonlinear systems, there exists no general framework for systematic convex controller design which incorporates performance shaping. The Linear Parameter-Varying (LPV) framework sought to…
Koopman operator theory provides a global linear representation of nonlinear dynamics and underpins many data-driven methods. In practice, however, finite-dimensional feature spaces induced by a user-chosen dictionary are rarely invariant,…
This paper presents a methodology to achieve lower-dimensional Koopman quasi-linear representations of nonlinear system dynamics using Koopman generalized eigenfunctions. The proposed approach considers the analytically derived Koopman…
Linear Time Invariant (LTI) systems are ubiquitous in control applications. Unbounded-time reachability analysis that can cope with industrial-scale models with thousands of variables is needed. To tackle this problem, we use abstract…
We propose a data-driven linear modeling framework for controlled nonlinear hereditary systems that combines Koopman lifting with a truncated Grunwald-Letnikov memory term. The key idea is to model nonlinear state dependence through a…