Pub Date : 2025-12-01DOI: 10.1016/j.rico.2025.100630
Battula Tirumala Krishna
The primary goal of this study is to look into the analysis, design, and applications of fractional order digital differentiators and integrators. First, different existing procedures for the calculation of the Rational Approximation of the fractional-order operator, are explored. The discretization of , is a crucial step in the construction of digital differentiators and integrators. The to transformations used in this investigation, including those by Al-Alaoui, Tahar, and Gujan Stancic, are reviewed. Direct and indirect discretization methods can be used to design fractional order digital differentiators and integrators. This paper discusses the development of fractional order differentiators and integrators of order using the indirect discretization technique. The created fractional order differentiators have been used in the processing of Electro Cardio Gram (ECG) Signal and localization of edges in an Image. The reported findings are being compared to standard approaches. All simulations are performed using MATLAB. The Root Mean Square Error (RMSE) Values obtained using Guran Stancic Transform based Fractional Order Differentiator for the detection of the Edges in an Image is 0.0014265. The Signal to Noise Ratio (SNR) Values obtained using Al-Alaoui Transform based Fractional Order Differentiator for the detection of the Edges in an Image is dB.
{"title":"The development of novel fractional order differentiators and their applications","authors":"Battula Tirumala Krishna","doi":"10.1016/j.rico.2025.100630","DOIUrl":"10.1016/j.rico.2025.100630","url":null,"abstract":"<div><div>The primary goal of this study is to look into the analysis, design, and applications of fractional order digital differentiators and integrators. First, different existing procedures for the calculation of the Rational Approximation of the fractional-order operator, <span><math><msup><mrow><mi>s</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span> are explored. The discretization of <span><math><msup><mrow><mi>s</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>, is a crucial step in the construction of digital differentiators and integrators. The <span><math><mi>s</mi></math></span> to <span><math><mi>z</mi></math></span> transformations used in this investigation, including those by Al-Alaoui, Tahar, and Gujan Stancic, are reviewed. Direct and indirect discretization methods can be used to design fractional order digital differentiators and integrators. This paper discusses the development of fractional order differentiators and integrators of order <span><math><mi>α</mi></math></span> using the indirect discretization technique. The created fractional order differentiators have been used in the processing of Electro Cardio Gram (ECG) Signal and localization of edges in an Image. The reported findings are being compared to standard approaches. All simulations are performed using MATLAB. The Root Mean Square Error (RMSE) Values obtained using Guran Stancic Transform based Fractional Order Differentiator for the detection of the Edges in an Image is 0.0014265. The Signal to Noise Ratio (SNR) Values obtained using Al-Alaoui Transform based Fractional Order Differentiator for the detection of the Edges in an Image is <span><math><mrow><mo>−</mo><mn>108</mn><mo>.</mo><mn>9501</mn></mrow></math></span> dB.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"21 ","pages":"Article 100630"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145614418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01DOI: 10.1016/j.rico.2025.100634
Asmaa Shareef , Salah Al-darraji , Suhaib Al-Ansarry , Zaid Ameen Abduljabbar , Vincent Omollo Nyangaresi , Ali Hasan Ali , Husam A. Neamah
Robot navigation and path planning are among the most critical challenges facing mobile robots. Modern techniques have surpassed traditional methods in reducing high complexity by utilizing probabilistic or optimal solutions, such as algorithms based on swarm intelligence. This work proposes a novel global path planning using a bipopulation grasshopper optimization algorithm (BiGOA). Superior performance results were obtained compared to the original grasshopper optimization algorithm regarding time, cost, and path length for an average of 1000 times executions in environments of varying complexities. On the other hand, the optimal path, local path planning, and dynamic obstacle avoidance are done by the Dynamic Window Approach (DWA) algorithm that works within the follow-waypoint technique in mobile vehicles in the Robot Operating System (ROS). During robot movement, it tends to find a shorter and optimal path using a modified version of the waypoint method. A state machine determines the optimal path using the improved follow-waypoint algorithm during the robot’s real-time movement, thereby controlling the path’s smoothing, shortening, and continuity. This study compares the BiGOA algorithm with an optimal path method based on arrival time over ten trials. The results show that BiGOA paths were, on average, 33 s longer. Additionally, the robot’s performance using the proposed method was tested in a dynamic and complex environment, where the results indicated a reduction in both time and effort.
{"title":"Local path planning based on Bi-population Swarms optimization algorithms","authors":"Asmaa Shareef , Salah Al-darraji , Suhaib Al-Ansarry , Zaid Ameen Abduljabbar , Vincent Omollo Nyangaresi , Ali Hasan Ali , Husam A. Neamah","doi":"10.1016/j.rico.2025.100634","DOIUrl":"10.1016/j.rico.2025.100634","url":null,"abstract":"<div><div>Robot navigation and path planning are among the most critical challenges facing mobile robots. Modern techniques have surpassed traditional methods in reducing high complexity by utilizing probabilistic or optimal solutions, such as algorithms based on swarm intelligence. This work proposes a novel global path planning using a bipopulation grasshopper optimization algorithm (BiGOA). Superior performance results were obtained compared to the original grasshopper optimization algorithm regarding time, cost, and path length for an average of 1000 times executions in environments of varying complexities. On the other hand, the optimal path, local path planning, and dynamic obstacle avoidance are done by the Dynamic Window Approach (DWA) algorithm that works within the follow-waypoint technique in mobile vehicles in the Robot Operating System (ROS). During robot movement, it tends to find a shorter and optimal path using a modified version of the waypoint method. A state machine determines the optimal path using the improved follow-waypoint algorithm during the robot’s real-time movement, thereby controlling the path’s smoothing, shortening, and continuity. This study compares the BiGOA algorithm with an optimal path method based on arrival time over ten trials. The results show that BiGOA paths were, on average, 33 s longer. Additionally, the robot’s performance using the proposed method was tested in a dynamic and complex environment, where the results indicated a reduction in both time and effort.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"21 ","pages":"Article 100634"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145681176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01DOI: 10.1016/j.rico.2025.100635
K. Divakar , Muni Reddy G. , N.M.G. Kumar , M. Ijaz Khan
In the chemical industry, integrating processes are often encountered. Examples of integrating processes include bottom level control of a distillation column, level control of a tank with a motor fixed at the outlet, current-controlled DC motor, fermentation reactors, spacecraft take-off dynamics, paper industry drying processes, continuous stirred tank reactor (CSTR) with exothermic reactor, and so on. This article describes a new PID controller with a 2/3 order filter for integrating processes with time delay. Time delay is approximated to ratio of two polynomials using a second-order Pade’s approximation. A set point filter is used to minimize overshoot and the settling time of servo responses. Simulation studies are conducted on some of the benchmarking process models utilized in the literature. The comparative assessment is based on various performance indices.
{"title":"Maximum sensitivity-based PID controller cascaded with 2/3 order filter for integrating processes with time delay","authors":"K. Divakar , Muni Reddy G. , N.M.G. Kumar , M. Ijaz Khan","doi":"10.1016/j.rico.2025.100635","DOIUrl":"10.1016/j.rico.2025.100635","url":null,"abstract":"<div><div>In the chemical industry, integrating processes are often encountered. Examples of integrating processes include bottom level control of a distillation column, level control of a tank with a motor fixed at the outlet, current-controlled DC motor, fermentation reactors, spacecraft take-off dynamics, paper industry drying processes, continuous stirred tank reactor (CSTR) with exothermic reactor, and so on. This article describes a new PID controller with a 2/3 order filter for integrating processes with time delay. Time delay is approximated to ratio of two polynomials using a second-order Pade’s approximation. A set point filter is used to minimize overshoot and the settling time of servo responses. Simulation studies are conducted on some of the benchmarking process models utilized in the literature. The comparative assessment is based on various performance indices.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"21 ","pages":"Article 100635"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145736391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-10DOI: 10.1016/j.rico.2025.100632
A. Agathiyan , Vinothkumar. B , Ali Akgul , Fahad Sameer Alshammari
Chaotic behavior in financial systems strongly influences investment strategies, risk management, and policy decisions. Conventional fractional calculus, however, has limitations in capturing the memory and scaling effects that characterize such complexity. To address this gap, the present study employs a novel differential operator that unifies fractal and fractional calculus through the Caputo and Atangana–Baleanu kernels. The objective is to investigate the nonlinear dynamics of a financial chaotic model using fractal–fractional derivative operators. A numerical scheme is implemented to generate system trajectories, and the Lyapunov exponent is applied to assess chaotic transitions. The results show that variations in saving rate, per-investment cost, and demand elasticity significantly affect system stability and regime shifts. Compared with classical fractional formulations, the proposed approach uncovers crossover phenomena in phase portraits and reveals novel attractor structures. These findings provide deeper insight into the mechanisms underlying financial complexity and demonstrate the effectiveness of fractal–fractional calculus as a powerful framework for modeling real-world economic dynamics.
{"title":"Fractal–fractional modeling and chaos analysis of a financial system with generalized memory kernels","authors":"A. Agathiyan , Vinothkumar. B , Ali Akgul , Fahad Sameer Alshammari","doi":"10.1016/j.rico.2025.100632","DOIUrl":"10.1016/j.rico.2025.100632","url":null,"abstract":"<div><div>Chaotic behavior in financial systems strongly influences investment strategies, risk management, and policy decisions. Conventional fractional calculus, however, has limitations in capturing the memory and scaling effects that characterize such complexity. To address this gap, the present study employs a novel differential operator that unifies fractal and fractional calculus through the Caputo and Atangana–Baleanu kernels. The objective is to investigate the nonlinear dynamics of a financial chaotic model using fractal–fractional derivative operators. A numerical scheme is implemented to generate system trajectories, and the Lyapunov exponent is applied to assess chaotic transitions. The results show that variations in saving rate, per-investment cost, and demand elasticity significantly affect system stability and regime shifts. Compared with classical fractional formulations, the proposed approach uncovers crossover phenomena in phase portraits and reveals novel attractor structures. These findings provide deeper insight into the mechanisms underlying financial complexity and demonstrate the effectiveness of fractal–fractional calculus as a powerful framework for modeling real-world economic dynamics.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"21 ","pages":"Article 100632"},"PeriodicalIF":3.2,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145520162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-07DOI: 10.1016/j.rico.2025.100633
Mohammad Hosein Sabzalian , Changdong Du , Ardashir Mohammadzadeh
The formation control (FC) for nonlinear mobile robots (MRs) during various operations is studied in this paper. An interval type-3 (T3) fuzzy logic system (FLS) based controller is introduced to enable the multiple MRs to follow the desired formation, without requiring measurement the relative pose or velocity of the follower robots. A camera is used to coordinate the motion between the leader and the followers. Additionally, the robustness of the system is analyzed in the presence of external disturbances and unknown uncertainties. T3-FLSs with novel online optimized tuning rules and adaptive mechanisms serve the dual purpose of approximating the unknown dynamics of MRs with nonholonomic constraints and implementing a fuzzy-based controller. By utilizing the Lyapunov approach, the adaptation mechanisms of the FLSs are computed, and it is proven that the closed-loop system achieves asymptotic stability. Furthermore, computer simulations are conducted to test the system’s performance in terms of appropriate transient responses and robust tracking against unknown dynamics and disturbances. Simulation results demonstrate accurate tracking, and robustness under various uncertainties. The proposed method provides a computationally efficient, adaptive, and theoretically sound solution for multi-robot formation control, highlighting its potential for practical cooperative robotics applications.
{"title":"A camera-based type-3 fuzzy formation control of multiple robots","authors":"Mohammad Hosein Sabzalian , Changdong Du , Ardashir Mohammadzadeh","doi":"10.1016/j.rico.2025.100633","DOIUrl":"10.1016/j.rico.2025.100633","url":null,"abstract":"<div><div>The formation control (FC) for nonlinear mobile robots (MRs) during various operations is studied in this paper. An interval type-3 (T3) fuzzy logic system (FLS) based controller is introduced to enable the multiple MRs to follow the desired formation, without requiring measurement the relative pose or velocity of the follower robots. A camera is used to coordinate the motion between the leader and the followers. Additionally, the robustness of the system is analyzed in the presence of external disturbances and unknown uncertainties. T3-FLSs with novel online optimized tuning rules and adaptive mechanisms serve the dual purpose of approximating the unknown dynamics of MRs with nonholonomic constraints and implementing a fuzzy-based controller. By utilizing the Lyapunov approach, the adaptation mechanisms of the FLSs are computed, and it is proven that the closed-loop system achieves asymptotic stability. Furthermore, computer simulations are conducted to test the system’s performance in terms of appropriate transient responses and robust tracking against unknown dynamics and disturbances. Simulation results demonstrate accurate tracking, and robustness under various uncertainties. The proposed method provides a computationally efficient, adaptive, and theoretically sound solution for multi-robot formation control, highlighting its potential for practical cooperative robotics applications.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"21 ","pages":"Article 100633"},"PeriodicalIF":3.2,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145520087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-07DOI: 10.1016/j.rico.2025.100631
Bulugu Ndulu Batume , Chacha Stephen Chacha
We present a matrix-free Newton–Krylov solver with exact line search (Algorithm 3) for algebraic Riccati equations and benchmark it against standard Newton variants and common baselines. Using the enhancement percentage metric, , the method delivers consistent and often dramatic gains across problem sizes and settings. On large problems (), wall-clock time improves by 99.8–99.9% relative to classical Newton methods while achieving up to 97% EP in accuracy (final/relative residuals). In an aircraft control instance (), Algorithm 3 attains 99.6% EP in time, reduces iterations by 50–57%, and improves residuals by 82–98%. For large diagonal families (), Algorithm 3 converges in approximately 5 Newton steps with predictable scaling (about 0.30 s, 3.92 s, and 36.72 s, respectively), remaining well-competitive with direct solvers (e.g., dare()) while avoiding Kronecker products and explicit Jacobians. Overall, the results indicate a robust, low-iteration, and near-instant approach that is attractive for real-time and embedded control contexts where both speed and solution quality are paramount.
{"title":"A fast-converging Newton-based iterative scheme for the algebraic Riccati equation with step-size optimization","authors":"Bulugu Ndulu Batume , Chacha Stephen Chacha","doi":"10.1016/j.rico.2025.100631","DOIUrl":"10.1016/j.rico.2025.100631","url":null,"abstract":"<div><div>We present a matrix-free Newton–Krylov solver with exact line search (Algorithm 3) for algebraic Riccati equations and benchmark it against standard Newton variants and common baselines. Using the enhancement percentage metric, <span><math><mrow><mi>EP</mi><mrow><mo>(</mo><mtext>%</mtext><mo>)</mo></mrow><mo>=</mo><mn>100</mn><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mtext>Proposed</mtext><mo>/</mo><mtext>Other</mtext><mo>)</mo></mrow></mrow></math></span>, the method delivers consistent and often dramatic gains across problem sizes and settings. On large problems (<span><math><mrow><mi>n</mi><mo>=</mo><mn>100</mn></mrow></math></span>), wall-clock time improves by 99.8–99.9% relative to classical Newton methods while achieving up to 97% EP in accuracy (final/relative residuals). In an aircraft control instance (<span><math><mrow><mi>n</mi><mo>=</mo><mn>70</mn><mo>,</mo><mi>m</mi><mo>=</mo><mn>35</mn></mrow></math></span>), Algorithm 3 attains 99.6% EP in time, reduces iterations by 50–57%, and improves residuals by 82–98%. For large diagonal families (<span><math><mrow><mi>n</mi><mo>=</mo><mn>500</mn><mo>,</mo><mn>1000</mn><mo>,</mo><mn>2000</mn></mrow></math></span>), Algorithm 3 converges in approximately 5 Newton steps with predictable scaling (about 0.30<!--> <!-->s, 3.92<!--> <!-->s, and 36.72<!--> <!-->s, respectively), remaining well-competitive with direct solvers (e.g., <span>dare()</span>) while avoiding Kronecker products and explicit Jacobians. Overall, the results indicate a robust, low-iteration, and near-instant approach that is attractive for real-time and embedded control contexts where both speed and solution quality are paramount.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"21 ","pages":"Article 100631"},"PeriodicalIF":3.2,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145568189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-07DOI: 10.1016/j.rico.2025.100628
Jhon-Ronald Terreros-Barreto , Walter Gil-González , Alejandro Garcés-Ruiz
The use of power converter devices in the integration of hydrokinetic turbine (HKT) systems is essential since these devices enable controlling the turbine rotation speed to manage the active power provided into grid, as well as, the reactive power compensation. This paper presents an advanced model predictive control (MPC) approach for the maximum power tracking and output frequency control of an HKT connected by a back-to-back converter. The system consists of a horizontal propeller turbine, permanent magnet synchronous generator, rectifier, and inverter. The systems were implemented in MATLAB with the proposed control, and verified through simulations where performance was evaluated based on state variables of the system. A comparison based on a classical proportional-integral (PI) control approach indicates that MPC can achieve superior transitory response and better settling time for high-efficiency implementations, while simultaneously maintaining easy-to-handle implementation. The MPC controller was four times faster than the PI controller in terms of setting time.
{"title":"Model predictive control to manage the hydrokinetic systems connected into grid by a back-to-back converter","authors":"Jhon-Ronald Terreros-Barreto , Walter Gil-González , Alejandro Garcés-Ruiz","doi":"10.1016/j.rico.2025.100628","DOIUrl":"10.1016/j.rico.2025.100628","url":null,"abstract":"<div><div>The use of power converter devices in the integration of hydrokinetic turbine (HKT) systems is essential since these devices enable controlling the turbine rotation speed to manage the active power provided into grid, as well as, the reactive power compensation. This paper presents an advanced model predictive control (MPC) approach for the maximum power tracking and output frequency control of an HKT connected by a back-to-back converter. The system consists of a horizontal propeller turbine, permanent magnet synchronous generator, rectifier, and inverter. The systems were implemented in MATLAB with the proposed control, and verified through simulations where performance was evaluated based on state variables of the system. A comparison based on a classical proportional-integral (PI) control approach indicates that MPC can achieve superior transitory response and better settling time for high-efficiency implementations, while simultaneously maintaining easy-to-handle implementation. The MPC controller was four times faster than the PI controller in terms of setting time.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"21 ","pages":"Article 100628"},"PeriodicalIF":3.2,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145520086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Brucellosis is one of the most prevalent zoonotic diseases worldwide, with significant impacts on human health, animal productivity, and the economy. Animal movement is a key factor influencing its transmission; however, the understanding of how such movements shape disease dynamics and the effectiveness of applied control measures remains limited. This study presents an optimal control model for brucellosis transmission among domestic animals, given the uncertainty in animal movement patterns. The model incorporates and evaluates the effectiveness of different control strategies under varying movement patterns. The effective reproduction number is computed, compared with the basic reproduction number , and used to quantify the potential for brucellosis spread and the effectiveness of different control measures for different time proportions a domestic animal spends in low or high-risk patches. Global sensitivity analysis was performed using the Latin Hypercube Sampling (LHS) approach, where the Partial Rank Correlation Coefficient (PRCC) index was computed. The results show that the time spent by domestic animals in high-risk areas limits the control of brucellosis. The findings also reveal that vaccination is the most effective strategy for significantly reducing the spread of brucellosis, even when domestic animals from low-risk areas spend extended periods in high-risk zones. This underscores the pivotal role of vaccination as the cornerstone of brucellosis control and prevention efforts.
{"title":"The role of temporary displacement of domestic animals in brucellosis control","authors":"Rehema Msuya , Silas Mirau , Nkuba Nyerere , Isambi Mbalawata","doi":"10.1016/j.rico.2025.100627","DOIUrl":"10.1016/j.rico.2025.100627","url":null,"abstract":"<div><div>Brucellosis is one of the most prevalent zoonotic diseases worldwide, with significant impacts on human health, animal productivity, and the economy. Animal movement is a key factor influencing its transmission; however, the understanding of how such movements shape disease dynamics and the effectiveness of applied control measures remains limited. This study presents an optimal control model for brucellosis transmission among domestic animals, given the uncertainty in animal movement patterns. The model incorporates and evaluates the effectiveness of different control strategies under varying movement patterns. The effective reproduction number <span><math><mrow><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>)</mo></mrow></math></span> is computed, compared with the basic reproduction number <span><math><mrow><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow></math></span>, and used to quantify the potential for brucellosis spread and the effectiveness of different control measures for different time proportions a domestic animal spends in low or high-risk patches. Global sensitivity analysis was performed using the Latin Hypercube Sampling (LHS) approach, where the Partial Rank Correlation Coefficient (PRCC) index was computed. The results show that the time spent by domestic animals in high-risk areas limits the control of brucellosis. The findings also reveal that vaccination is the most effective strategy for significantly reducing the spread of brucellosis, even when domestic animals from low-risk areas spend extended periods in high-risk zones. This underscores the pivotal role of vaccination as the cornerstone of brucellosis control and prevention efforts.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"21 ","pages":"Article 100627"},"PeriodicalIF":3.2,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-24DOI: 10.1016/j.rico.2025.100626
Muhammad Farman , Ali Hasan , Sana Ullah Saqib , Ali Akbar , Aceng Sambas , Mohamed Hafez
<div><div>In this paper, we developed a framework that describes the transmission of a hepatitis C model with fractional and machine learning approach for analysis and numerical outcome. The model consists of four groups: viral load, susceptible hepatocytes, infected hepatocytes, and the humoral immune response that the host triggers to fight the virus. Biological feasibility of the model, such as positivity, uniqueness solution through fixed point results. The fractional-order power law kernel solution function was used to set up the numerical simulation. Using data collected by Fractional Order Differential Equations (FODEs) with a fractional order power law kernel solution function, MATLAB was implemented to perform the simulations in question. This is accomplished through the application of the Bayesian Regularization Backpropagation Artificial Neural Network (BRB-ANN) intelligent computing technique. The data set for training the BRB-ANNs is created using Fractional Order Differential Equations (FODEs). The Bayesian Regularization Method with Backpropagation Artificial Neural Nets (BRB-ANNs), the fractional-order hepatitis C virus (FOHCV) model’s precision and effectiveness were significantly improved. The effectiveness of the proposed strategies is evidenced by achieving exceptionally low absolute errors ranging from <span><math><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo>)</mo></mrow></math></span> to <span><math><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>9</mn></mrow></msup><mo>)</mo></mrow></math></span>, minimal Mean Square Error (MSE) values between <span><math><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup><mo>)</mo></mrow></math></span> and <span><math><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>10</mn></mrow></msup><mo>)</mo></mrow></math></span>, and an almost perfect coefficient of determination <span><math><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>≈</mo><mn>0</mn><mo>.</mo><mn>999</mn><mo>)</mo></mrow></math></span>. Furthermore, the error histograms (Er.Hgs), ranging from <span><math><mrow><mo>(</mo><mo>−</mo><mn>9</mn><mo>.</mo><mn>4</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>10</mn></mrow></msup><mo>)</mo></mrow></math></span> to <span><math><mrow><mo>(</mo><mo>−</mo><mn>4</mn><mo>.</mo><mn>12</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup><mo>)</mo></mrow></math></span>, along with the corresponding time series plots (TSP), further validate the precision and reliability of the developed models. Dynamically and graphically, demonstrations indicate the achievement of AI with BRB-ANNs compared to the standard solution, and 3D Lorenz curves for FOHCV are analyzed. These results support the theoretical observation of Hepatitis C disease epidemics and the pr
{"title":"ANN computing framework for modeling and predicting the dynamics of fractional order hepatitis C virus model","authors":"Muhammad Farman , Ali Hasan , Sana Ullah Saqib , Ali Akbar , Aceng Sambas , Mohamed Hafez","doi":"10.1016/j.rico.2025.100626","DOIUrl":"10.1016/j.rico.2025.100626","url":null,"abstract":"<div><div>In this paper, we developed a framework that describes the transmission of a hepatitis C model with fractional and machine learning approach for analysis and numerical outcome. The model consists of four groups: viral load, susceptible hepatocytes, infected hepatocytes, and the humoral immune response that the host triggers to fight the virus. Biological feasibility of the model, such as positivity, uniqueness solution through fixed point results. The fractional-order power law kernel solution function was used to set up the numerical simulation. Using data collected by Fractional Order Differential Equations (FODEs) with a fractional order power law kernel solution function, MATLAB was implemented to perform the simulations in question. This is accomplished through the application of the Bayesian Regularization Backpropagation Artificial Neural Network (BRB-ANN) intelligent computing technique. The data set for training the BRB-ANNs is created using Fractional Order Differential Equations (FODEs). The Bayesian Regularization Method with Backpropagation Artificial Neural Nets (BRB-ANNs), the fractional-order hepatitis C virus (FOHCV) model’s precision and effectiveness were significantly improved. The effectiveness of the proposed strategies is evidenced by achieving exceptionally low absolute errors ranging from <span><math><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo>)</mo></mrow></math></span> to <span><math><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>9</mn></mrow></msup><mo>)</mo></mrow></math></span>, minimal Mean Square Error (MSE) values between <span><math><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup><mo>)</mo></mrow></math></span> and <span><math><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>10</mn></mrow></msup><mo>)</mo></mrow></math></span>, and an almost perfect coefficient of determination <span><math><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>≈</mo><mn>0</mn><mo>.</mo><mn>999</mn><mo>)</mo></mrow></math></span>. Furthermore, the error histograms (Er.Hgs), ranging from <span><math><mrow><mo>(</mo><mo>−</mo><mn>9</mn><mo>.</mo><mn>4</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>10</mn></mrow></msup><mo>)</mo></mrow></math></span> to <span><math><mrow><mo>(</mo><mo>−</mo><mn>4</mn><mo>.</mo><mn>12</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup><mo>)</mo></mrow></math></span>, along with the corresponding time series plots (TSP), further validate the precision and reliability of the developed models. Dynamically and graphically, demonstrations indicate the achievement of AI with BRB-ANNs compared to the standard solution, and 3D Lorenz curves for FOHCV are analyzed. These results support the theoretical observation of Hepatitis C disease epidemics and the pr","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"21 ","pages":"Article 100626"},"PeriodicalIF":3.2,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-22DOI: 10.1016/j.rico.2025.100623
Eiji Mizutani , Stuart Dreyfus
Backpropagation (BP) is widely employed for training deep neural networks with many layers (or stages). We describe a new efficient BP-based approach to a general multi-point boundary value (MPBV) problem for differential equations. Given an MPBV problem, we transform it via discretization to a discrete-stage problem involving many stages for integration, and then approach it by stage-wise BP-based gradient and Newton methods. Our BP formulas are derived from discrete-stage optimal-control gradient-based methods. Through numerical examples, we demonstrate how easy to implement our new BP-based approach is to MPBV problems, showing that the results are convincing.
{"title":"A new backpropagation approach to multi-point boundary value problems","authors":"Eiji Mizutani , Stuart Dreyfus","doi":"10.1016/j.rico.2025.100623","DOIUrl":"10.1016/j.rico.2025.100623","url":null,"abstract":"<div><div>Backpropagation (BP) is widely employed for training deep neural networks with many layers (or stages). We describe a new efficient BP-based approach to a general multi-point boundary value (MPBV) problem for differential equations. Given an MPBV problem, we transform it via <em>discretization</em> to a discrete-stage problem involving many stages for integration, and then approach it by stage-wise BP-based gradient and Newton methods. Our BP formulas are derived from discrete-stage optimal-control gradient-based methods. Through numerical examples, we demonstrate how easy to implement our new BP-based approach is to MPBV problems, showing that the results are convincing.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"21 ","pages":"Article 100623"},"PeriodicalIF":3.2,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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