Article
Automation & Control Systems
Arvo Kaldmae
Summary: This paper presents a novel solution for verifying difference flatness of a nonlinear discrete-time control system, where a condition based on a sequence of vector spaces of differential 1-forms is proved. The proposed condition is more general than most cases as it allows the flat output to depend on backward shifts of states and inputs, without actually computing the flat output. Algorithms are provided to compute all necessary vector spaces, with results illustrated through two examples.
INTERNATIONAL JOURNAL OF CONTROL
(2022)
Article
Automation & Control Systems
Mathieu Bajodek, Frederic Gouaisbaut, Alexandre Seuret
Summary: Recently, the necessary conditions of stability for time-delay systems based on the handling of the Lyapunov-Krasovskii functional have been studied. This article proposes an extension of the existing results, where the uniform discretization of the state has been replaced by projections on the first Legendre polynomials. The improved method allows for a significantly reduced order to ensure stability and provides an analytical expression for the matrix size and convergence rate.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Engineering, Electrical & Electronic
Zhi-Yuan Wang, Hsiao-Dong Chiang
Summary: This paper focuses on developing the necessary and sufficient conditions for optimal power flow (OPF) solutions, including local solutions and Karush-Kuhn-Tucker (KKT) solutions. Numerical verification was conducted on actual systems, and the derived conditions also assist existing OPF methods in obtaining solutions.
IEEE TRANSACTIONS ON POWER SYSTEMS
(2023)
Article
Engineering, Mechanical
Durgesh Haribhau Salunkhe, Christoforos Spartalis, Jose Capco, Damien Chablat, Philippe Wenger
Summary: This paper proves that the existence of a cusp point is a necessary and sufficient condition for any 3R generic robot to be cuspidal, and revisits the geometrical interpretation of the inverse kinematics of 3R robots.
MECHANISM AND MACHINE THEORY
(2022)
Article
Automation & Control Systems
Mirko Fiacchini
Summary: This article introduces a computational method for testing the stabilizability of discrete-time switched linear systems. It proves that the existence of a conic cover of the space on whose elements a convex condition holds is necessary and sufficient for stabilizability. An algorithm is provided for computing a conic partition that satisfies the new necessary and sufficient condition. The algorithm proves to overcome the conservatism of conditions equivalent to periodic stabilizability and is applied to a 4-D system.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Automation & Control Systems
Yifeng Li, Jiandong Zhu, Bowen Li, Yang Liu, Jianquan Lu
Summary: The paper proposes a necessary and sufficient graphical condition for the original disturbance decoupling in a Boolean network with disturbances and outputs. It introduces the concept of a concolorous perfect vertex partition (CP-VP) and discusses its implications for disturbance effects on outputs. Additionally, an algorithm is designed to check for the existence of a CP-VP.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2021)
Article
Mathematics
Duncan Dauvergne
Summary: The study investigates the weak convergence of the zero measure of random polynomials and provides necessary and sufficient conditions for polynomial convergence. The proofs rely on small ball probability results and the structure of general orthogonal polynomials.
ADVANCES IN MATHEMATICS
(2021)
Article
Automation & Control Systems
Hai-Tao Zhang, Haosen Cao, Zhiyong Chen
Summary: The addition of a reverse edge has a significant impact on the convergence rate of a directed acyclic graph. The existence of interfering reverse edges can reduce the dominant convergence rate, even for large networks.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Biodiversity Conservation
Alice C. Hughes, Kevin Tougeron, Dominic A. Martin, Filippo Menga, Bruno H. P. Rosado, Sebastian Villasante, Shweta Madgulkar, Fernando Goncalves, Davide Geneletti, Luisa Maria Diele-Viegas, Sebastian Berger, Sheila R. Colla, Vitor de Andrade Kamimura, Holly Caggiano, Felipe Melo, Marcelo Guilherme de Oliveira Dias, Elke Kellner, Edivando Vitor do Couto
Summary: The blame on human population as the main cause of biodiversity loss is not true. The growth of commodities for export, particularly soybean and oil-palm, primarily for livestock feed or biofuel consumption in higher income economies, is the actual driver of habitat loss. Instead of population, reducing unsustainable consumption, tracking supply chains, technological innovation, and ensuring sustainable production are the key measures for biodiversity conservation.
BIOLOGICAL CONSERVATION
(2023)
Article
Mathematics, Applied
Ning Bi, Wai-Shing Tang
Summary: This paper focuses on the l(1) - l(2) minimization model for recovering vectors from measurement matrix A. The paper presents necessary and sufficient conditions for local and global minimization in recovering sparse vectors x from Ax. The null space property of A is crucial for successful recovery using the l(1) - l(2) minimization model.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2022)
Article
Mathematics, Applied
Xiaoling Zou, Qingwei Li, Jingliang Lv
Summary: The stochastic bifurcation phenomena in a stochastic Beddington-DeAngelis predator-prey model were investigated from the perspective of dynamic bifurcation. A critical value of the stochastic model was considered, showing species x(t) to be persistent while species y(t) goes extinct. Necessary and sufficient conditions for persistence and extinction under certain conditions were obtained and verified through examples and numerical simulations.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Automation & Control Systems
YuanYuan Liu, Wei Zhang
Summary: This paper discusses the global controllability of general nonlinear control systems and presents four approaches to enlarge the defining set of vector fields without changing controllability. The power of these approaches is demonstrated through examples.
ASIAN JOURNAL OF CONTROL
(2022)
Article
Mathematics
Yang Guo
Summary: This paper proposes a new method for determining the positivity of a binary quartic form using the theory of the pencil of conics, showing degenerate members of the pencil of conics and deriving inequalities for parameters of the degenerate members based on the properties of the degenerate conics. Ultimately, a criterion for determining positivity without the discriminant is derived from these inequalities.
JOURNAL OF MATHEMATICS
(2021)
Article
Automation & Control Systems
Xueyan Zhao, Feiqi Deng
Summary: This article reveals some essential features of stochastic control systems with sampled data (SCSwSD). By using numerical simulations and equivalence propositions, the moment asymptotic stability of the system is derived, and the construction procedure of accurate schemes is introduced. The mean square asymptotic stability of linear SCSwSD is investigated, and the almost sure stability of a kind of controlled system with sampled noise is analyzed via the discrete scheme approach. Accurate numerical computation and simulation (ANCS) are proposed, and the distinctive character of sampled data based control (SDBC) is reported and studied preliminarily.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Automation & Control Systems
Bernd Kolar, Johannes Diwold, Markus Schoeberl
Summary: In this article, it is demonstrated that the flatness of a nonlinear discrete-time system can be determined by computing a unique sequence of involutive distributions. The well-known test for static feedback linearizability is a specific case of this approach. The computation of the distributions can be efficiently implemented in a computer algebra program as it only involves solving algebraic equations. If successful, the Frobenius theorem can be used to obtain a flat output by straightening the involutive distributions.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)