Automatic Control and Soft Computing in Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 23254

Special Issue Editors


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Faculty of Automatic Control and Computers, Department of Automatic Control and Systems Engineering, Politehnica University of Bucharest, 313 Splaiul Independentei, Sector 6, 060042 Bucharest, Romania
Interests: signal processing (basic, digital filtering, orthogonal transforms, speech and image processing, time frequency-scale analysis with wavelets, data compression); system identification (linear and nonlinear, advanced techniques, fast algorithms); evolutionary computing; metaheuristic control; robotics; applied mathematics

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Guest Editor
Faculty of Automatic Control and Computers, Department of Computers, Politehnica University of Bucharest, 060042 Bucharest, Romania
Interests: computer architecture; parallel and distributed systems; cluster and grid systems architecture; embedded systems; local area networks; Internet of Things

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Guest Editor
Faculty of Automatic Control and Computers, Department of Automatic Control and Systems Engineering, Politehnica University of Bucharest, 060042 Bucharest, Romania
Interests: system modeling and identification; evolutionary computing; metaheuristic control; deep learning; discrete event systems

Special Issue Information

Dear Colleagues,

Archimedes once said: “The number was in the beginning.” Through this synthetic statement, he foresaw that Mathematics would become one of the science foundations. Automatic Control and Computer Science, as modern and very dynamic fields of science, benefit from many mathematical results and prove that theory can find real-world applications in engineering. This Special Issue of Mathematics on “Automatic Control and Soft Computing in Engineering” is devoted to professionals who have succeeded (or, at least, are trying) to fill the gap between theory and practice. Therefore, all researchers who have obtained new and valuable results in Automatic Control and/or in Soft Computing are cordially invited to submit their work to be considered for publication within this Special Issue.

Potential topics include but are not limited to the following:

Optimal control and supervision;

Metaheuristic control;

Advanced techniques in automatic control;

Computational methods in engineering;

Parallel computing;

Evolutionary computing;

Artificial intelligence;

Internet of Things;

Quantum computing;

Big data;

Cluster, GRID and cloud computing;

Electrical engineering research based on old and new mathematical tools.

Prof. Dr. Dan Stefanoiu
Prof. Dr. Nicolae Tapus
Dr. Janetta Culita
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

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Published Papers (14 papers)

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32 pages, 11156 KiB  
Article
Medical Image-Based Diagnosis Using a Hybrid Adaptive Neuro-Fuzzy Inferences System (ANFIS) Optimized by GA with a Deep Network Model for Features Extraction
by Baidaa Mutasher Rashed and Nirvana Popescu
Mathematics 2024, 12(5), 633; https://doi.org/10.3390/math12050633 - 21 Feb 2024
Viewed by 603
Abstract
Predicting diseases in the early stages is extremely important. By taking advantage of advances in deep learning and fuzzy logic techniques, a new model is proposed in this paper for disease evaluation depending on the adaptive neuro-fuzzy inference system (ANFIS) with a genetic [...] Read more.
Predicting diseases in the early stages is extremely important. By taking advantage of advances in deep learning and fuzzy logic techniques, a new model is proposed in this paper for disease evaluation depending on the adaptive neuro-fuzzy inference system (ANFIS) with a genetic algorithm (GA) for classification, and the pre-trained DenseNet-201 model for feature extraction, in addition to the whale optimization algorithm (WOA) for feature selection. Two medical databases (chest X-ray and MRI brain tumor) for the diagnosis of two disease types were used as input in the suggested model. The optimization of ANFIS parameters was performed by GA to achieve the optimum prediction capability. DenseNet-201 for feature extraction was employed to obtain better classification accuracy. Having more features sometimes leads to lower accuracy, and this issue can be rectified using a feature selection strategy WOA which gave good results. The proposed model was evaluated utilizing statistical metrics root mean square error (RMSE), mean square error (MSE), standard deviation (STD), and coefficient of determination (R2), and it was compared with the conventional ANFIS model, with the proposed model (ANFIS-GA) showing a superior prediction capability over the ANFIS model. As a result, it can be concluded that the proposed ANFIS-GA model is efficient and has the potential for a robust diseases evaluation with good accuracy. Also, we conclude from this work that integrating optimization algorithms with ANFIS boosts its performance, resulting in a more accurate and reliable model. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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40 pages, 14026 KiB  
Article
John von Neumann’s Time-Frequency Orthogonal Transforms
by Dan Stefanoiu and Janetta Culita
Mathematics 2023, 11(12), 2607; https://doi.org/10.3390/math11122607 - 07 Jun 2023
Cited by 1 | Viewed by 847
Abstract
John von Neumann (JvN) was one of the greatest scientists and minds of the 20th century. His research encompassed a large variety of topics (especially from mathematics), and the results he obtained essentially contributed to the progress of science and technology. Within this [...] Read more.
John von Neumann (JvN) was one of the greatest scientists and minds of the 20th century. His research encompassed a large variety of topics (especially from mathematics), and the results he obtained essentially contributed to the progress of science and technology. Within this article, one function that JvN defined long time ago, namely the cardinal sinus (sinc), was employed to define transforms to be applied on 1D signals, either in continuous or discrete time. The main characteristics of JvN Transforms (JvNTs) are founded on a theory described at length in the article. Two properties are of particular interest: orthogonality and invertibility. Both are important in the context of data compression. After building the theoretical foundation of JvNTs, the corresponding numerical algorithms were designed, implemented and tested on artificial and real signals. The last part of the article is devoted to simulations with such algorithms by using 1D signals. An extensive analysis on JvNTs effectiveness is performed as well, based on simulation results. In conclusion, JvNTs prove to be useful tools in signal processing. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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17 pages, 12233 KiB  
Article
Energy Consumption Forecasts by Gradient Boosting Regression Trees
by Luca Di Persio and Nicola Fraccarolo
Mathematics 2023, 11(5), 1068; https://doi.org/10.3390/math11051068 - 21 Feb 2023
Cited by 4 | Viewed by 1918
Abstract
Recent years have seen an increasing interest in developing robust, accurate and possibly fast forecasting methods for both energy production and consumption. Traditional approaches based on linear architectures are not able to fully model the relationships between variables, particularly when dealing with many [...] Read more.
Recent years have seen an increasing interest in developing robust, accurate and possibly fast forecasting methods for both energy production and consumption. Traditional approaches based on linear architectures are not able to fully model the relationships between variables, particularly when dealing with many features. We propose a Gradient-Boosting–Machine-based framework to forecast the demand of mixed customers of an energy dispatching company, aggregated according to their location within the seven Italian electricity market zones. The main challenge is to provide precise one-day-ahead predictions, despite the most recent data being two months old. This requires exogenous regressors, e.g., as historical features of part of the customers and air temperature, to be incorporated in the scheme and tailored to the specific case. Numerical simulations are conducted, resulting in a MAPE of 5–15% according to the market zone. The Gradient Boosting performs significantly better when compared to classical statistical models for time series, such as ARMA, unable to capture holidays. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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15 pages, 3361 KiB  
Article
Newton-Based Extremum Seeking for Dynamic Systems Using Kalman Filtering: Application to Anaerobic Digestion Process Control
by Yang Tian, Ning Pan, Maobo Hu, Haoping Wang, Ivan Simeonov, Lyudmila Kabaivanova and Nicolai Christov
Mathematics 2023, 11(1), 251; https://doi.org/10.3390/math11010251 - 03 Jan 2023
Cited by 1 | Viewed by 1486
Abstract
In this paper, a new Newton-based extremum-seeking control for dynamic systems is proposed using Kalman filter for gradient and Hessian estimation as well as a stochastic perturbation signal with time-varying amplitude. The obtained Kalman filter based Newton extremum-seeking control (KFNESC) makes it possible [...] Read more.
In this paper, a new Newton-based extremum-seeking control for dynamic systems is proposed using Kalman filter for gradient and Hessian estimation as well as a stochastic perturbation signal with time-varying amplitude. The obtained Kalman filter based Newton extremum-seeking control (KFNESC) makes it possible to accelerate the convergence to the extremum and attenuate the steady-state oscillations. The convergence and oscillation attenuation properties of the closed-loop system with KFNESC are considered, and the proposed control is applied to a two-stages anaerobic digestion process in order to maximize the hydrogen production rate, which has better robustness and a slower steady-state oscillation with the comparison of Newton-based ESC and sliding mode ESC. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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16 pages, 1577 KiB  
Article
Backstepping Control Strategy of an Autonomous Underwater Vehicle Based on Probability Gain
by Yudong Peng, Longchuan Guo and Qinghua Meng
Mathematics 2022, 10(21), 3958; https://doi.org/10.3390/math10213958 - 25 Oct 2022
Cited by 4 | Viewed by 1129
Abstract
In this paper, an underwater robot system with nonlinear characteristics is studied by a backstepping method. Based on the state preservation problem of an Autonomous Underwater Vehicle (AUV), this paper applies the backstepping probabilistic gain controller to the nonlinear system of the AUV [...] Read more.
In this paper, an underwater robot system with nonlinear characteristics is studied by a backstepping method. Based on the state preservation problem of an Autonomous Underwater Vehicle (AUV), this paper applies the backstepping probabilistic gain controller to the nonlinear system of the AUV for the first time. Under the comprehensive influence of underwater resistance, turbulence, and driving force, the motion of the AUV has strong coupling, strong nonlinearity, and an unpredictable state. At this time, the system’s output feedback can solve the problem of an unmeasurable state. In order to achieve a good control effect and extend the cruising range of the AUV, first, this paper will select the state error to make it a new control objective. The system’s control is transformed into the selection of system parameters, which greatly simplifies the degree of calculation. Second, this paper introduces the concept of a stochastic backstepping control strategy, in which the robot’s actuators work discontinuously. The actuator works only when there is a random disturbance, and the control effect is not diminished. Finally, the backstepping probabilistic gain controller is designed according to the nonlinear system applied to the simulation model for verification, and the final result confirms the effect of the controller design. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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20 pages, 1027 KiB  
Article
An Integral Sliding Mode Stator Current Control for Industrial Induction Motor
by Fahimeh Shiravani, Patxi Alkorta, Jose Antonio Cortajarena and Oscar Barambones
Mathematics 2022, 10(15), 2765; https://doi.org/10.3390/math10152765 - 04 Aug 2022
Cited by 3 | Viewed by 1294
Abstract
An integral sliding mode control (ISMC) for stator currents of the induction motor (IM) is developed in this work. The proposed controller is developed in the d-q synchronous reference frame, by using the indirect field-oriented control (FOC) method. Robust asymptotic tracking of stator [...] Read more.
An integral sliding mode control (ISMC) for stator currents of the induction motor (IM) is developed in this work. The proposed controller is developed in the d-q synchronous reference frame, by using the indirect field-oriented control (FOC) method. Robust asymptotic tracking of stator current components in the presence of model uncertainties and current coupling disturbance terms has been guaranteed by using an enhanced ISMC surface. More precisely, the stationary error of stator currents has been eliminated, and the accuracy of the regulators has been enhanced. According to the Lyapunov approach, it has been proven that the stator currents tracking happens asymptotically, and consequently, the stability of each loop has been demonstrated. Simulation and experimental results show the capability of the new controller in diminishing system chattering and increasing the robustness of the designed scheme, considering the variation of the plant parameters and current disturbance terms. It has been illustrated that compared with the conventional ISMC and PI regulators, the proposed current controllers provide smoother control actions and excellent dynamics. In addition, because of the precise control over the rotor flux, the rotor flux weakening method is employed to run the motor at a higher speed than the rated value. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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20 pages, 448 KiB  
Article
Quantized Fault-Tolerant Control for Descriptor Systems with Intermittent Actuator Faults, Randomly Occurring Sensor Non-Linearity, and Missing Data
by Mourad Kchaou, Houssem Jerbi, Dan Stefanoiu and Dumitru Popescu
Mathematics 2022, 10(11), 1872; https://doi.org/10.3390/math10111872 - 30 May 2022
Cited by 2 | Viewed by 1201
Abstract
This paper examines the fault-tolerant control problem for discrete-time descriptor systems that are susceptible to intermittent actuator failures, nonlinear sensor data, and probability-based missing data. The discrete-time non-homogeneous Markov chain was adopted to describe the stochastic behavior of actuator faults. Moreover, Bernoulli-distributed stochastic [...] Read more.
This paper examines the fault-tolerant control problem for discrete-time descriptor systems that are susceptible to intermittent actuator failures, nonlinear sensor data, and probability-based missing data. The discrete-time non-homogeneous Markov chain was adopted to describe the stochastic behavior of actuator faults. Moreover, Bernoulli-distributed stochastic variables with known conditional probabilities were employed to describe the practical features of random sensor non-linearity and missing data. In this study, the output signals were quantized and a dynamic output feedback controller was synthesized such that the closed-loop system was stochastically admissible and satisfied the strictly (Q,S,R)-γ-dissipative performance index. The theoretical developments are illustrated through numerical simulations of an infinite machine bus. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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17 pages, 1567 KiB  
Article
On Generalizing Sarle’s Bimodality Coefficient as a Path towards a Newly Composite Bimodality Coefficient
by Nicolae Tarbă, Mihai-Lucian Voncilă and Costin-Anton Boiangiu
Mathematics 2022, 10(7), 1042; https://doi.org/10.3390/math10071042 - 24 Mar 2022
Cited by 1 | Viewed by 2347
Abstract
Determining whether a distribution is bimodal is of great interest for many applications. Several tests have been developed, but the only ones that can be run extremely fast, in constant time on any variable-size signal window, are based on Sarle’s bimodality coefficient. We [...] Read more.
Determining whether a distribution is bimodal is of great interest for many applications. Several tests have been developed, but the only ones that can be run extremely fast, in constant time on any variable-size signal window, are based on Sarle’s bimodality coefficient. We propose in this paper a generalization of this coefficient, to prove its validity, and show how each coefficient can be computed in a fast manner, in constant time, for random regions pertaining to a large dataset. We present some of the caveats of these coefficients and potential ways to circumvent them. We also propose a composite bimodality coefficient obtained as a product of the weighted generalized coefficients. We determine the potential best set of weights to associate with our composite coefficient when using up to three generalized coefficients. Finally, we prove that the composite coefficient outperforms any individual generalized coefficient. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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20 pages, 597 KiB  
Article
Towards a Highly Available Model for Processing Service Requests Based on Distributed Hash Tables
by Voichiţa Iancu and Nicolae Ţăpuş
Mathematics 2022, 10(5), 831; https://doi.org/10.3390/math10050831 - 05 Mar 2022
Cited by 3 | Viewed by 1922
Abstract
This work aims to identify techniques leading to a highly available request processing service by using the natural decentralization and the dispersion power of the hash function involved in a Distributed Hash Table (DHT). High availability is present mainly in systems that: scale [...] Read more.
This work aims to identify techniques leading to a highly available request processing service by using the natural decentralization and the dispersion power of the hash function involved in a Distributed Hash Table (DHT). High availability is present mainly in systems that: scale well, are balanced and are fault tolerant. These are essential features of the Distributed Hash Tables (DHTs), which have been used mainly for storage purposes. The novelty of this paper’s approach is essentially based on hash functions and decentralized Distributed Hash Tables (DHTs), which lead to highly available data solutions, which a main building block to obtain an improved platform that offers high availability for processing clients’ requests. It is achieved by using a database constructed also on a DHT, which gives high availability to its data. Further, the model requires no changes in the interface, that the request processing service already has towards its clients. Subsequently, the DHT layer is added, for the service to run on top of it, and also a load balancing front end, in order to make it highly available, towards its clients. The paper shows, via experimental validation, the good qualities of the new request processing service, by arguing its improved scalability, load balancing and fault tolerance model. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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24 pages, 842 KiB  
Article
Balancing the Electromagnetic Field Exposure in Wireless Multi-Hop Networks: An EMF-Aware Routing Scheme
by Voichiţa Iancu, Luis Diez, Emil Sluşanschi and Ramón Agüero
Mathematics 2022, 10(4), 668; https://doi.org/10.3390/math10040668 - 21 Feb 2022
Viewed by 1227
Abstract
This work is situated at the conjunction of the fields of distributed systems, telecommunications, and mathematical modeling, aiming to offer solutions to the problem of people’s overexposure to electro-magnetic fields (EMF) radiation. In this paper, we propose a new routing scheme for wireless [...] Read more.
This work is situated at the conjunction of the fields of distributed systems, telecommunications, and mathematical modeling, aiming to offer solutions to the problem of people’s overexposure to electro-magnetic fields (EMF) radiation. In this paper, we propose a new routing scheme for wireless multi-hop networks, which seeks a fairer distribution of the exposure to electromagnetic fields, by leveraging a combination of the transmitted power and the accumulated exposure as a routing metric. We carry out a holistic approach, including: (1) an algorithmic study, (2) an analytical model of the aforementioned novel routing metric, and (3) the specification of a routing protocol. We make a performance assessment of our novel routing protocol and the corresponding algorithm, by means of an extensive simulation campaign over the NS-3 simulator. The obtained results yield that the proposed novel solution is able to not only fairly distribute the exposure, but also to reduce its average value, thus enhancing the user experience. We also show that the power consumption using the EMF-aware proposed solution, based on Cycle Canceling Algorithm (CCA), and that observed with an approach seeking power reduction are alike. Indeed, even if there exist key-differences from the user experience’s point of view between both routing approaches, there is no statistically relevant power increase between them. Thus, our solution manages to keep the consumed power at a low level, and at the same time it reduces the overall nodes’ exposure to EMF. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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18 pages, 1154 KiB  
Article
Automatic Control for Time Delay Markov Jump Systems under Polytopic Uncertainties
by Khalid A. Alattas, Ardashir Mohammadzadeh, Saleh Mobayen, Hala M. Abo-Dief, Abdullah K. Alanazi, Mai The Vu and Arthur Chang
Mathematics 2022, 10(2), 187; https://doi.org/10.3390/math10020187 - 07 Jan 2022
Cited by 6 | Viewed by 1578
Abstract
The Markov jump systems (MJSs) are a special case of parametric switching system. However, we know that time delay inevitably exists in many practical systems, and is known as the main source of efficiency reduction, and even instability. In this paper, the stochastic [...] Read more.
The Markov jump systems (MJSs) are a special case of parametric switching system. However, we know that time delay inevitably exists in many practical systems, and is known as the main source of efficiency reduction, and even instability. In this paper, the stochastic stable control design is discussed for time delay MJSs. In this regard, first, the problem of modeling of MJSs and their stability analysis using Lyapunov-Krasovsky functions is studied. Then, a state-feedback controller (SFC) is designed and its stability is proved on the basis of the Lyapunov theorem and linear matrix inequalities (LMIs), in the presence of polytopic uncertainties and time delays. Finally, by various simulations, the accuracy and efficiency of the proposed methods for robust stabilization of MJSs are demonstrated. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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18 pages, 3870 KiB  
Article
Continuous Stability TS Fuzzy Systems Novel Frame Controlled by a Discrete Approach and Based on SOS Methodology
by Ameni Ellouze, Omar Kahouli, Mohamed Ksantini, Ali Rebhi, Nidhal Hnaien and François Delmotte
Mathematics 2021, 9(23), 3129; https://doi.org/10.3390/math9233129 - 04 Dec 2021
Cited by 1 | Viewed by 1278
Abstract
Generally, the continuous and discrete TS fuzzy systems’ control is studied independently. Unlike the discrete systems, stability results for the continuous systems suffer from conservatism because it is still quite difficult to apply non-quadratic Lyapunov functions, something which is much easier for the [...] Read more.
Generally, the continuous and discrete TS fuzzy systems’ control is studied independently. Unlike the discrete systems, stability results for the continuous systems suffer from conservatism because it is still quite difficult to apply non-quadratic Lyapunov functions, something which is much easier for the discrete systems. In this paper and in order to obtain new results for the continuous case, we proposed to connect the continuous with the discrete cases and then check the stability of the continuous TS fuzzy systems by means of the discrete design approach. To this end, a novel frame was proposed using the sum of square approach (SOS) to check the stability of the continuous Takagi Sugeno (TS) fuzzy models based on the discrete controller. Indeed, the control of the continuous TS fuzzy models is ensured by the discrete gains obtained from the Euler discrete form and based on the non-quadratic Lyapunov function. The simulation examples applied for various models, by modifying the order of the Euler discrete fuzzy system, are presented to show the effectiveness of the proposed methodology. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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30 pages, 6312 KiB  
Article
A Chaotic Krill Herd Optimization Algorithm for Global Numerical Estimation of the Attraction Domain for Nonlinear Systems
by Messaoud Aloui, Faiçal Hamidi, Houssem Jerbi, Mohamed Omri, Dumitru Popescu and Rabeh Abbassi
Mathematics 2021, 9(15), 1743; https://doi.org/10.3390/math9151743 - 23 Jul 2021
Cited by 14 | Viewed by 2075
Abstract
Nowadays, solving constrained engineering problems related to optimization approaches is an attractive research topic. The chaotic krill herd approach is considered as one of most advanced optimization techniques. An advanced hybrid technique is exploited in this paper to solve the challenging problem of [...] Read more.
Nowadays, solving constrained engineering problems related to optimization approaches is an attractive research topic. The chaotic krill herd approach is considered as one of most advanced optimization techniques. An advanced hybrid technique is exploited in this paper to solve the challenging problem of estimating the largest domain of attraction for nonlinear systems. Indeed, an intelligent methodology for the estimation of the largest stable equilibrium domain of attraction established on quadratic Lyapunov functions is developed. The designed technique aims at computing and characterizing a largest level set of a Lyapunov function that is included in a particular region, satisfying some hard and delicate algebraic constraints. The formulated optimization problem searches to solve a tangency constraint between the LF derivative sign and constraints on the level sets. Such formulation avoids possible dummy solutions for the nonlinear optimization solver. The analytical development of the solution exploits the Chebyshev chaotic map function that ensures high search space capabilities. The accuracy and efficiency of the chaotic krill herd technique has been evaluated by benchmark models of nonlinear systems. The optimization solution shows that the chaotic krill herd approach is effective in determining the largest estimate of the attraction domain. Moreover, since global optimality is needed for proper estimation, a bound type meta-heuristic optimization solver is implemented. In contrast to existing strategies, the synthesized technique can be exploited for both rational and polynomial Lyapunov functions. Moreover, it permits the exploitation of a chaotic operative optimization algorithm which guarantees converging to an expanded domain of attraction in an essentially restricted running time. The synthesized methodology is discussed, with several examples to illustrate the advantageous aspects of the designed approach. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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Review

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15 pages, 322 KiB  
Review
A Concise Review of State Estimation Techniques for Partial Differential Equation Systems
by Ivan Francisco Yupanqui Tello, Alain Vande Wouwer and Daniel Coutinho
Mathematics 2021, 9(24), 3180; https://doi.org/10.3390/math9243180 - 09 Dec 2021
Cited by 6 | Viewed by 2403
Abstract
While state estimation techniques are routinely applied to systems represented by ordinary differential equation (ODE) models, it remains a challenging task to design an observer for a distributed parameter system described by partial differential equations (PDEs). Indeed, PDE systems present a number of [...] Read more.
While state estimation techniques are routinely applied to systems represented by ordinary differential equation (ODE) models, it remains a challenging task to design an observer for a distributed parameter system described by partial differential equations (PDEs). Indeed, PDE systems present a number of unique challenges related to the space-time dependence of the states, and well-established methods for ODE systems do not translate directly. However, the steady progresses in computational power allows executing increasingly sophisticated algorithms, and the field of state estimation for PDE systems has received revived interest in the last decades, also from a theoretical point of view. This paper provides a concise overview of some of the available methods for the design of state observers, or software sensors, for linear and semilinear PDE systems based on both early and late lumping approaches. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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