Archives of Control Sciences

Keywords:

Abstract

In this paper, we consider an optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation. First we get the linearized maximum principle. Further, the concept of a quasi-singular control is introduced and, on this basis, an analogue of the Legendre-Clebsch conditions is obtained. When the analogue of Legendre- Clebsch condition degenerates, a necessary high-order optimality condition is derived. An illustrative example is considered.
Go to article

Authors and Affiliations

Shakir Sh. Yusubov
1
Elimhan N. MahmudoV
2 3
ORCID:

1. Department of Mechanics and Mathematics, Baku State University, Baku, Azerbaijan
2. Department of Mathematics, Istanbul Technical University, Istanbul, Turkey
3. Azerbaijan National Aviation Academy, Baku, Azerbaijan
Keywords:

Abstract

In this article, we extended the concept of controllability, traditionally used to control the final state of a system, to the exact control of its final speed. Inspired by Kalman’s theory, we have established some conditions to characterize the control that allows the system to reach a desired final speed exactly. When the assumptions ensuring speed-controllability are not met, we adopt a regulation strategy that involves determining the control law to make the system’s final speed approach as closely as possible to the predefined final speed, and this at a lower cost. The theoretical results obtained are illustrated through three examples.
Go to article

Authors and Affiliations

Mostafa Rachik
1
ORCID:
Issam Khaloufi
1
ORCID:
Youssef Benfatah
1
ORCID:
Hamza Boutayeb
1
ORCID:
Hassan Laarabi
1
ORCID:

1. Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco
Keywords:

Abstract

The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen from the closed ball of the space Lq (Ω; ℝ<sup>m</sup>), q > 1, with radius r and centered at the origin. The trajectory of the system is defined as p-integrable multivariable function from the space Lq (Ω; ℝ<sup>n</sup>), (1/q) + (1/p) = 1, satisfying the system’s equation almost everywhere. It is shown that the system’s trajectories are robust with respect to the fast consumption of the remaining control resource. Applying this result it is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the total control resource.

Go to article

Authors and Affiliations

Nesir Huseyin
1
ORCID:
Anar Huseyin
2
ORCID:
Khalik G. Guseinov
3
ORCID:

1. Department of Mathematics and Science Education, Sivas Cumhuriyet University, 58140 Sivas, Turkey
2. Department of Statistics and Computer Sciences, Sivas Cumhuriyet University, 58140 Sivas, Turkey
3. Department of Mathematics, Eskisehir Technical University, 26470 Eskisehir, Turkey
Keywords:

Abstract

This paper introduces a fractional-order PD approach (F-oPD) designed to control a large class of dynamical systems known as fractional-order chaotic systems (F-oCSs). The design process involves formulating an optimization problem to determine the parameters of the developed controller while satisfying the desired performance criteria. The stability of the control loop is initially assessed using the Lyapunov’s direct method and the latest stability assumptions for fractional-order systems. Additionally, an optimization algorithm inspired by the flight skills and foraging behavior of hummingbirds, known as the Artificial Hummingbird Algorithm (AHA), is employed as a tool for optimization. To evaluate the effectiveness of the proposed design approach, the fractional-order energy resources demand-supply (Fo-ERDS) hyperchaotic system is utilized as an illustrative example.
Go to article

Authors and Affiliations

Ammar Soukkou
1
Yassine Soukkou
2
1
Mohamed Benghanem
3
Abdelhamid Rabhi
4

1. Renewable Energy Laboratory, Faculty of Science and Technology, Department of Electronics, University of MSBY Jijel, BP. 98, Ouled Aissa, Jijel, Algeria
2. Research Center in Industrial Technologies CRTI, P. O. Box. 64, Cheraga 16014, Algiers, Algeria
3. Physics Department, Faculty of Science, Islamic University of Madinah, Madinah, KSA
4. Modeling, Information and Systems Laboratory, University of Picardie Jules Verne, Amiens, France.
Keywords:

Abstract

Identification plays an important role in relation to control objects and processes as it enables the control system to be properly tuned. The identification methods described in this paper use the Stochastic Gradient Descent algorithms, which have so far been successfully presented in machine learning. The article presents the results of the Adam and AMSGrad algorithms for online estimation of the Dielectric Electroactive Polymer actuator (DEAP) parameters. This work also aims to validate the learning by batch methodology, which allows to obtain faster convergence and more reliable parameter estimation. This approach is innovative in the field of identification of control systems. The researchwas supplemented with the analysis of the variable amplitude of the input signal. The dynamics of the DEAP parameter convergence depending on the normalization process was presented. Our research has shown how to effectively identify parameters with the use of innovative optimization methods. The results presented graphically confirm that this approach can be successfully applied in the field of control systems.
Go to article

Authors and Affiliations

Jakub Bernat
1
ORCID:
Jakub Kołota
1
ORCID:

1. Institute of Automatic Control and Robotics, Poznan University of Technology, Poznan, Poland
Keywords:

Abstract

Rotating element bearings are the backbone of every rotating machine. Vibration signals measured from these bearings are used to diagnose the health of the machine, but when the signal-to-noise ratio is low, it is challenging to diagnose the fault frequency. In this paper, a new method is proposed to enhance the signal-to-noise ratio by applying the Asymmetric Real Laplace wavelet Bandpass Filter (ARL-wavelet-BPF). The Gaussian function of the ARLwavelet represents an excellent BPF with smooth edges which helps to minimize the ripple effects. The bandwidth and center frequency of the ARL-wavelet-BPF are optimized using the Particle Swarm Optimization (PSO) algorithm. Spectral kurtosis (SK) of the envelope spectrum is employed as a fitness function for the PSO algorithm which helps to track the periodic spikes generated by the fault frequency in the vibration signal. To validate the performance of the ARL-wavelet-BPF, different vibration signals with low signal-to-noise ratio are used and faults are diagnosed.
Go to article

Authors and Affiliations

1
ORCID:
Dariusz Bismor
1
ORCID:
2

1. Department of Measurements and Control Systems, Silesian University of Technology, 44-100 Gliwice, Poland
2. Department of Natural Language Processing, Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE

Abstract

We investigate a scalar characteristic exponential polynomial with complex coefficients associated with a first order scalar differential-difference equation. Our analysis provides necessary and sufficient conditions for allocation of the roots in the complex open left half-plane what guarantees asymptotic stability of the differential-difference equation. The conditions are expressed explicitly in terms of complex coefficients of the characteristic exponential polynomial, what makes them easy to use in applications. We show examples including those for retarded PDEs in an abstract formulation.
Go to article

Authors and Affiliations

Rafał Kapica
1
ORCID:
2
ORCID:

1. Faculty of Applied Mathematics, AGH University of Science and Technology, al.Mickiewicza 30, 30-059 Kraków
2. Department of Automatic Control and Robotics, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice
Keywords:

Abstract

In this paper, the observer design problem for a T-S fuzzy bilinear control system is investigated. First, an observer of Kalman type is designed to estimate the system states for the linear case. Then, some new sufficient conditions are derived to show the exponential convergence of the solutions of the error equation for fuzzy bilinear systems. Furthermore, we consider some uncertainties of the system that are bounded and satisfy a certain condition where an observer is designed. Moreover, an application to Van de Vusse system is given.
Go to article

Authors and Affiliations

François Delmotte
1
2
Mohamed Ali Hammami
3
Houria Meghnafi
3

1. University of Artois, Bethune, France
2. University of Sfax, IPEIS Sfax, Tunisia
3. University of Sfax, Faculty of Sciences of Sfax, Tunisia
Keywords:

Abstract

We build a mathematical game model of pandemic transmission, including vaccinations of population and budget costs of different acting to eliminate pandemic. We assume the interactions among different groups: vaccinated, susceptible, exposed, infectious, super-spreaders, hospitalized and fatality, defining a system of ordinary differential equations, which describes compartment model of disease and costs of the treatment. The goal of the game is to describe the development disease under different types of treatment, but including costs of them and social restrictions, during the shortest time period. To this effect we construct a dual dynamic programming method to describe open-loop Nash equilibrium for treatment, a group of people having antibodies and budget costs. Next, we calculate numerically an approximate open-loop Nash equilibrium.
Go to article

Authors and Affiliations

1
ORCID:
Andrzej Nowakowski
1
ORCID:

1. Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, Łódz, 90-238, Poland
Keywords:

Abstract

The main purpose of this work is to provide an extensive, simulation-based comparison of robustness of PID and MPC algorithms in control of blood glucose levels in patients with type 1 diabetes and thus answer the question of their safety. Cohort testing, with 1000 simulated, randomized patients allowed to analyze specific control quality indicators, such as number of hypoglycemic events, and length of hypo- and hyperglycemia periods. Results show that both algorithms provide a reasonable safety level, taking into account natural changes of patients’ physiological parameters. At the same time, we point out drawbacks of each solution, as well as general problems arising in close-loop control of blood glucose level.
Go to article

Authors and Affiliations

Artur Wyciślok
1
ORCID:
Jarosław Śmieja
1

1. Department of Biology and Systems Engineering, Silesian University of Technology, Gliwice, Poland

Instructions for authors

Each paper submitted is subject to a review procedure, and the publication decision is based on reviers' comments on the paper. To avoid delay, please prepare the manuscript carefully following the suggestions listed below.

Computer file of the manuscript may be sent by e-mail to the address of Assistant Editor or acs@polsl.pl. Preferred text processors is TeX or LaTeX, however Word and other processors are also acceptable. In case of difficulties in processing the text, the author may be asked to supply the ASCII export of the original file.

Manuscripts sent via ordinary post should be typewritten double-spaced on one side of a standard size (A4) paper. Left side margin should be approximately 3cm (1.2'') wide. Each page should contain approximately 30 lines of 60 characters each. The manuscript including figures and tables together with their captions should be submitted. A separate signed letter giving the Author's preferred address for correspondence and return of proofs should be enclosed. Manuscript is the basis for editorial work.

First page should include the title of the paper, first name(s) and surname(s) of the Author(s), and a short summary (abstract), not longer than 20 lines.

Keywords of max. 5 - 7 items should be included in manuscript.

Numeration. All chapters, including the introduction, should be numbered in arabic numerals. Equations, tables and figures as well as theorems, corollaries, examples etc., should be numbered consecutively throughout the paper in arabic numerals, except in appendices. Appendices should be numbered with capital letters, and numeration should be closed within individual appendices.

If the manuscript is not prepared with TeX, mathematical expressions should be carefully written so as not to arouse confusion. Care should be taken that subscripts and superscripts are easily readable.

Tables and figures should be placed as desired by the Author within the text or on separate sheets with their suggested location indicated by the number of table or figure in the text. Figures, graphs and pictures (referred to as Fig. in the manuscript) should be numbered at the beginning of their caption following the figure. All figures should be prepared as PostScript EPS files or LaTeX picture files; in special cases, bitmaps of figure are also acceptable. The numbers and titles of tables should be placed above the main body of each table.

References should be listed alphabetically at the end of the manuscript. They should be numbered in ascending order and the numbers should be inserted in square brackets. References should be organized as follows. First initial(s), surname(s) of the author(s) and title of article or book. Then, for papers: title of periodical or collective work, volume number (year of issue), issue number, and numbers of the first and the last page; for books: publisher's name(s), place and year of issue. Example:

1. R. E. Kalman: Mathematical description of linear dynamical system. SIAM J. Control. 1(2), (1963), 152-192.
2. F. C. Shweppe: Uncertain dynamic systems. Prentice-Hall, Englewood Cliffs, N.J. 1970.

Please, give full titles of journals; only common words like Journal, Proceedings, Conference, etc. may be abbreviated ( to J., Proc., Conf., ... respectively). References to publications in the body of the manuscript should be indicated by the numbers of the adequate references in square brackets. When the paper is set in TeX the preferable form of preparing references is Bib TeX bib database.

Footnotes should be placed in the manuscript, beginning with "Received..." (date to be filled in by Editor), the author's institutional affiliation and acknowledgement of financial support,