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Abstract

In this work, we present optimal control formulation and numerical algorithm for fractional order discrete time singular system (DTSS) for fixed terminal state and fixed terminal time endpoint condition. The performance index (PI) is in quadratic form, and the system dynamics is in the sense of Riemann-Liouville fractional derivative (RLFD). A coordinate transformation is used to convert the fractional-order DTSS into its equivalent non-singular form, and then the optimal control problem (OCP) is formulated. The Hamiltonian technique is used to derive the necessary conditions. A solution algorithm is presented for solving the OCP. To validate the formulation and the solution algorithm, an example for fixed terminal state and fixed terminal time case is presented.
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[13] T. Chiranjeevi and R.K. Biswas: Closed-form solution of optimal control problem of a fractional order system. Journal of King Saud University – Science, 31(4), (2019), 1042–1047, DOI: 10.1016/j.jksus.2019.02.010.
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[17] M. Gomoyunov: Optimal control problems with a fixed terminal time in linear fractional-order systems. Archives of Control Sciences, 30(2), (2019), 295–324, DOI: 10.24425/acs.2020.135849.
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[20] T. Chiranjeevi, R.K. Biswas, and N.R. Babu: Effect of initialization on optimal control problem of fractional order discrete-time system. Journal of Interdisciplinary Mathematics, 23(1), (2020), 293–302, DOI: 10.1080/09720502.2020.1721924.
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[26] R.K. Biswas and S. Sen: Fractional optimal control within Caputo’s derivative. In: Proceedings of the ASME IDETC/CIE Conference, (2012), 353– 360, DOI: 10.1115/DETC2011-48045.
[27] T. Chiranjeevi, R.K. Biswas, and C. Sethi: Optimal control of fractional order singular system. The International Journal of Electrical Engineering & Education, p. 0020720919833031, (2019), DOI: 10.1177/0020720919833031.
[28] T. Chiranjeevi and R.K. Biswas: Numerical approach to the fractional optimal control problem of continuous-time singular system. In: Advances in Electrical Control and Signal Systems, Singapore, (2020), 239–248, DOI: 10.1007/978-981-15-5262-5_16.
[29] T. Chiranjeevi and R.K. Biswas: Linear quadratic optimal control problem of fractional order continuous-time singular system. Procedia Computer Science, 171 (2020), 1261–1268, DOI: 10.1016/j.procs.2020.04.134.
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Authors and Affiliations

Tirumalasetty Chiranjeevi
1
Raj Kumar Biswas
2
Ramesh Devarapalli
3
ORCID: ORCID
Naladi Ram Babu
2
Fausto Pedro García Márquez
4

  1. Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U. P., India
  2. Department of Electrical Engineering, National Institute of Technology, Silchar, India
  3. Department of Electrical Engineering, BIT Sindri, Dhanbad 828123, Jharkhand, India
  4. Ingenium Research Group, University of Castilla-La Mancha, Spain
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Abstract

A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control affine systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation.
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Authors and Affiliations

Liviu Popescu
1
Ramona Dimitrov
1

  1. University of Craiova, Faculty of Economics and Business Administration, Department of Statistics and Economic Informatics, Al. I. Cuza st., No. 13, Craiova 200585, Romania
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Abstract

Small bucket models with many short fictitious micro-periods ensure high-quality schedules in multi-level systems, i.e., with multiple stages or dependent demand. In such models, setup times longer than a single period are, however, more likely. This paper presents new mixedinteger programming models for the proportional lot-sizing and scheduling problem (PLSP) with setup operations overlapping multiple periods with variable capacity.
A new model is proposed that explicitly determines periods overlapped by each setup operation and the time spent on setup execution during each period. The model assumes that most periods have the same length; however, a few of them are shorter, and the time interval determined by two consecutive shorter periods is always longer than a single setup operation. The computational experiments showthat the newmodel requires a significantly smaller computation effort than known models.
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Authors and Affiliations

Waldemar Kaczmarczyk
1

  1. Department of Strategic Management, AGH University of Science and Technology, Al.Mickiewicza 30, 30-059, Kraków, Poland
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Abstract

Dynamics and control of discrete chaotic systems of fractional-order have received considerable attention over the last few years. So far, nonlinear control laws have been mainly used for stabilizing at zero the chaotic dynamics of fractional maps. This article provides a further contribution to such research field by presenting simple linear control laws for stabilizing three fractional chaotic maps in regard to their dynamics. Specifically, a one-dimensional linear control law and a scalar control law are proposed for stabilizing at the origin the chaotic dynamics of the Zeraoulia-Sprott rational map and the Ikeda map, respectively. Additionally, a two-dimensional linear control law is developed to stabilize the chaotic fractional flow map. All the results have been achieved by exploiting new theorems based on the Lyapunov method as well as on the properties of the Caputo h-difference operator. The relevant simulation findings are implemented to confirm the validity of the established linear control scheme.
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Authors and Affiliations

A. Othman Almatroud
1
Adel Ouannas
2
Giuseppe Grassi
3
Iqbal M. Batiha
4
Ahlem Gasri
5
M. Mossa Al-Sawalha
1

  1. Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 81451, Saudi Arabia
  2. Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
  3. Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy
  4. Department of Mathematics, Faculty of Science and Information Technology, Irbid National University, Irbid, Jordan and Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
  5. Department of Mathematics, University of Larbi Tebessi, Tebessa 12002, Algeria
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Abstract

Hybrid systems (HS) are roughly described as a set of discrete state transitions and continuous dynamics modeled by differential equations. Parametric HS may be constructed by having parameters on the differential equations, initial conditions, jump conditions, or a combination of the previous ones. In real applications, the best solution is obtained by a set of metrics functional over the set of solutions generated from a finite set of parameters. This paper examines the choice of parameters on delta-reachability bounded hybrid systems.We present an efficient model based on the tool pHL-MT to benchmark the HS solutions (based on dReach), and a non-parametric frontier analysis approach, relying on multidirectional efficiency analysis (MEA). Three numerical examples of epidemic models with variable growth infectivity are presented, namely: when the variable of infected individuals oscillates around some endemic (non-autonomous) equilibrium; when there is an asymptotically stable non-trivial attractor; and in the presence of bump functions.
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Authors and Affiliations

Eugénio Miguel Alexandre Rocha
1
Kelly Patricia Murillo
1

  1. Center for Research and Development in Mathematics and Applications, and Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
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Abstract

The paper is concerned with the presentation and analysis of the Dynamic Matrix Control (DMC) model predictive control algorithm with the representation of the process input trajectories by parametrised sums of Laguerre functions. First the formulation of the DMCL (DMC with Laguerre functions) algorithm is presented. The algorithm differs from the standard DMC one in the formulation of the decision variables of the optimization problem – coefficients of approximations by the Laguerre functions instead of control input values are these variables. Then the DMCL algorithm is applied to two multivariable benchmark problems to investigate properties of the algorithm and to provide a concise comparison with the standard DMC one. The problems with difficult dynamics are selected, which usually leads to longer prediction and control horizons. Benefits from using Laguerre functions were shown, especially evident for smaller sampling intervals.
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Authors and Affiliations

Piotr Tatjewski
1

  1. Warsaw University of Technology, Nowowiejska15/19, 00-665 Warszawa, Poland
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Abstract

The paper is a newapproach to the Duhamel integral. It contains an overviewof formulas and applications of Duhamel’s integral as well as a number of new results on the Duhamel integral and principle. Basic definitions are recalled and formulas for Duhamel’s integral are derived via Laplace transformation and Leibniz integral rule. Applications of Duhamel’s integral for solving certain types of differential and integral equations are presented. Moreover, an interpretation of Duhamel’s formula in the theory of operator semigroups is given. Some applications of Duhamel’s formula in control systems analysis are discussed. The work is also devoted to the usage of Duhamel’s integral for differential equations with fractional order derivative.
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Authors and Affiliations

Michał Różański
1
Beata Sikora
1
ORCID: ORCID
Adrian Smuda
1
Roman Wituła
1

  1. Department of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
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Abstract

This paper presents low-cost, configurable PCI Express (PCIe) direct memory access (DMA) interface for implementation on Intel Cyclone V FPGAs. The DMA engine was designed to support DAQ tasks including pre-triggering acquisition for transient analysis and multichannel transmission. Performance of the interface has been evaluated on Terasic OVSK board (PCIe Gen2 x4). Target configuration of this interface is based on the Avalon-MM Hard IP for Cyclone V PCIe core and Jungo WinDriver x64 for Windows. A sample speed of 1200 MB/s has been reported for DMA writes to PCIe memory.
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Authors and Affiliations

Krzysztof Mroczek
1

  1. Institute of Radioelectronics and Multimedia Technology, Warsaw University of Technology, Poland
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Abstract

Lane detection is one of the key steps for developing driver assistance and vehicle automation features. A number of techniques are available for lane detection as part of computer vision tools to perform lane detection with different levels of accuracies. In this paper a unique method has been proposed for lane detection based on dynamic origin (DOT). This method provides better flexibility to adjust the outcome as per the specific needs of the intended application compared to other techniques. As the method offers better degree of control during the lane detection process, it can be adapted to detect lanes in varied situations like poor lighting or low quality road markings. Moreover, the Piecewise Linear Stretching Function (PLSF) has also been incorporated into the proposed method to improve the contrast of the input image source. Adding the PLSF method to the proposed lane detection technique, has significantly improved the accuracy of lane detection when compared to hough transform method from 87.88% to 98.25% in day light situations and from 94.15% to 97% in low light situations.
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Authors and Affiliations

P. Maya
1
C. Tharini
2

  1. B S Abdur Rahman Crescent Institute of Science and Technology, Chennai, India
  2. B S Abdur Rahman Crescent Institute of Science and Technology,Chennai, India
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Abstract

RADAR plays a vital role in military applications since its origin in the 2nd world war. Recently it has been used in surface inception, health monitoring, infrastructure health monitoring, etc. In these applications, Ultra-wideband RADAR systems are more popular than traditional RADAR systems. Impulse RADAR is a special kind of ultra-wideband RADAR, which is mostly used for surface penetration, through-wall imaging, antimissile detection, anti-stealth technology, etc. because of its high resolution and low center frequency. Out of all these applications, impulse RADAR has been used intensively as a ground-penetrating RADAR for the detection of land mines, underlying pipelines, buried objects, etc. This report has attempted to provide the steps for designing the impulse ground penetrating RADAR (GPR) as well as provides the value of crucial parameters required in the design process of commercial GPR systems.
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Authors and Affiliations

Saket Kumar
1
Amit Kumar
2
Vikrant Singh
3
Abhishek Kumar Singh
4

  1. Department of Electronics and Communication Engineering, Muzaffarpur Institute of Technology, Muzaffarpur, Bihar, India
  2. Department of Electronics and Communication Engineering, Bharati Vidyapeeth (Deemed to be University) College of Engineering, Pune, India
  3. Department of Electrical and Electronics Engineering, IIT Guwahati, India
  4. School of Advanced Sciences, Department of Physics, Vellore Institute of Technology, Vellore, Tamil Naidu, India
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Abstract

The world is heading towards deployment of 5G commercially by the year 2020. But providing broadband 5G connectivity to remote rural regions is a significant challenge. Fiber connectivity has attempted to penetrate rural regions but last mile connectivity is still a problem in many rural sectors due to improper land demarcation and hostile terrain. A scheme which is based on the Integrated Access and Backhaul (IAB) concept is proposed to provide last mile 5G connectivity to satisfy the broadband needs of rural subscribers. A wireless 5G downlink environment following 3GPP NR specifications with a significantly high throughput is simulated. The last mile link is provided through a 28GHz carrier from a proposed IAB node delivering a data throughput of 4.301 Gbps for singleuser carrier aggregation and 5.733 Gbps for multi-user carrier aggregation which is quite promising for broadband service, like high-speed Internet and streaming video. The results presented in this work are observed to agree favourably with the results of other researchers in the field.
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Authors and Affiliations

Ardhendu Shekhar Biswas
1
Sanjib Sil
2
Rabindranath Bera
3
Monojit Mitra
4

  1. Department of Electronics and Communication Engineering, Techno International New Town, Kolkata - 700156, India
  2. Department of Electronics and Communication Engineering, Calcutta Institute of Engineering and Management, Kolkata -700040, India
  3. Department of Electronics Communication Engineering, Sikkim Manipal Institute of Technology, Sikkim, India
  4. Department of Electronics and Telecommunication Engineering, IIEST Shibpur, Howrah, India
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Abstract

The power distribution internet of things (PD-IoT) has the complex network architecture, various emerging services, and the enormous number of terminal devices, which poses rigid requirements on substrate network infrastructure. However, the traditional PD-IoT has the characteristics of single network function, management and maintenance difficulties, and poor service flexibility, which makes it hard to meet the differentiated quality of service (QoS) requirements of different services. In this paper, we propose the software-defined networking (SDN)- enabled PD-IoT framework to improve network compatibility and flexibility, and investigate the virtual network function (VNF) embedding problem of service orchestration in PD-IoT. To solve the preference conflicts among different VNFs towards the network function node (NFV) and provide differentiated service for services in various priorities, a matching-based priorityaware VNF embedding (MPVE) algorithm is proposed to reduce energy consumption while minimizing the total task processing delay. Simulation results demonstrate that MPVE significantly outperforms existing matching algorithm and random matching algorithm in terms of delay and energy consumption while ensuring the task processing requirements of high-priority services.
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Authors and Affiliations

Xiaoyue Li
1
Xiankai Chen
1
Chaoqun Zhou
1
Zilong Liang
1
Shubo Liu
1
Qiao Yu
1

  1. State Grid Qingdao Power Supply Company, China
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Abstract

The Internet of Things has a set of smart objects with smart connectivity that assists in monitoring real world environment during emergency situations. It could monitor the various applications of emergency situations such as road accidents, criminal acts including physical assaults, kidnap cases, and other threats to people’s way of life. In this work, the proposed work is to afford real time services to users in emergency situations through Convolutional Neural Networks in terms of efficiency and reliable services. Finally, the proposed work has simulated with respect to the performance parameters of the proposed scheme like the probability of accuracy and processing time.
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Authors and Affiliations

Lokesh B. Bhajantri
1
Ramesh M. Kagalkar
2
Pundalik Ranjolekar
3

  1. Department of Information Science and Engineering, India
  2. KLE College of Engineering and Technology, Chikodi, Karnataka, India
  3. Department of CSE, KLE Society's Dr. M. S. Sheshgiri College of Engineering and Technology, Karnataka, India
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Abstract

Atmospheric turbulence is considered as major threat to Free Space Optical (FSO) communication as it causes irradiance and phase fluctuations of the transmitted signal which degrade the performance of FSO system. Wavelength diversity is one of the techniques to mitigate these effects. In this paper, the wavelength diversity technique is applied to FSO system to improve the performance under different turbulence conditions which are modeled using Exponentiated Weibull (EW) channel. In this technique, the data was communicated through 1.55 μm, 1.31 μm, and 0.85 μm carrier wavelengths. Optimal Combining (OC) scheme has been considered to receive the signals at receiver. Mathematical equation for average BER is derived for wavelength diversity based FSO system. Results are obtained for the different link length under different turbulence conditions. The obtained average BER results for different turbulence conditions characterized by EW channel is compared with the published result of average BER for different turbulence which is presented by classical channel model. A comparative BER analysis shows that maximum advantage of wavelength diversity technique is obtained when different turbulence conditions are modeled by EW channel.
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Authors and Affiliations

Dhaval Shah
1
Hardik Joshi
1
Dilipkumar Kothari
1

  1. Faculty of Electronics and Communication Engineering, Institute of Technology, Nirma University, Ahmedabad, India
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Abstract

RFID systems are one of the essential technologies and used many diverse applications. The security and privacy are the primary concern in RFID systems which are overcome by using suitable authentication protocols. In this manuscript, the costeffective RFID-Mutual Authentication (MA) using a lightweight Extended Tiny encryption algorithm (XTEA) is designed to overcome the security and privacy issues on Hardware Platform. The proposed design provides two levels of security, which includes secured Tag identification and mutual authentication. The RFIDMA mainly has Reader and Tag along with the backend Server. It establishes the secured authentication between Tag and Reader using XTEA. The XTEA with Cipher block chaining (CBC) is incorporated in RFID for secured MA purposes. The authentication process completed based on the challenge and response between Reader and Tag using XTEA-CBC. The present work is designed using Verilog-HDL on the Xilinx environment and implemented on Artix-7 FPGA. The simulation and synthesis results discussed with hardware constraints like Area, power, and time. The present work is compared with existing similar approaches with hardware constraints improvements.
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Authors and Affiliations

R. Anusha
1
V. Veena Devi Shastrimath
1

  1. Department of Electronics and Communication Engineering, N.M.A.M Institute of Technology, Visvesvaraya Technological University, Belagavi, Karnataka, India
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Abstract

As day by day the population is increasing, the use of mobile phones and different applications is increasing which requires high data rate for transmission. Homogeneous cellular network cannot fulfill the demand of mobile users, so creating a heterogeneous cellular network (HCN) is a better choice for higher coverage and capacity to fulfil the increasing demand of upcoming 5G and ultra-dense cellular networks. In this research, the impact of antenna heights and gains under varying pico to macro base stations density ratio from 2G to 5G and beyond on two-tier heterogeneous cellular network has been analyzed for obtaining optimum results of coverage and area spectral efficiency. Furthermore, how the association of UEs affects the coverage and ASE while changing the BSs antenna heights and gains has been explored for the two-tier HCN network model. The simulation results show that by considering the maximum macro BS antenna height, pico BS antenna height equal to user equipment (UE) antenna height and unity gains for both macro and pico tiers, the optimum coverage and area spectral efficiency (ASE) for a two-tier fully loaded heterogeneous cellular network can be obtained.
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Authors and Affiliations

Anum Abbasi
1
M. Mujtaba Shaikh
1
Safia Amir Dahri
1
Sarfraz Ahmed Soomro
1
Fozia Aijaz Panhwar
1

  1. Department of Telecommunication Engineering, Quaid-e-Awam University of Engineering, Science & Technology (QUEST), Nawabshah, Sindh, Pakistan
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Abstract

Real-time data processing systems utilize Digital Signal Processing (DSP) functions as the base modules. Most of the DSP functions involve the implementation of Fast Fourier Transform (FFT) to convert the signals from one domain to another domain. The major bottleneck of Decimation in frequency- Fast Fourier Transform (DIF-FFT) implementation lies in using a number of Multipliers. Distributed arithmetic (DA) is considered as one of the efficient techniques to implement DIF-FFT. In this approach, the multipliers are not used. The proposed technique exploits the very advantage of the look-up table by storing the Twiddle factors, thereby avoiding the multipliers required in the butterfly structure. DIF-FFT using Distributed Arithmetic (DIF-FFT DA) models, with different adders such as Ripple carry adder (RCA), Carry-lookahead adder (CLA), and Sklansky prefix graph adder, are proposed in this paper. The three proposed models are synthesized using Cadence 6.1 EDA tools with a 45nm CMOS technology. Compared to the traditional method, it is observed that the area is improved by 53.11%, 53.35%, and 50.15%, power is improved by 42.31%, 42.52%, and 40.39%, and delay is improved by 45.26%, 45.42%, 41.80%, respectively.
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Authors and Affiliations

Kusma Kumari Cheepurupalli
1
Muntha Charan
1
Jammu Bhaskara Rao
1
Mahammad S. Noor
1

  1. Dept. of ECE, Gayatri Vidya Parishad College of Engineering, India
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Abstract

The paper introduces the distributed framework for determining the shortest path of robots in the logistic applications, i.e. the warehouse with a swarm of robots cooperating in the Real- Time mode. The proposed solution uses the optimization routine to avoid the downtime and collisions between robots. The presented approach uses the reference model based on Dijkstra, Floyd- Warshall and Bellman-Ford algorithms, which search the path in the weighted undirected graph. Their application in the onboard robot’s computer requires the analysis of the time efficiency. Results of comparative simulations for the implemented algorithms are presented. For their evaluation the data sets reflecting actual processes were used. Outcomes of experiments have shown that the tested algorithms are applicable for the logistic purposes, however their ability to operate in the Real-Time requires the detailed analysis.
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Authors and Affiliations

Tomasz Markowski
1
Piotr Bilski
2
ORCID: ORCID

  1. Lukasiewicz – Institute of Logistics and Warehousing, Poland
  2. Warsaw University of Technology, Poland
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Abstract

This research is developing the analog value from the NPK sensor to digital using the YL 38 comparator module to obtain detailed Nitrogen (N), Phosphorus (P), and potassium (K) values according to the NPK sensor datasheet. This system is a network based on the Internet of Things (IoT) and LoRa. The IoT and LoRa features installed on this device, meanwhile the measurement and fertilization data can be monitored easily through an Android application. This research using a frequency of 922.4 Mhz, 125 kHz bandwidth, 10 spreading factors, and a code rate of 5. The Network Quality of Services testing i.e. delay, packet loss, SNR, and RSSI. The QoS was measured at 6 locations. different, 1 location 0 km, 4 locations 1 km, 1 location 2.5 km from BTS LoRa. It was concluded that the parameters used are by the conditions and distances in the data collection. It is proven that all the standards in each parameter are met. In testing the LoRa network it can be concluded that the farther the distance from the LoRa BTS the data transmission quality is getting worse.
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Authors and Affiliations

Doan Perdana
1
Wahyu Rizal Panca Kusuma
1
Ibnu Alinursafa
2

  1. Telkom University, Indonesia
  2. PT Telkom Indonesia, Indonesia
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Abstract

A principle diagram of a high-voltage low-power power supply for devices comprising a microchannel plate (MCP) has been developed. A mathematical model was built according to the developed scheme for a detailed study of the operation of the power supply and the selection of the optimal parameters of its components and obtaining the best output voltages. The power supply circuit comprises a control circuit, a pulse transformer, a voltage multiplier circuit, a feedback circuit, and an input stabilizer. The input stabilizer provides the maintenance of the voltage switched in the primary winding of the transformer at a given level regardless of the voltage drop of the power supply primary source. Moreover the stabilizer provides constant voltage maintenance when the load resistance changes. (with Rload changing from 100 to 200 MΩ, Uout did not exceed 3 V).
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Authors and Affiliations

Boris Martemianov
1
Alexander Ryzhkov
1
Grigoriy Vdovin
1

  1. Limited Liability Company Vladikavkaz Technological Center "BASPIK", North Osetia
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Abstract

This article is a presentation of the analysis of new class of logarithmic analog-to-digital converter (LADC) with accumulation of charge and impulse feedback. Development of mathematical models of errors, quantitative assessment of these errors taking into account modern components and assessing the accuracy of logarithmic analog-to-digital converter (LADC) with accumulation of charge and impulse feedback were presented. (Logarithmic ADC with accumulation of charge and impulse feedback – analysis and modeling).
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Authors and Affiliations

Zynoviy Mychuda
1
Lesya Mychuda
1
Uliana Antoniv
1
Adam Szcześniak
2

  1. Lviv Polytechnic National University, Department of the Computer-Assisted Systems of Automation, Ukraine
  2. University of Technology in Kielce, Department of Mechatronics and Machine Building, Poland
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Abstract

This paper discusses the identification of garbage using the YOLO algorithm. In the rivers, it is usually difficult to distinguish between garbage and plants, especially when it is done in real-time and at the time of too much light. Therefore, there is a need of an appropriate method. The HSV and SIFT methods were used as preliminary tests. The tests were quite successful even in close condition, however, there were still many problems faced in using this method since it is only based on pixel and shape readings. Meanwhile, YOLO algorithm was able to identify garbage and water hyacinth even though they were closed to each other.
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Authors and Affiliations

Bhakti Yudho Suprapto
1
Kelvin
1
Muhammad Arief Kurniawan
1
Muhammad Kevin Ardela
1
Hera Hikmarika
1
Zainal Husin
1
Suci Dwijayanti
1

  1. Department of Electrical Engineering, Faculty of Engineering, Universitas Sriwijaya, Indonesia
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Abstract

In this paper we construct and consider a new group-based digital signature scheme with evolving secret key, which is built using a bilinear map. This map is an asymmetric pairing of Type 3, and although, for the reason of this paper, it is treated in a completely abstract fashion it ought to be viewed as being actually defined over E(Fqn)[p] × E(Fqnk )[p] → Fqnk [p]. The crucial element of the scheme is the key updater algorithm. With the adoption of pairings and binary trees where a number of leaves is the same as a number of time periods, we are assured that an updated secret key can not be used to recover any of its predecessors. This, in consequence, means that the scheme is forward-secure. To formally justify this assertion, we conduct analysis in fu-cma security model by reducing the security of the scheme to the computational hardness of solving the Weak ℓ-th Bilinear Diffie-Hellman Inversion problem type. We define this problem and explain why it can be treated as a source of security for cryptographic schemes. As for the reduction itself, in general case, it could be possible to make only in the random oracle model.
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Authors and Affiliations

Mariusz Jurkiewicz
1

  1. Faculty of Cybernetics, Military University of Technology, Warsaw, Poland

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