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

We consider a heat conduction problem <italic>S</italic> with mixed boundary conditions in an <italic>n</italic>-dimensional domain Ω with regular boundary and a family of problems <italic>Sα</italic> with also mixed boundary conditions in Ω, where <italic>α ></italic> 0 is the heat transfer coefficient on the portion of the boundary Γ1. In relation to these state systems, we formulate <italic>Neumann boundary</italic> optimal control problems on the heat flux <italic>q</italic> which is definite on the complementary portion Γ2 of the boundary of Ω. We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system state and the adjoint state when the heat transfer coefficient <italic>α</italic> goes to infinity. Furthermore, we formulate particular <italic>boundary</italic> optimal control problems on a real parameter <italic>λ</italic>, in relation to the parabolic problems <italic>S</italic> and <italic>Sα</italic> and to mixed elliptic problems <italic>P</italic> and <italic>Pα</italic>. We find an explicit form for the optimal controls, we prove monotony properties and we obtain convergence results when the parameter time goes to infinity.
</abstract>

Neumann boundary optimal control problems governed by parabolic variational equalities

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

The article studies the nutrient transfer mechanism for cropping systems in polluted soils from a mathematical and optimal control point of view. The problem under consideration is governed by an advection-diffusion PDE in a bounded domain.
The existence of a solution is obtained. We also determine the optimal amount of required nutrients at the root surface for plants where the soil is polluted by an unknown source. The characterization of the optimal control by a singular optimality system is obtained.
</abstract>

Optimal control of advection-diffusion problems for cropping systems in polluted soils

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

In this work, we consider the partial observability problem for finite dimensional dynamical linear systems that are not necessarily observable. For that purpose we introduce the so called “observable subspaces” and “partial observability” to find a way to reconstruct the observable part of the system state. Some characterizations of “observable subspaces” have been provided. The reconstruction of the orthogonal projection of the state on the observable subspace is obtained. We give some examples to illustrate our theoretical approach.
</abstract>

Partial observability of finite dimensional linear systems

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

The paper proposes a method for solving systems of linear inequalities. This method determines in a finite number of iterations whether the given system of linear ineqalities has a solution. If it does, the solution for the given system of linear inequalities is provided. The computational complexity of the proposed method is locally polynomial.
</abstract>

Siedlce University of Natural Sciences and Humanities

A locally polynomial method for solving a system of linear inequalities

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

The article is devoted to the development and study of a model of a minimal risk portfolio under conditions of hybrid uncertainty of possibilistic-probabilistic type. In this model, the interaction of fuzzy parameters is described by both the strongest and the weakest triangular norms. The formula for variance of a portfolio is given that allows for estimating its risk. Models of acceptable portfolios are based on the principle of expected possibility or on the basis of fulfilling the restriction on the possibility/necessity and probability of the level of portfolio return that is acceptable to an investor. Equivalent deterministic analogues of the models are constructed and their solution methods are developed. Theorems describing a set of investment opportunities are proven. The obtained results are demonstrated on a model example.
</abstract>

Model of a minimal risk portfolio under hybrid uncertainty

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

In this paper, we introduce a <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_candc-2021-0017_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>Q</mi></mrow><mn>2</mn><mi>n</mi></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>
<tex-math>Q_2^n\left( x \right)</tex-math>
</alternatives>
</inline-formula> matrix, whose elements are balancing polynomials, and develop a new coding and decoding method following from the <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_candc-2021-0017_eq_002.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>Q</mi></mrow><mn>2</mn><mi>n</mi></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>
<tex-math>Q_2^n\left( x \right)</tex-math>
</alternatives>
</inline-formula> matrix. We establish the relations between the code matrix elements, error detection and correction for this coding theory.
</abstract>

Coding theory based on balancing polynomials

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

The problem of finding the maximum number of d-vertices cliques (<italic>d</italic> = 3) in <italic>d</italic>-partite graph (<italic>d</italic> = 3) when graph density <italic>q</italic> is lower than 1 is an important problem in combinatorial optimization and it is one of many NP-complete problems. For this problem a meta-heuristic algorithm has been developed, namely an ant colony optimization algorithm. In this paper a new development of this ant algorithm and experimental results are presented. The problem of finding the maximum number of 3-vertices cliques can be encountered in computer image analysis, computer vision applications, automation and robotic vision systems. The optimal solution of this problem boils down to finding a set of 3-vertices cliques in a 3-partite graph and this set should have cardinality as high as possible. The elaborated ant colony algorithm can be easily modified for d-dimensional problems, that is for finding the maximum number of d-vertices cliques in a d-partite graph.
</abstract>

An ant algorithm for the maximum number of 3-cliques in 3-partite graphs

AHEAD OF PRINT

Volume 52 (2023): Issue 2 (June 2023)

Volume 52 (2023): Issue 1 (March 2023)

Volume 51 (2022): Issue 4 (December 2022)

Volume 51 (2022): Issue 3 (September 2022)

Volume 51 (2022): Issue 2 (June 2022)

Volume 51 (2022): Issue 1 (March 2022)

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

Volume 50 (2021): Issue 3 (September 2021)

Volume 50 (2021): Issue 2 (June 2021)

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. 