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1

Extended Identification-Based Predictive Control for adaptive impact mitigation

Graczykowski Cezary, Faraj Rami

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2023

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Vol. 71, nr 4

art. no. e145937

EN

The paper introduces Extended Identification-Based Predictive Control (EIPC), which is a novel control method developed for the problem of adaptive impact mitigation. The model-based approach utilizing the paradigm of Model Predictive Control is combined with sequential identification of selected system parameters and process disturbances. The elaborated method is implemented in the shock-absorber control system and tested under impact loading conditions. The presented numerical study proves the successful and efficient adaptation of the absorber to unknown excitation conditions as well as to unknown force and leakage disturbances appearing during the process. The EIPC is used for both semi-active and active control of the impact mitigation process, which are compared in detail. In addition, the influence of selected control parameters and disturbance identification on the efficiency of the impact absorption process is assessed. As a result, it can be concluded that an efficient and robust control method was developed and successfully applied to the problem of adaptive impact mitigation.

2

Mathematical modeling and optimal control of the impact of rumors on the banking crisis

Tadmon Calvin, Njike-Tchaptchet Eric Rostand

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

90--118

EN

The bank run phenomenon, mostly due to rumor spread about the financial health of given financial institutions, is prejudicious to the stability of financial systems. In this paper, by using the epidemiological approach, we propose a nonlinear model for describing the impact of rumor on the banking crisis spread. We establish conditions under which the crisis dies out or remains permanent. We also solve an optimal control problem focusing on the minimization, at the lowest cost, of the number of stressed banks, as well as the number of banks undergoing the restructuring process. Numerical simulations are performed to illustrate theoretical results obtained.

3

Structure of Optimal Control in Optimal Shaping of the Steel Arch

Mikulski Leszek, Jasińska Dorota, Dąbrowska Olga

Civil and Environmental Engineering Reports

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2022

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Vol. 32, no. 3

143--165

EN

The paper presents the problem of optimal shaping of the H-bar cross-section of a steel arch that ensures minimal mass. Nineteen combinations of nine basic load states are considered simultaneously in the problem formulation. The optimal shaping task is formulated as a control theory problem within the formal structure of the maximum Pontriagin’s principle. Since the ranges of constraint activity defining the control structure are a priori unknown and must be determined numerically, assuming the proper control structure plays a key role in the task solution. The main achievement of the present work is the determination of a solution of the multi-decision and multi-constraint optimization problem of the arch constituting a primary structural system of the existing building assuring the reduction of the structure mass up to 42%. In addition, the impact of the assumed state constraint value on the solution structure is examined.

4

Control of perishable inventory system with uncertain perishability process using neural networks and robust multicriteria optimization

Chołodowicz Ewelina, Orłowski Przemysław

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 3

art. no. e141182

EN

The inventory systems are highly variable and uncertain due to market demand instability, increased environmental impact, and perishability processes. The reduction of waste and minimization of holding and shortage costs are the main topics studied within the inventory management area. The main difficulty is the variability of perishability and other processes that occurred in inventory systems and the solution for a trade-off between sufficient inventory level and waste of products. In this paper, the approach for resolving this trade-off is proposed. The presented approach assumes the application of a state-feedback neural network controller to generate the optimal quantity of orders considering an uncertain deterioration process and the FIFO issuing policy. The development of the control system is based on state-space close loop control along with neural networks. For modelling the perishability process Weibull distribution and FIFO policy are applied. For the optimization of the designed control system, the evolutionary NSGA-II algorithm is used. The robustness of the proposed approach is provided using the minimax decision rule. The worst-case scenario of an uncertain perishability process is considered. For assessing the proposed approach, simulation research is conducted for different variants of controller structure and model parameters. We perform extensive numerical simulations in which the assessment process of obtained solutions is conducted using hyper volume indicator and average absolute deviation between results obtained for the learning and testing set. The results indicate that the proposed approach can significantly improve the performance of the perishable inventory system and provides robustness for the uncertain changes in the perishability process.

5

Model Predictive Control application in the energy saving technology of basic oxygen furnace

Stepanets Oleksandr, Mariiash Yurii

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2020

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T. 10, nr 2

70--74

EN

The fulfilment of the condition for the simultaneous achievement of the desired chemical composition and temperature of the metal is ensured by controlling the oxygen consumption and the position of the oxygen impeller lance. The method for solving Model Predictive Control with quadratic functionality in the presence of constraints is given. Implementation of the described solutions will contribute to increasing the proportion of scrap and reducing the melting period without changing of technological process.

PL

Spełnienie warunku jednoczesnego osiągnięcia pożądanego składu chemicznego i temperatury metalu jest zapewnione poprzez kontrolę zużycia tlenu i położenia palnika tlenowego. Zaprezentowano metodę rozwiązania Modelu Sterowania Predykcyjnego z funkcjonalnością kwadratową w obecności ograniczeń. Wdrożenie opisanego rozwiązania przyczyni się do zwiększenia udziału złomu i skrócenia czasu topnienia bez zmiany procesu technologicznego.

6

Bi-level Optimization Application for Urban Traffic Management

Stoilova Krasimira, Stoilov Todor

Annals of Computer Science and Information Systems

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2020

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Vol. 21

327--336

EN

A bi-level modeling for traffic lights optimization is presented. The bi-level modeling allows increasing the set of control influences, the number of constraints and applies two goal functions in hierarchical order. The bi-level formalism allows integration of small optimization problems in hierarchical order to a complex interconnected and complicated optimization problem. These features have been applied for optimal control of traffic lights in urban network. The bi-level problem formulation allows to minimize the queue lengths of vehicles and to maximize the outgoing flows from arterial direction. Both control influences of the green light durations and time cycles are evaluated as optimal bi-level control influences.

7

Energy-optimal current distribution in an electrical network – controlling by the differential or the integral systems

Siwczyński M., Żaba S., Drwal A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 3

613--620

EN

In the complex RLC network, apart from the currents flows arising from the normal laws of Kirchhoff, other distributions of current, resulting from certain optimization criteria, may also be received. This paper is the development of research on distribution that meets the condition of the minimum energy losses within the network called energy-optimal distribution. Optimal distribution is not reachable itself, but in order to trigger it off, it is necessary to introduce the control system in current-dependent voltage sources vector, entered into a mesh set of a complex RLC network. For energy-optimal controlling, to obtain the control operator, the inversion of R(s) operator is required. It is the matrix operator and the dispersive operator (it depends on frequency). Inversion of such operators is inconvenient because it is algorithmically complicated. To avoid this the operator R(s) is replaced by the R’ operator which is a?matrix, but non-dispersive one (it does not depend on s). This type of control is called the suboptimal control. Therefore, it is important to make appropriate selection of the R’ operator and hence the suboptimal control. This article shows how to implement such control through the use of matrix operators of multiple differentiation or integration. The key aspect is the distribution of a single rational function H(s) in a series of ‘s’ or ‘s1’. The paper presents a new way of developing a given, stable rational transmittance with real coefficients in power series of ‘s/s1. The formulas to determine values of series coefficients (with ‘s/s1’) have been shown and the conditions for convergence of differential/integral operators given as series of ‘s/s1’ have been defined.

8

The Revised Method for Calculating of The Optimal Train Control Mode

Zhelieznov Konstantun I., Akulov Artem S., Zabolotniy Oleksandr M., Ursulyak Lyudmila V., Chabanuk Evgenij V., Shvets Angela O., Kuznetsov Valeriy G., Radkevych Anatolii V.

Archives of Transport

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2019

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Vol. 51, iss. 3

7--19

EN

Development of a method for calculating the optimal mode of conducting a train in terms of energy saving meet the safety requirements and schedules. The method of calculation must solve the assigned tasks without significant time spent on the calculation. To implement this method of calculation was used a simplified model of the train as a controlled system. The existing mathematical and algorithmic methods for solving isoperimetric problems of finding the optimal solution in the presence of restrictions on resources were the information base for methodology development. Scientific works of domestic and foreign scientists, professional periodicals, materials of scientific and practical conferences, methodical and normative materials, currently in force on Ukrainian Railways. The results of these studies were used to create simulators on the basis of computer technology for the training of locomotive drivers. The scientific novelty of the proposed calculation method consists in applying the simplified calculations of the status of the train as a controlled system, without the use of differential equations of motion that allows to significantly increase the speed of the calculations. This, in turn, will solve the problems of finding optimal control in real time, taking into account changing conditions during the movement of the train. The practical significance of the obtained results is the use of such a calculation method that does not require significant time for its implementation and can be used as a subsystem of the on-board train control system capable of performing calculations taking into account changes in the current train situation.

9

Optimal digital control of an uncertain parameter 2nd order plant

Oprzędkiewicz K.

Science, Technology and Innovation

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2018

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Vol. 2, no. 1

59--63

EN

In the paper a construction of a control system for 2nd order, uncertain-parameter plant is discussed. The considered model of the plant is described by state space equation or by equivalent transfer function and it describes a huge class of real control plants, for example – electric drives or oriented PV systems. As a controller the digital proportional (P) controller was employed. The control system is going to be implemented at the microcontroller platform. Results are by the example depicted.

10

Application of differential games in mechatronic control system

Hendzel Z., Penar P.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 4

867--878

EN

Differential games are a combination of game theory and optimum control methods. Their solutions are based on Bellman's principle of optimality. In this paper, the zero-sum differential game theory has been used for the purposes of controlling a mechatronic object: a single-link manipulator. In this case, analytical solutions are unavailable, thus approximate solutions were used. Two approximation methods were compared with the use of numerical simulations and selected quality indicators. The results confirm previous assumptions and the connection between the differential game theory and H∞ control problems.

11

Energy-optimal current distribution in a complex linear electrical network with pulse or periodic voltage and current signals. Optimal control

Siwczyński M., Żaba S., Drwal A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

|

Vol. 64, nr 1

45--50

EN

The article presents that in the circuits of electrical signals belonging to the L1-impulses space or periodic signals space, real distribution of electrical currents occurs which does not meet the principle of minimum energy losses. The paper presents a solution of this problem by using the control system in the form of current-dependent voltage sources entering it into a meshes set of a complex RLC network. It has been shown that the control is energy-neutral.

12

Investigation of multicriteria optimal control with time-variable weight coefficients

Lozynskyy A., Demkiv L.

Przegląd Elektrotechniczny

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2013

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R. 89, nr 2a

195-198

EN

A new approach for construction of quality functional at multicriteria optimization is proposed. A two-mass dynamical system which consists of two subsystems is considered. A case when in the area of large errors unstable subsystem dominates is considered. Function L is chosen for switching between subsystems and its optimal parameters are found.

PL

W artykule zaproponowano nowe podejście do opracowania funkcji jakości w optymalizacji wielokryterialnej. Badania przeprowadzono na systemie dynamicznych dwóch mas, dla przypadku przeważającej niestabilności jednej z nich. Zoptymalizowano parametry funkcji L, wybranej do określania przejść między obiektami.

13

A Surveillance of Dynamic Processes on Selected Mechatronic Systems

Kaliński K., Galewski M., Mazur M.

Archive of Mechanical Engineering

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2013

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Vol. LX, nr 3

347--367

EN

The paper concerns development of original method of optimal control at energy performance index and its application to dynamic processes surveillance of some mechatronic systems. The latter concerns chatter vibration surveillance during highspeed slender milling of rigid details, as well as motion control of two-wheeled mobile platform. Results of on-line computer simulations and real performance on the target objects reflect a great efficiency of the processes surveillance.

PL

Artykuł poświęcony jest przedstawieniu oryginalnej metody sterowania optymalnego z wykorzystaniem energetycznego wskaźnika jakości i jej zastosowaniu do nadzorowania procesów dynamicznych w wybranych systemach mechatronicznych. W szczególności dotyczy to nadzorowania drgań chatter podczas obróbki szybkościowej przedmiotów sztywnych z wykorzystaniem narzędzi smukłych oraz sterowania ruchem dwukołowej platformy mobilnej. Rezultaty symulacji komputerowych oraz przeprowadzone badania eksperymentalne na rzeczywistych obiektach pokazują dużą efektywność proponowanej metody.

14

O niektórych wynikach analizy i optymalizacji HM-sieci i ich zastosowaniach

Kiturko O., Kołuzajewa K., Matałycki M.

Studia Informatica

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2011

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Vol. 32, nr 3A

21-30

PL

W artykule przeprowadzono badanie HM-sieci kolejkowych z dochodami, w przypadku gdy intensywność wchodzącego strumienia zgłoszeń i intensywności obsługiwania zgłoszeń w systemach obsługi zależą od ich ilości w systemach i od czasu. Rozpatrywane są zadania optymalizacji i optymalnej kontroli dla tych sieci. Przedstawione zostały przykłady zastosowań HM-sieci do prognozowania dochodów różnych obiektów komputerowych.

EN

Investigation of HM queueing networks with incomes in case when arrival rate of messages and service rates of messages in queueing systems depend on their number and time is carried out. Optimization and optimal control problems for these networks are observed. Examples of HM-networks applications for income forecasting of different computer objects are presented.

15

Modelling and control of mechatronic systems by the descriptor approach

Muller P. C.

Journal of Theoretical and Applied Mechanics

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2005

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Vol. 43 nr 3

593--607

EN

In recent years, the analysis and synthesis of control systems in a descriptor form has been established. The general description of dynamical systems by differential-algebraic equations (DAE) is important for many applications in various disciplines, but particularly in mechatronics. In this contribution, the pros and cons of the modelling of mechatronic systems by differential-algebraic equations are discussed with application of subsystem modelling. Additionally, the actual state of the art simulation, analysis and design of descriptor systems are presented.

PL

W ostatnich latach sformułowano i spopularyzowano problem analizy i syntezy układów sterujących w postaci deskrypcyjnej. Ogólny opis układów dynamicznych za pomocą równań różniczkowo-algebraicznych (DAE) ma ogromne znaczenie aplikacyjne w różnych dziedzinach nauki, w szczególności w zakresie mechatroniki. W prezentowanej pracy przedyskutowano wszystkie "za" i "przeciw" modelowania układów mechatronicznych równaniami różniczkowo-algebraicznymi z zastosowaniem podziału opisywanego układu na podsystemy. Ponadto przedstawiono najnowocześniejsze metody symulacji, analizy i projektowania układów deskrypcyjnych.

16

Finite dimensional models of drug resistant and phase specific cancer chemotherapy

Ledzewicz U., Schättler H., Świerniak A.

Journal of Medical Informatics & Technologies

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2004

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Vol. 8

IP5--14

EN

The problem of modelling drug resistance and phase specificity of cancer chemotherapy using finite dimensional models were considered. We formulate optimal control problems arising in protocol design for such models and discuss research issues resulting from these formulations.

17

Optimal multidrug treatment in the presence of drug resistance stemming from gene amplification

Śmieja J., Świerniak A.

Journal of Medical Informatics & Technologies

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2002

|

Vol. 3

MI13--19

EN

The paper is concerned with development of optimal treatment protocols that take into account both action of several drugs and the evolution of drug resistance. It is a result of analysis of evolution of drug resistance in cancer population but presented methodology can be applied in any case involving drug resistance stemming from gene amplification. First, a biological background is given. In subsequent sections of the paper, the developed technique is presented and some early analytical results, which form a basis for more precise modeling, are shown. Afterwards, the model description is transformed into a vector integro-differential equation, which makes it possible to define necessary conditions of optimal solution to the minimization problem arising from the search for the optimal treatment. Finally, some remarks on the model applicability are presented.

18

Mathematical analysis and optimal control problems for the perturbation of the primitive equations of the ocean with vertical viscosity

Belmiloudi A.

Journal of Applied Analysis

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2002

|

Vol. 8, nr 2

153-200

EN

In this paper we consider an oceanic domain in R3, in which there exists, at initial time, a current Uo, a pressure po and a density po. The perturbation U, p and p of the velocity, the pressure and the density are induced by a perturbation of the mean windstress. The equations are of Navier-Stokes type for the velocity and pressure, of transport-diffusion type for the density. They are linearized around a given mean circulation and modified by the physical assumptions including the Boussinesq approximation and the Hydrostatic approximation with vertical viscosity. The existence and uniqueness of the solution for the variational problem are studied for the three-dimensional problem, and for the two-dimensional cyclic problem derived by assuming a sinusoidal .x-dependence for the perturbation of mean flow. The latter corresponds to a modelization of tropical instability waves which are illustrated by El Nino phenomenon.

19

Maximization of flight time for airplane with an electrical power plant

Serokhvostov S.

Research Bulletin / Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics

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2001

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nr 12

131-134

EN

Considered herein is the problem of flight time maximization for an airplane with an electrical power plant. Energy is supplied by the on-board batteries during the flight at a stationary altitude with the specified initial and final speeds. The rational control laws are searched using the Pontryagin principle of maximum. On the basis of this solution some recommendations for the power plant arrangement have been drawn up.