Related papers: EBIF: Exact Bilinearization Iterative Form for Con…
The challenge of finding exact and finite-dimensional Koopman embeddings of nonlinear systems has been largely circumvented by employing data-driven techniques to learn models of different complexities (e.g., linear, bilinear, input…
Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…
Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation…
Koopman linear representations have become a popular tool for control design of nonlinear systems, yet it remains unclear when such representations are exact. In this paper, we establish sufficient and necessary conditions under which a…
Complete enumeration of finite models of first-order logic (FOL) formulas is pivotal to universal algebra, which studies and catalogs algebraic structures. Efficient finite model enumeration is highly challenging because the number of…
In this paper, we consider the computation of controlled invariant sets (CIS) of discrete-time nonlinear control affine systems. We propose an iterative refinement procedure based on polytopic inclusion functions, which is able to…
In this work, we present a numerical optimal control framework for reachable set computation using \emph{normotopes}, a new set representation as a norm ball with a shaping matrix. In reachable set computations, we expect to continuously…
This paper extends the Willems' Fundamental Lemma to nonlinear control-affine systems using the Koopman bilinear realization. This enables us to bypass the Extended Dynamic Mode Decomposition (EDMD)-based system identification step in…
Optimal control of bilinear systems has been a well-studied subject in the areas of mathematical and computational optimal control. However, effective methods for solving emerging optimal control problems involving an ensemble of…
In this paper, a learning-based approach is proposed for optimizing downlink beamforming in multiple-input multiple-output (MIMO) systems that employ continuous aperture arrays (CAPAs) at both the base station (BS) and the user. Beamforming…
The Koopman framework is a popular approach to transform a finite dimensional nonlinear system into an infinite dimensional, but linear model through a lifting process, using so-called observable functions. While there is an extensive…
This note aims to provide a systematic investigation of direct data-driven control, enriching the existing literature not by adding another isolated result, but rather by offering a unifying, versatile, and broad framework that enables the…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…
In this paper we propose an end-to-end algorithm for indirect data-driven control for bilinear systems with stability guarantees. We consider the case where the collected i.i.d. data is affected by probabilistic noise with possibly…
This paper presents a Carleman-Fourier linearization method for nonlinear dynamical systems with periodic vector fields involving multiple fundamental frequencies. By employing Fourier basis functions, the nonlinear dynamical system is…
This article presents a scalable implementation of nonlinear Gramian-based control synthesis for control-affine systems, including a minimum energy control construction. These synthesis advances are achieved by addressing key computational…
We introduce Multiresolution Deep Implicit Functions (MDIF), a hierarchical representation that can recover fine geometry detail, while being able to perform global operations such as shape completion. Our model represents a complex 3D…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
In many physical applications, the system's state varies with spatial variables as well as time. The state of such systems is modelled by partial differential equations and evolves on an infinite-dimensional space. Systems modelled by…
State estimation of nonlinear dynamical systems has long aimed to balance accuracy, computational efficiency, robustness, and reliability. The rapid evolution of various industries has amplified the demand for estimation frameworks that…