<abstract xmlns="http://www.w3.org/1999/xhtml">

In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider <italic>mixed</italic> two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into <italic>virtual control</italic> problems on smaller time domains.
</abstract>

Friedrich-Alexander-Universität Erlangen-Nürnberg

Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions

<abstract xmlns="http://www.w3.org/1999/xhtml">

This note presents sufficient conditions for the property of strong metric subregularity (SMSr) of the system of first order optimality conditions for a mathematical programming problem in a Banach space (the Karush-Kuhn-Tucker conditions). The constraints of the problem consist of equations in a Banach space setting and a finite number of inequalities. The conditions, under which SMSr is proven, assume that the data are twice continuously Fréchet differentiable, the strict Mangasarian-Fromovitz constraint qualification is satisfied, and the second-order sufficient optimality condition holds. The obtained result extends the one known for finite-dimensional problems. Although the applicability of the result is limited to the Banach space setting (due to the twice Fréchet differentiability assumptions and the finite number of inequality constraints), the paper can be valuable due to the self-contained exposition, and provides a ground for extensions. One possible extension was recently implemented in Osmolovskii and Veliov (2021).
</abstract>

On the strong metric subregularity in mathematical programming

<abstract xmlns="http://www.w3.org/1999/xhtml">

Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase both shape and volume mesh quality. For this, we employ pre-shape calculus as established in Luft and Schulz (2021). Existence of regularized solutions is guaranteed. Further, consistency of modified pre-shape gradient systems is established. We present pre-shape gradient system modifications, which permit simultaneous shape optimization with mesh quality improvement. Optimal shapes to the original problem are left invariant under regularization. The computational burden of our approach is limited, since additional solution of possibly larger (non-)linear systems for regularized shape gradients is not necessary. We implement and compare pre-shape gradient regularization approaches for a 2D problem, which is prone to mesh degeneration. As our approach does not depend on the choice of metrics representing shape gradients, we employ and compare several different metrics.
</abstract>

Simultaneous shape and mesh quality optimization using pre-shape calculus

<abstract xmlns="http://www.w3.org/1999/xhtml">

This paper studies the output controllability of discrete linear time invariant systems (<italic>LTI</italic>) with non-negative input constraints. Some geometrical arguments and positive invariance concepts are used to derive the necessary and/or sufficient conditions for the positive output controllability of discrete <italic>LTI</italic> systems. The paper also provides several academic examples, which support the theoretical results.
</abstract>

Positive output controllability of linear discrete–time invariant systems

<abstract xmlns="http://www.w3.org/1999/xhtml">

The convex linear combination of the controllability pairs of linear continuous-time linear systems is defined and its properties are discussed. The main result is obtained using pure algebraic methods. In the illustrative examples different cases of linear convex combinations are analyzed.
</abstract>

Convex linear combination of the controllability pairs for linear systems

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper the solution for hesitant fuzzy system as <italic>AX</italic> = <italic>B</italic> is introduced where <italic>A</italic> is an <italic>n</italic> × <italic>n</italic> known hesitant fuzzy matrix, <italic>B</italic> is an <italic>n</italic> × 1 known hesitant fuzzy vector and <italic>X</italic> is an <italic>n</italic> × 1 unknown hesitant fuzzy vector.
First, <italic>L</italic>∞-norm and <italic>L</italic>1-norm of a hesitant fuzzy vector are introduced. Then, the concepts of hesitant fuzzy zero, ’almost equal’ and ’less than’ and ’equal’ are defined for two hesitant fuzzy numbers. Finally, using a minimization problem; the hesitant fuzzy system is solved. At the end, some numerical examples are presented to show the effectiveness of the proposed method.
</abstract>

Introducing and solving the hesitant fuzzy system <italic>AX</italic> = <italic>B</italic>

Table of contents of volume 50 (2021) AUTHOR(S), title, initial page number

Alphabetical list of contributors of volume 50 (2021) AUTHOR, issue number, pages

List of referees having reviewed papers for <italic>Control &amp; Cybernetics</italic> with respect to the issues of the publishing year 2021 (vol. 50)

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Volume 50 (2021): Issue 1 (March 2021) Special Issue Dedicated to the memory of Gregory E. Kersten Guest Edited by Tomasz Wachowicz, Ewa Roszkowska and Bogumił Kamiński

Control and Cybernetics

 This journal is edited and published by the Systems Research Institute of the Polish Academy of Sciences.  eISSN: 2720-4278 ISSN: 0324-8569   Its main objective is to stimulate the development of broadly conceived systems theory and analysis.  The field of interest covers general concepts, theories, methods, and techniques associated with analysis, modelling, control and management in various systems (e.g., technological, economic, ecological, social).  The journal is particularly interested in results in the following areas of research:  Systems and control theory   General systems theory  Optimal control  Optimization theory  Optimization algorithms  Decomposition and coordination methods  Structural optimization  Data analysis and learning  Artificial intelligence  Machine learning  Modeling and identification  Game theory and polioptimization  Decision and negotiation systems  Stochastic and fuzzy systems  Systems control and management   Systems analysis of national and regional development  Modelling and control of complex systems (in energy, water, industry, agriculture)  Applications of operations research methods  Computer aided management, control and optimal design  Methodological aspects of applications of control and systems methods  The Quarterly journal CONTROL AND CYBERNETICS is being indexed and abstracted in a number of worldwide services (Scopus and Index Copernicus, etc.). Its current issues can be obtained from the Publisher, or via EBSCO and GALE, while issues older than one year are freely available on the web.  Reviews of individual papers from the journal appear in International Abstracts in Operations Research, Mathematical Reviews, and Zentralblatt für Mathematik.  Abstracted in Applied Mechanical Reviews. Indexed also by Polish services BazTech and BazEkon.  See the website control.ibspan.waw.pl.  We hope that Control and Cybernetics will contribute to the development of systems and control sciences and will stimulate and encourage application of systems approach in different areas.  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. 

Control and Cybernetics

Volume 50 (2021): Issue 4 (December 2021)

Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions

On the strong metric subregularity in mathematical programming

Simultaneous shape and mesh quality optimization using pre-shape calculus

Positive output controllability of linear discrete–time invariant systems

Convex linear combination of the controllability pairs for linear systems

Introducing and solving the hesitant fuzzy system AX = B

Table of contents of volume 50 (2021) AUTHOR(S), title, initial page number

Alphabetical list of contributors of volume 50 (2021) AUTHOR, issue number, pages

List of referees having reviewed papers for Control & Cybernetics with respect to the issues of the publishing year 2021 (vol. 50)

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