Acta Cybernetica

Preface

Andreas Rauh — 2023-05-23

Preface

The 19th International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computation (SCAN) was originally planned to be organized by the Institute of Informatics of the University of Szeged (SZTE) in Szeged, Hungary, in the year 2020. Due to the pandemic situation, the Scientific Committee of SCAN decided to postpone the meeting to September 13–15, 2021 and to have it in a fully online format.
The members of the Scientific Committee were the following representatives of the topics of the conference: G. Alefeld (Karlsruhe, Germany), A. Bauer (Ljubljana, Slovenia), J. B. van den Berg (Amsterdam, the Netherlands), G.F. Corliss (Milwaukee, USA), T. Csendes (Szeged, Hungary), R.B. Kearfott (Lafayette, USA), V. Kreinovich (El Paso, USA), J.-P. Lessard (Montreal, Canada), W. Luther (Duisburg, Germany), S. Markov (Sofia, Bulgaria), G. Mayer (Rostock, Germany), J.-M. Muller (Lyon, France), M. Nakao (Tokyo, Japan), T. Ogita (Tokyo, Japan), S. Oishi (Tokyo, Japan), K. Ozaki (Tokyo, Japan), M. Plum (Karlsruhe, Germany), A. Rauh (Brest, France), N. Revol (Lyon, France), J. Rohn (Prague, Czech Republic), S. Rump (Hamburg, Germany/Tokyo, Japan), S. Shary (Novosibirsk, Russia), W. Tucker (Uppsala, Sweden), W. Walter (Dresden, Germany), J. Wolff von Gudenberg (Würzburg, Germany), and N. Yamamoto (Tokyo, Japan). The members of the Organizing Committee were: Balázs Bánhelyi, Tibor Csendes, Boglárka G.-Tóth, Viktor Homolya, Tamás Vinkó, and Dániel Zombori.
During SCAN, more than 50 participants were present and 48 talks in several fields of reliable computation and its applications were given, and organized in 18 thematic sessions. The plenary speakers were Fabienne Jézéquel (Sorbonne University, France), Marko Lange (Hamburg University of Technology, Germany), J.D. Mireles James (Florida Atlantic University, USA), together with the Moore Prize winners Marko Lange and Siegfried Rump (Waseda University, Japan).
The open-access scientific journal Acta Cybernetica offered to publish paper versions of selected presentations after a careful peer review process. Altogether, 7 papers were accepted for publication in the present special issue of Acta Cybernetica. The full program of the conference, the collection of all abstracts, and further information can be found at https://www.inf.u-szeged.hu/scan2020/.

Andreas Rauh, Balázs Bánhelyi
Guest Editors

Proving the Stability of the Rolling Navigation

Auguste Bourgois — 2023-02-23

In this paper, we propose to study the stability of a navigation method that allows a robot to move in an unstructured environment without compass by measuring a scalar function ϕ which only depends on the position. The principle is to ask the robot to roll along an isovalue of ϕ . Using an interval method, we prove the stability of our closed loop system in the special case where ϕ is linear.

The Inventory Control Problem for a Supply Chain With a Mixed Type of Demand Uncertainty

Elena Chausova — 2022-09-02

This paper is concerned with a dynamic inventory control system described by a network model where the nodes are warehouses and the arcs represent production and distribution activities. We assume that an uncertain demand may take any value in an assigned interval and we allow that the system is disturbed by noise inputs. These assumptions yield a model with a mix of interval and stochastic demand uncertainties. We use the method of model predictive control to derive the control strategy. To deal with interval uncertainty we use the interval analysis tools and act according to the interval analysis theory. The developed results are illustrated using a numerical example.

Inverses of Rational Functions

Tamás Dózsa — 2022-10-28

We consider the numerical construction of inverses for a class of rational functions. We propose two inverse algorithms, which can be used to simultaneously identify every zero of a rational function or polynomial. In the first case, we propose a generalization of an inverse algorithm based on our previous work and specify a class of rational functions, for which this generalized algorithm is applicable. In the second case, we provide a method to construct Blaschke-products, whose roots match the roots of a polynomial or a rational function. We also consider different iterative methods to numerically calculate the inverse points and discuss their properties.

On Some Convergence Properties for Finite Element Approximations to the Inverse of Linear Elliptic Operators

Takehiko Kinoshita — 2022-09-02

This paper deals with convergence theorems of the Galerkin finite element approximation for the second-order elliptic boundary value problems. Under some quite general settings, we show not only the pointwise convergence but also prove that the norm of approximate operator converges to the corresponding norm for the inverse of a linear elliptic operator. Since the approximate norm estimates of linearized inverse operator play an essential role in the numerical verification method of solutions for non-linear elliptic problems, our result is also important in terms of guaranteeing its validity. Furthermore, the present method can also be applied to more general elliptic problems, e.g., biharmonic problems and so on.

B^R_π-Matrices, B-Matrices, and Doubly B-Matrices in the Interval Setting

Matyáš Lorenc — 2022-09-02

In this paper we focus on generalizing B^R_π-matrices into the interval setting, including some results regarding this class. There are two possible ways to generalize B^R_π-matrices into the interval setting, but we will prove that, in a sense, they are one. We derive mainly means of recognition for this interval matrices class, such as characterizations, necessary conditions and sufficient ones. Next we will take a look at interval B-matrices and interval doubly B-matrices, which were introduced recently, and present their characterizations through reduction, as well as such characterization for B^R_π-matrices.

Quantification of Time-Domain Truncation Errors for the Reinitialization of Fractional Integrators

Andreas Rauh — 2022-10-28

In recent years, fractional differential equations have received a significant increase in their use for modeling a wide range of engineering applications. In such cases, they are mostly employed to represent non-standard dynamics that involve long-term memory effects or to represent the dynamics of system models that are identified from measured frequency response data in which magnitude and phase variations are observed that could be captured either by low-order fractional models or high-order rational ones. Fractional models arise also when synthesizing CRONE (Commande Robuste d'Ordre Non Entier) and/or fractional PID controllers for rational or fractional systems. In all these applications, it is frequently required to transform the frequency domain representation into time domain. When doing so, it is necessary to carefully address the issue of the initialization of the pseudo state variables of the time domain system model. This issue is discussed in this article for the reinitialization of fractional integrators which arises among others when solving state estimation tasks for continuous-time systems with discrete-time measurements. To quantify the arising time-domain truncation errors due to integrator resets, a novel interval observer-based approach is presented and, finally, visualized for a simplified battery model.

Affine Iterations and Wrapping Effect: Various Approaches

Nathalie Revol — 2023-06-02

Affine iterations of the form x(n+1)=Ax(n)+b converge, using real arithmetic, if the spectral radius of the matrix A is less than 1. However, substituting interval arithmetic to real arithmetic may lead to divergence of these iterations, in particular if the spectral radius of the absolute value of A is greater than 1. We will review different approaches to limit the overestimation of the iterates, when the components of the initial vector x(0) and b are intervals. We will compare, both theoretically and experimentally, the widths of the iterates computed by these different methods: the naive iteration, methods based on the QR- and SVD-factorization of A, and Lohner's QR-factorization method. The method based on the SVD-factorization is computationally less demanding and gives good results when the matrix is poorly scaled, it is superseded either by the naive iteration or by Lohner's method otherwise.