Article
Mathematics
P. Frankl
Summary: The text introduces the definition and related conclusions of pseudo sunflowers, pointing out the conclusion that a collection with more than a specific number of distinct k-element sets must contain a pseudo sunflower.
EUROPEAN JOURNAL OF COMBINATORICS
(2022)
Article
Mathematics
Tolson Bell, Suchakree Chueluecha, Lutz Warnke
Summary: The sunflower problem aims to find the smallest r such that any family of r distinct k-element sets contains a sunflower with p petals. It has been shown that r = O(p log k) suffices by using a minor variant of recent proofs.
DISCRETE MATHEMATICS
(2021)
Article
Operations Research & Management Science
Wei Zhuang
Summary: This paper investigates the definition and properties of disjunctive dominating sets in graphs, and provides bounds for the disjunctive domination number of trees of order n. The paper also characterizes the families of trees that attain these bounds.
RAIRO-OPERATIONS RESEARCH
(2022)
Article
Mathematics, Applied
Alexander D. Bruno
Summary: This article firstly introduces the normal form and properties of an analytic autonomous ODE system near its stationary point. It then proposes a generalization that works near infinities in some coordinates and can be simplified to a lower order system without linear part. A simple example is considered to illustrate the method.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Engineering, Multidisciplinary
Marina Esteban, Emilio Freire, Enrique Ponce, Francisco Torres
Summary: This paper extends some previous results on computable normal forms for two-dimensional systems with a pseudo-focus within its discontinuity line. Specifically, it shows how the standard theory of normal forms can be used to analyze pseudo-focus points when the contact order with the discontinuity boundary is different on each side. The computation of half-return maps is almost direct once the associated canonical forms are obtained, making it easier to characterize the pseudo-focus. While the methodology is developed in its entire generality, an illustrating example with contacts of order 2 and 4 is studied in detail.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Applied
Suzanna Parkinson, Hayden Ringer, Kate Wall, Erik Parkinson, Lukas Erekson, Daniel Christensen, Tyler J. Jarvis
Summary: This study examines the performance of several normal-form multivariate polynomial rootfinding methods and their variants proposed by Telen, Mourrain, and Van Barel. The analysis reveals that all variants of the algorithms encounter difficulties when dealing with systems in which the roots are very close together. By scrutinizing a devastating example, the authors demonstrate that the problems arise from a large number of closely clustered roots.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
Krzysztof Tchon, Joanna Ratajczak
Summary: This paper proposes the normal form approach as a tool for analyzing robot singularities, demonstrating its effectiveness in detecting, describing, and explaining the behavior of robots at singular points through examples of earth and space robots.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Automation & Control Systems
Johannes Diwold, Bernd Kolar, Markus Schoeberl
Summary: The study demonstrates that every forward-flat nonlinear discrete-time system with two inputs can be transformed into a structurally flat normal form, allowing for a systematic construction of parameterisation of system variables by the flat output. However, for flat continuous-time systems, no comparable normal form exists.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2021)
Article
Mathematics
Shahriar Aslani, Patrick Bernard
Summary: The paper discusses the study of Hamiltonian systems on cotangent bundles, focusing on perturbing Hamiltonians by small additive potentials and positive factors close to one to change generic properties. The impact of perturbations on Hamiltonians that are convex in p and the relationship between small additive potentials and positive factors close to one were explored.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2022)
Article
Operations Research & Management Science
Andreas Ernst, Lars Gruene, Janosch Rieger
Summary: The infinite time reachable set of a strictly stable linear control system is the Hausdorff limit of the finite time reachable set of the origin as time tends to infinity. We propose a new method for computing this set based on the invariance properties of the control system and the desired set.
JOURNAL OF GLOBAL OPTIMIZATION
(2023)
Article
Automation & Control Systems
Chao Ding, Ruixuan Wei
Summary: This article proposes a low-complexity control design for a class of nonlinear systems in p-normal form with completely unknown control directions. The novel contributions include the construction of a novel Nussbaum function with changing frequency to relax the conditional inequality regarding the derivative of Lyapunov function, the design of an improved Nussbaum gain technical lemma for establishing closed-loop boundedness for all time, and the introduction of the concept of separable characteristic to handle nonaffine terms. Theoretical results are validated through numerical simulation.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Automation & Control Systems
Francisco Javier Bejarano
Summary: This study focuses on the zero dynamics of linear systems with commensurate delays, revealing conditions for transforming the system into a normal form to identify its zero dynamics. By utilizing the obtained decomposition, the disturbance decoupling problem is easily solved. The results are extended to systems with distributed delays, and the effectiveness is illustrated through examples of physical systems.
Article
Mathematics, Applied
Jie Liu, Lilia Ghaffour, Driss Boutat, Da-Yan Liu, Xue-Feng Zhang
Summary: This paper presents a transformation method for a class of nonlinear MIMO dynamical systems into extended nonlinear normal forms that are compatible with high-gain observers. The method involves a series of transformations using the dynamics extension method. It fills the gap in transformations specifically developed for MIMO systems and provides a better understanding of their structures. The effectiveness of the proposed high-gain observer is verified through a numerical example.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics
Matheus M. Castro, Ricardo M. Martins, Douglas D. Novaes
Summary: The Vishik's Normal Form provides a local smooth conjugation with a linear vector field for smooth vector fields near contacts with a manifold. Our study focuses on the analytic case, and our main result ensures that the conjugation with the Vishik's normal form for analytic vector field and manifold is also analytic. As an application, we investigate the analyticity of Poincare Half Maps defined locally near contacts between analytic vector field and manifold.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Automation & Control Systems
Jingtao Hu, Weiming Wu, Fukai Zhang, Cong Wang
Summary: This paper investigates the learning and control problem of sampled-data systems with only output measurements. A unified approach is presented by integrating the sampled-data observer and deterministic learning. First, an adaptive radial basis function network (RBFN) learning controller with a sampled-data observer is designed to track a recurrent reference model. Second, it is proven that the RBFN weights can exponentially converge to their ideal values and the closed-loop dynamics can be accurately learned during the output-feedback process. Ultimately, a knowledge-based output-feedback controller is developed to improve the tracking performance based on the learned dynamics.
IET CONTROL THEORY AND APPLICATIONS
(2023)
