Results in Control and Optimization最新文献_第3页

Global mild solutions and total controllability of fuzzy conformable fractional stochastic delay systems with non-instantaneous impulses and Poisson jumps 具有非瞬时脉冲和泊松跳的模糊适形分数阶随机时滞系统的全局温和解和全可控性

IF 3.2 Q3 Mathematics

Results in Control and Optimization

Pub Date : 2026-03-01 Epub Date: 2026-01-28 DOI: 10.1016/j.rico.2026.100663

Nageshwari Sivakumar, Durga Nagarajan

This manuscript is concerned with the solvability and total controllability of the fuzzy stochastic delay differential system with non-instantaneous impulses and Poisson jumps under the conformable fractional derivative, which is new to the literature. Such systems naturally arise in real-world processes where uncertainty, memory effects, and abrupt dynamic changes occur simultaneously. The existence and uniqueness results are obtained for the proposed system using the Banach contraction principle. Next, the global solution is derived with the help of generalised Gronwall’s inequality. Furthermore, the total controllability results are established for the presented fuzzy system. A new class of control functions is introduced to regulate the system at the termination of time intervals and on each impulsive event, while incorporating stochastic disturbances. This approach yields to comprehensive controllability outcomes, often termed as total controllability. In support, an example is given to validate the obtained theoretical outcomes. Furthermore, numerical simulations are presented to illustrate the presented model. The technology under discussion will also be used in a number of practical applications, such as traffic flow regulation, population dynamics, climate-driven environmental processes, communication networks, and medical treatment response systems.

本文研究了具有非瞬时脉冲和泊松跳的模糊随机时滞微分系统在适形分数阶导数下的可解性和全可控性，这是文献中的一个新问题。这样的系统自然出现在不确定性、记忆效应和突然动态变化同时发生的现实世界过程中。利用Banach收缩原理，得到了系统的存在唯一性结果。其次，利用广义Gronwall不等式导出了全局解。进一步，建立了该模糊系统的总可控性结果。在引入随机扰动的同时，引入了一类新的控制函数来调节系统在时间间隔的末端和每个脉冲事件。这种方法产生综合可控性结果，通常称为完全可控性。最后通过算例验证了所得理论结果的正确性。最后，通过数值模拟对模型进行了验证。讨论中的技术还将用于许多实际应用，例如交通流量调节、人口动态、气候驱动的环境过程、通信网络和医疗响应系统。

{"title":"Global mild solutions and total controllability of fuzzy conformable fractional stochastic delay systems with non-instantaneous impulses and Poisson jumps","authors":"Nageshwari Sivakumar, Durga Nagarajan","doi":"10.1016/j.rico.2026.100663","DOIUrl":"10.1016/j.rico.2026.100663","url":null,"abstract":"<div><div>This manuscript is concerned with the solvability and total controllability of the fuzzy stochastic delay differential system with non-instantaneous impulses and Poisson jumps under the conformable fractional derivative, which is new to the literature. Such systems naturally arise in real-world processes where uncertainty, memory effects, and abrupt dynamic changes occur simultaneously. The existence and uniqueness results are obtained for the proposed system using the Banach contraction principle. Next, the global solution is derived with the help of generalised Gronwall’s inequality. Furthermore, the total controllability results are established for the presented fuzzy system. A new class of control functions is introduced to regulate the system at the termination of time intervals and on each impulsive event, while incorporating stochastic disturbances. This approach yields to comprehensive controllability outcomes, often termed as total controllability. In support, an example is given to validate the obtained theoretical outcomes. Furthermore, numerical simulations are presented to illustrate the presented model. The technology under discussion will also be used in a number of practical applications, such as traffic flow regulation, population dynamics, climate-driven environmental processes, communication networks, and medical treatment response systems.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100663"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077457","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}

引用次数: 0

Exponential cone-based OPF formulation for monopolar DC electrical networks 基于指数锥的单极直流电网OPF公式

IF 3.2 Q3 Mathematics

Results in Control and Optimization

Pub Date : 2026-03-01 Epub Date: 2026-03-04 DOI: 10.1016/j.rico.2026.100683

Oscar Danilo Montoya , Walter Gil-González , Alejandro Garcés-Ruiz

This paper presents a convex reformulation of the optimal power flow problem for monopolar DC distribution networks with integrated distributed energy resources, including photovoltaic generators, wind turbines, and battery storage systems. The non-convexity introduced by bilinear voltage terms in the power balance and loss equations is addressed using an exponential cone-based transformation. By introducing logarithmic auxiliary variables, the bilinear terms are embedded into the convex domain, enabling the use of efficient conic optimization solvers. The proposed model is implemented using the JuMP modeling framework in Julia and evaluated on benchmark DC feeders ranging from 27 to 123 buses. The results demonstrate that the exponential cone-based formulation achieves highly accurate approximations of the exact nonlinear solution, with relative errors as low as

1 0^{- 5}

, while significantly outperforming standard second-order cone programming relaxations in terms of both accuracy and scalability. The proposed approach offers a reliable and computationally tractable tool for the optimal dispatch and voltage regulation of large-scale DC networks.

本文提出了具有集成分布式能源（包括光伏发电机、风力涡轮机和电池存储系统）的单极直流配电网的最优潮流问题的凸重构。利用指数锥变换解决了功率平衡和损耗方程中双线性电压项的非凸性问题。通过引入对数辅助变量，双线性项被嵌入到凸域，从而能够使用高效的二次优化求解器。所提出的模型使用Julia中的JuMP建模框架实现，并在27到123总线的基准直流馈线上进行评估。结果表明，基于指数锥的公式实现了精确非线性解的高精度近似，相对误差低至10−5，同时在精度和可扩展性方面显著优于标准二阶锥规划松弛。该方法为大规模直流电网的优化调度和电压调节提供了一种可靠且易于计算的工具。

{"title":"Exponential cone-based OPF formulation for monopolar DC electrical networks","authors":"Oscar Danilo Montoya , Walter Gil-González , Alejandro Garcés-Ruiz","doi":"10.1016/j.rico.2026.100683","DOIUrl":"10.1016/j.rico.2026.100683","url":null,"abstract":"<div><div>This paper presents a convex reformulation of the optimal power flow problem for monopolar DC distribution networks with integrated distributed energy resources, including photovoltaic generators, wind turbines, and battery storage systems. The non-convexity introduced by bilinear voltage terms in the power balance and loss equations is addressed using an exponential cone-based transformation. By introducing logarithmic auxiliary variables, the bilinear terms are embedded into the convex domain, enabling the use of efficient conic optimization solvers. The proposed model is implemented using the JuMP modeling framework in Julia and evaluated on benchmark DC feeders ranging from 27 to 123 buses. The results demonstrate that the exponential cone-based formulation achieves highly accurate approximations of the exact nonlinear solution, with relative errors as low as <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></mrow></math></span>, while significantly outperforming standard second-order cone programming relaxations in terms of both accuracy and scalability. The proposed approach offers a reliable and computationally tractable tool for the optimal dispatch and voltage regulation of large-scale DC networks.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100683"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147396385","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}

引用次数: 0

Modal LMI-based observer design with performance guarantees for semilinear parabolic PDEs: Application to bioreactor system 半线性抛物型偏微分方程基于模态lmi的性能保证观测器设计：在生物反应器系统中的应用

IF 3.2 Q3 Mathematics

Results in Control and Optimization

Pub Date : 2026-03-01 Epub Date: 2026-02-26 DOI: 10.1016/j.rico.2026.100679

Ivan Yupanqui, Gustavo Pérez-Zuñiga, Luis Enciso-Salas

This paper presents a systematic modal LMI-based framework for infinite-dimensional state observer design of semilinear parabolic partial differential equation (PDE) systems. The proposed methodology exploits the Riesz-spectral decomposition property of parabolic operators to partition the infinite-dimensional dynamics into finite-dimensional slow and infinite-dimensional fast subsystems, enabling late-lumping observer synthesis with guaranteed exponential stability. A modal output injection operator is designed through systematic eigenvalue assignment, while Lipschitz continuity assumptions on the nonlinear terms facilitate rigorous stability analysis of the estimation error dynamics. The design conditions are formulated as computationally tractable linear matrix inequalities (LMIs) derived from Lyapunov stability theory, directly incorporating prescribed decay rate specifications and observer gain magnitude constraints. To address practical implementation considerations, we develop a modal truncation strategy supported by center manifold theory and establish ellipsoidal stability regions through polytopic constraint analysis. The effectiveness of the proposed approach is demonstrated through application to a tubular bioreactor system, where numerical simulations confirm exponential convergence with prescribed performance and validate the practical viability of the infinite-dimensional observer design methodology for distributed parameter systems.

提出了一种基于系统模态lmi的半线性抛物型偏微分方程（PDE）系统无限维状态观测器设计框架。该方法利用抛物算子的riesz -谱分解特性，将无限维动力学划分为有限维慢速子系统和无限维快速子系统，实现了具有指数稳定性保证的晚集总观测器合成。通过系统的特征值赋值设计了模态输出注入算子，并对非线性项进行了Lipschitz连续性假设，便于对估计误差动态进行严格的稳定性分析。设计条件由李雅普诺夫稳定性理论推导而来，直接结合规定的衰减率规范和观测器增益大小约束，可计算地表达为易于处理的线性矩阵不等式（lmi）。为了解决实际实现问题，我们开发了一种基于中心流形理论的模态截断策略，并通过多面体约束分析建立了椭球体稳定区域。通过对管式生物反应器系统的应用证明了该方法的有效性，其中数值模拟证实了指数收敛性与规定性能，并验证了分布参数系统的无限维观测器设计方法的实际可行性。

{"title":"Modal LMI-based observer design with performance guarantees for semilinear parabolic PDEs: Application to bioreactor system","authors":"Ivan Yupanqui, Gustavo Pérez-Zuñiga, Luis Enciso-Salas","doi":"10.1016/j.rico.2026.100679","DOIUrl":"10.1016/j.rico.2026.100679","url":null,"abstract":"<div><div>This paper presents a systematic modal LMI-based framework for infinite-dimensional state observer design of semilinear parabolic partial differential equation (PDE) systems. The proposed methodology exploits the Riesz-spectral decomposition property of parabolic operators to partition the infinite-dimensional dynamics into finite-dimensional slow and infinite-dimensional fast subsystems, enabling late-lumping observer synthesis with guaranteed exponential stability. A modal output injection operator is designed through systematic eigenvalue assignment, while Lipschitz continuity assumptions on the nonlinear terms facilitate rigorous stability analysis of the estimation error dynamics. The design conditions are formulated as computationally tractable linear matrix inequalities (LMIs) derived from Lyapunov stability theory, directly incorporating prescribed decay rate specifications and observer gain magnitude constraints. To address practical implementation considerations, we develop a modal truncation strategy supported by center manifold theory and establish ellipsoidal stability regions through polytopic constraint analysis. The effectiveness of the proposed approach is demonstrated through application to a tubular bioreactor system, where numerical simulations confirm exponential convergence with prescribed performance and validate the practical viability of the infinite-dimensional observer design methodology for distributed parameter systems.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100679"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147396390","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}

引用次数: 0

A stochastic differential model of energy-dependent neural stability 能量依赖神经稳定性的随机微分模型

IF 3.2 Q3 Mathematics

Results in Control and Optimization

Pub Date : 2026-03-01 Epub Date: 2025-12-15 DOI: 10.1016/j.rico.2025.100645

Zhiwei Xu , Qiang Sun , Zhenhui Liu , Qi Yang

We presented and analyzed a stochastic differential equation model of neural population dynamics leveraging synaptic plasticity energy regulation and noise-driven bifurcation. The model integrates the spike-timing-dependent plasticity and energy evolution equations modulated by a control parameter

λ

, which governs the tradeoff between metabolic expenditure and stochastic suppression. We derived the critical energy threshold

E_{crit}

which ensures stability against stochastic perturbations, and we formulated the cost function to determine the optimal

λ_{opt}

minimizing cost of balancing noise suppression and metabolic expenditure. Through numerical simulation on Ring, Erdős–Rényi, and Scale-Free network topologies, we demonstrate that the system consistently operates above

E_{crit}

, maintains stability via the Jacobian eigenvalue spectrum, and undergoes a bifurcation only beyond high noise amplitudes. Additional entropy and Lyapunov analyses reveal that the system supports high-dimensional, non-synchronous activity. Our results provide a quantitative framework for understanding how neural circuits achieve noise-robust computation under energetic constraints.

我们提出并分析了利用突触可塑性、能量调节和噪声驱动分岔的神经种群动态随机微分方程模型。该模型集成了峰值时间依赖的可塑性和能量演化方程，由控制参数λ调节，控制代谢消耗和随机抑制之间的权衡。我们推导出了保证稳定对抗随机扰动的临界能量阈值Ecrit，并制定了成本函数来确定平衡噪声抑制和代谢消耗的最优λopt最小成本。通过在Ring、Erdős-Rényi和Scale-Free网络拓扑上的数值模拟，我们证明了系统在Ecrit之上持续运行，通过雅可比特征值谱保持稳定性，并且只有在高噪声幅值之外才会发生分岔。附加熵和李亚普诺夫分析表明，该系统支持高维、非同步活动。我们的结果为理解神经回路如何在能量约束下实现噪声鲁棒计算提供了一个定量框架。

{"title":"A stochastic differential model of energy-dependent neural stability","authors":"Zhiwei Xu , Qiang Sun , Zhenhui Liu , Qi Yang","doi":"10.1016/j.rico.2025.100645","DOIUrl":"10.1016/j.rico.2025.100645","url":null,"abstract":"<div><div>We presented and analyzed a stochastic differential equation model of neural population dynamics leveraging synaptic plasticity energy regulation and noise-driven bifurcation. The model integrates the spike-timing-dependent plasticity and energy evolution equations modulated by a control parameter <span><math><mi>λ</mi></math></span>, which governs the tradeoff between metabolic expenditure and stochastic suppression. We derived the critical energy threshold <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>crit</mi></mrow></msub></math></span> which ensures stability against stochastic perturbations, and we formulated the cost function to determine the optimal <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>opt</mi></mrow></msub></math></span> minimizing cost of balancing noise suppression and metabolic expenditure. Through numerical simulation on Ring, Erdős–Rényi, and Scale-Free network topologies, we demonstrate that the system consistently operates above <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>crit</mi></mrow></msub></math></span>, maintains stability via the Jacobian eigenvalue spectrum, and undergoes a bifurcation only beyond high noise amplitudes. Additional entropy and Lyapunov analyses reveal that the system supports high-dimensional, non-synchronous activity. Our results provide a quantitative framework for understanding how neural circuits achieve noise-robust computation under energetic constraints.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100645"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926630","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}

引用次数: 0

An innovative two-stage method for balancing time, cost, quality, and additional objectives in multi-mode resource-constrained project scheduling: A case study of a food product packaging production line project 在多模式资源约束项目调度中平衡时间、成本、质量和附加目标的创新两阶段方法：以食品包装生产线项目为例研究

IF 3.2 Q3 Mathematics

Results in Control and Optimization

Pub Date : 2026-03-01 Epub Date: 2025-12-19 DOI: 10.1016/j.rico.2025.100649

Hossein Edrisi, Meghdad Jahromi, Narges Norouzi

This paper presents a novel two-stage approach for optimizing the scheduling of multi-objective construction projects, validated through a real-world case study of a food product packaging production line. Beyond the conventional objectives of time, cost, and quality, five additional factors—risk, scope creep, environmental impacts, stakeholder satisfaction, and safety—are quantitatively incorporated based on expert judgment and normalized performance ratings. In the first stage, a TOPSIS-based similarity index is calculated for each execution mode of the project activities, aggregating the additional objectives into a single comparable criterion derived from the weighted expert assessments. In the second stage, a four-objective optimization model is formulated to balance project makespan, cost, quality, and the similarity index. Integrating the similarity index ensures simultaneous consideration of both traditional and supplementary objectives. The multi-mode resource-constrained project scheduling problem (MRCPSP) is solved on small instances using the epsilon-constraint method, and for medium- and large-scale problems, two metaheuristics—NSGA-II and MOPSO—are employed. Computational results and sensitivity analyses conducted on the case study demonstrate the model’s capability to produce a diverse set of high-quality Pareto-optimal solutions within reasonable computational timeframes. The proposed framework’s flexibility makes it suitable for projects with varying objective priorities, offering a comprehensive and practical decision-support tool for project managers aiming for more balanced and precise scheduling decisions.

本文提出了一种新的两阶段方法来优化多目标建设项目的调度，并通过食品包装生产线的实际案例研究进行了验证。除了时间、成本和质量的传统目标之外，还有五个额外的因素——风险、范围蔓延、环境影响、利益相关者满意度和安全性——基于专家判断和标准化的绩效评级，被定量地纳入其中。在第一阶段，为项目活动的每一种执行模式计算基于topsis的相似性指数，将额外的目标汇总到从加权专家评估得出的单一可比标准中。在第二阶段，建立了一个四目标优化模型，以平衡项目完工时间、成本、质量和相似度指数。整合相似度指数可确保同时考虑传统目标和补充目标。采用epsilon约束方法求解小实例上的多模式资源约束项目调度问题，采用nsga - ii和mopso两种元启发式方法求解中大规模问题。对案例研究进行的计算结果和敏感性分析表明，该模型能够在合理的计算时间框架内产生各种高质量的帕累托最优解。所建议的框架的灵活性使其适合具有不同目标优先级的项目，为项目经理提供全面和实用的决策支持工具，以实现更平衡和精确的调度决策。

{"title":"An innovative two-stage method for balancing time, cost, quality, and additional objectives in multi-mode resource-constrained project scheduling: A case study of a food product packaging production line project","authors":"Hossein Edrisi, Meghdad Jahromi, Narges Norouzi","doi":"10.1016/j.rico.2025.100649","DOIUrl":"10.1016/j.rico.2025.100649","url":null,"abstract":"<div><div>This paper presents a novel two-stage approach for optimizing the scheduling of multi-objective construction projects, validated through a real-world case study of a food product packaging production line. Beyond the conventional objectives of time, cost, and quality, five additional factors—risk, scope creep, environmental impacts, stakeholder satisfaction, and safety—are quantitatively incorporated based on expert judgment and normalized performance ratings. In the first stage, a TOPSIS-based similarity index is calculated for each execution mode of the project activities, aggregating the additional objectives into a single comparable criterion derived from the weighted expert assessments. In the second stage, a four-objective optimization model is formulated to balance project makespan, cost, quality, and the similarity index. Integrating the similarity index ensures simultaneous consideration of both traditional and supplementary objectives. The multi-mode resource-constrained project scheduling problem (MRCPSP) is solved on small instances using the epsilon-constraint method, and for medium- and large-scale problems, two metaheuristics—NSGA-II and MOPSO—are employed. Computational results and sensitivity analyses conducted on the case study demonstrate the model’s capability to produce a diverse set of high-quality Pareto-optimal solutions within reasonable computational timeframes. The proposed framework’s flexibility makes it suitable for projects with varying objective priorities, offering a comprehensive and practical decision-support tool for project managers aiming for more balanced and precise scheduling decisions.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100649"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926633","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}

引用次数: 0

Analysis of the efficacy of the risk-based X̄ control chart in statistical process control 基于风险的X′控制图在统计过程控制中的有效性分析

IF 3.2 Q3 Mathematics

Results in Control and Optimization

Pub Date : 2026-03-01 Epub Date: 2026-01-23 DOI: 10.1016/j.rico.2026.100661

Aamir Saghir , Attila I. Katona , Csaba Hegedũs , Zsolt T. Kosztyán

Risk-based control charts have recently been introduced to address measurement uncertainty. The statistical properties of a risk-based control chart for detecting a shift have not been studied. In addition to the control chart design, performance evaluation is important for detecting changes in the process. In this paper, the effectiveness of a risk-based

\bar{X}

control chart (recently introduced) in the presence of measurement uncertainty is investigated. By utilizing a risk-based model that considers the cost of decision outcomes, the impact of measurement uncertainty on the

\bar{X}

chart’s performance in both in- and out-of-control scenarios is designed and examined. To lessen the risk associated with measurement uncertainty, the Nelder–Mead search technique is employed to find the optimal control limits. The performance metrics include the total decision cost, cost ratio, probability ratio, and average run length. Simulation and real-world data analyses are employed to assess the efficiency of the risk-based chart via various performance metrics. A sensitivity analysis is conducted to identify the constraints and relevance of the risk-based

\bar{X}

chart in statistical process control.

基于风险的控制图最近被引入来解决测量的不确定性。基于风险的控制图用于检测位移的统计特性尚未得到研究。除了控制图设计之外，性能评估对于检测过程中的变化也很重要。在本文中，研究了基于风险的X ā控制图（最近引入）在测量不确定性存在下的有效性。通过利用考虑决策结果成本的基于风险的模型，设计和检查了在控制和失控情况下测量不确定性对X图表性能的影响。为了降低测量不确定度带来的风险，采用Nelder-Mead搜索技术寻找最优控制极限。性能指标包括总决策成本、成本比、概率比和平均运行长度。模拟和真实世界的数据分析被用来通过各种性能指标评估基于风险的图表的效率。进行敏感性分析，以确定统计过程控制中基于风险的X线图的约束和相关性。

{"title":"Analysis of the efficacy of the risk-based X̄ control chart in statistical process control","authors":"Aamir Saghir , Attila I. Katona , Csaba Hegedũs , Zsolt T. Kosztyán","doi":"10.1016/j.rico.2026.100661","DOIUrl":"10.1016/j.rico.2026.100661","url":null,"abstract":"<div><div>Risk-based control charts have recently been introduced to address measurement uncertainty. The statistical properties of a risk-based control chart for detecting a shift have not been studied. In addition to the control chart design, performance evaluation is important for detecting changes in the process. In this paper, the effectiveness of a risk-based <span><math><mover><mrow><mi>X</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> control chart (recently introduced) in the presence of measurement uncertainty is investigated. By utilizing a risk-based model that considers the cost of decision outcomes, the impact of measurement uncertainty on the <span><math><mover><mrow><mi>X</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> chart’s performance in both in- and out-of-control scenarios is designed and examined. To lessen the risk associated with measurement uncertainty, the Nelder–Mead search technique is employed to find the optimal control limits. The performance metrics include the total decision cost, cost ratio, probability ratio, and average run length. Simulation and real-world data analyses are employed to assess the efficiency of the risk-based chart via various performance metrics. A sensitivity analysis is conducted to identify the constraints and relevance of the risk-based <span><math><mover><mrow><mi>X</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> chart in statistical process control.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100661"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023010","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}

引用次数: 0

Optimal fractional order PI controller design for time-delayed processes 时滞过程的最优分数阶PI控制器设计

IF 3.2 Q3 Mathematics

Results in Control and Optimization

Pub Date : 2026-03-01 Epub Date: 2025-12-22 DOI: 10.1016/j.rico.2025.100651

Erdal Cokmez, Ibrahim Kaya

The usage of fractional calculus enables additional flexibility and precision regarding the control parameters. This study introduces a fully analytical design for a fractional-order Proportional-Integral (FOPI) controller, eliminating the need for predefined parameters or iterative optimization. The Åström recursive algorithm, previously applied to integer-order controllers, is adapted for the first time to optimize FOPI controllers based on integral of squared time error (ISTE), integral of squared time-squared error (IST²E), and integral of squared time-cubed error (IST³E) performance criteria. This study differs from others since instead of specific types, it combines three types of first-order plus time-delay processes: stable (SFOPTD), integrating (IFOPTD), and unstable (UFOPTD) processes. Analytical formulas have been derived for optimal parameter selection, while separate formulas provided for gain margin (GM), phase margin (PM), and maximum sensitivity (Ms) enable the pre-determination of system robustness. The controller's performance is validated using simulations of the step response, disturbance rejection, control effort, and perturbation response. In addition, real-time experiments on an inverted pendulum illustrate its utility in dynamic processes. This provides a comprehensive framework aimed to further the development of fractional-order control by providing a systematic solution to a large scope of industrial applications.

分数阶微积分的使用使控制参数具有额外的灵活性和精度。本研究介绍了分数阶比例积分（FOPI）控制器的完全解析设计，消除了预定义参数或迭代优化的需要。先前应用于整阶控制器的Åström递归算法首次适用于基于时间误差平方积分（ISTE）、时间误差平方积分（IST2E）和时间立方误差平方积分（IST3E）性能标准的FOPI控制器优化。本研究与其他研究的不同之处在于，它结合了三种一阶加时滞过程：稳定（SFOPTD）、整合（IFOPTD）和不稳定（UFOPTD）过程，而不是特定的类型。推导了最佳参数选择的解析公式，同时提供了增益裕度（GM），相位裕度（PM）和最大灵敏度（Ms）的单独公式，可以预先确定系统的鲁棒性。通过阶跃响应、扰动抑制、控制努力和扰动响应的仿真验证了控制器的性能。另外，在倒立摆上进行了实时实验，说明了该方法在动态过程中的应用。这提供了一个全面的框架，旨在通过为大范围的工业应用提供系统的解决方案，进一步发展分数阶控制。

{"title":"Optimal fractional order PI controller design for time-delayed processes","authors":"Erdal Cokmez, Ibrahim Kaya","doi":"10.1016/j.rico.2025.100651","DOIUrl":"10.1016/j.rico.2025.100651","url":null,"abstract":"<div><div>The usage of fractional calculus enables additional flexibility and precision regarding the control parameters. This study introduces a fully analytical design for a fractional-order Proportional-Integral (FOPI) controller, eliminating the need for predefined parameters or iterative optimization. The Åström recursive algorithm, previously applied to integer-order controllers, is adapted for the first time to optimize FOPI controllers based on integral of squared time error (ISTE), integral of squared time-squared error (IST<sup>2</sup>E), and integral of squared time-cubed error (IST<sup>3</sup>E) performance criteria. This study differs from others since instead of specific types, it combines three types of first-order plus time-delay processes: stable (SFOPTD), integrating (IFOPTD), and unstable (UFOPTD) processes. Analytical formulas have been derived for optimal parameter selection, while separate formulas provided for gain margin (GM), phase margin (PM), and maximum sensitivity (Ms) enable the pre-determination of system robustness. The controller's performance is validated using simulations of the step response, disturbance rejection, control effort, and perturbation response. In addition, real-time experiments on an inverted pendulum illustrate its utility in dynamic processes. This provides a comprehensive framework aimed to further the development of fractional-order control by providing a systematic solution to a large scope of industrial applications.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100651"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926631","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}

引用次数: 0

Recursive feasibility without terminal constraints via parent–child MPC architecture 通过父子MPC架构实现无终端约束的递归可行性

IF 3.2 Q3 Mathematics

Results in Control and Optimization

Pub Date : 2026-03-01 Epub Date: 2025-12-30 DOI: 10.1016/j.rico.2025.100653

Filip Surma, Anahita Jamshidnejad

This paper introduces a novel hierarchical model predictive control (MPC) framework, called the Parent–Child MPC architecture, designed to ensure recursive feasibility without relying on terminal constraints. The proposed architecture targets nonlinear constrained systems with Lipschitz continuous dynamics, such as quadrotors, helicopters and autonomous bicycles. For such systems, traditional MPC approaches may suffer from computational intractability or conservativeness due to needing terminal constraints. The proposed framework couples a small-horizon, high-fidelity Child MPC with one or more large-horizon, simplified Parent MPC layers. The Parent layers provide robust invariant tubes that replace terminal constraints, enabling scalable planning and stability guarantees. Two case studies, including a linear double integrator system and a nonlinear system, demonstrate the effectiveness of the architecture. Compared to standard robust tube-based MPC, the Parent–Child MPC achieves up to an eight-fold reduction in solver time and a three-fold increase in controllable prediction horizon. It also maintains performance within 3% of robust tube-based MPC. These results highlight the potential of this architecture for real-time control of complex, nonlinear systems under uncertainty.

本文介绍了一种新的层次模型预测控制（MPC）框架，称为亲子MPC架构，旨在确保递归的可行性，而不依赖于终端约束。所提出的架构针对具有Lipschitz连续动力学的非线性约束系统，例如四旋翼机，直升机和自动自行车。对于这样的系统，由于需要终端约束，传统的MPC方法可能存在计算难解性或保守性。提出的框架将一个小视界、高保真的子MPC与一个或多个大视界、简化的父MPC层耦合在一起。父层提供健壮的不变管道，取代终端约束，支持可伸缩的规划和稳定性保证。两个实例研究，包括一个线性双积分系统和一个非线性系统，证明了该架构的有效性。与标准的基于坚固管的MPC相比，亲子MPC的求解时间减少了8倍，可控预测范围增加了3倍。它还将性能保持在坚固的管基MPC的3%以内。这些结果突出了该体系结构在不确定情况下对复杂非线性系统进行实时控制的潜力。

{"title":"Recursive feasibility without terminal constraints via parent–child MPC architecture","authors":"Filip Surma, Anahita Jamshidnejad","doi":"10.1016/j.rico.2025.100653","DOIUrl":"10.1016/j.rico.2025.100653","url":null,"abstract":"<div><div>This paper introduces a novel hierarchical model predictive control (MPC) framework, called the Parent–Child MPC architecture, designed to ensure recursive feasibility without relying on terminal constraints. The proposed architecture targets nonlinear constrained systems with Lipschitz continuous dynamics, such as quadrotors, helicopters and autonomous bicycles. For such systems, traditional MPC approaches may suffer from computational intractability or conservativeness due to needing terminal constraints. The proposed framework couples a small-horizon, high-fidelity Child MPC with one or more large-horizon, simplified Parent MPC layers. The Parent layers provide robust invariant tubes that replace terminal constraints, enabling scalable planning and stability guarantees. Two case studies, including a linear double integrator system and a nonlinear system, demonstrate the effectiveness of the architecture. Compared to standard robust tube-based MPC, the Parent–Child MPC achieves up to an eight-fold reduction in solver time and a three-fold increase in controllable prediction horizon. It also maintains performance within 3% of robust tube-based MPC. These results highlight the potential of this architecture for real-time control of complex, nonlinear systems under uncertainty.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100653"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146173469","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}

引用次数: 0

Optimality in constrained fractional robust optimization problems 约束分式鲁棒优化问题的最优性

IF 3.2 Q3 Mathematics

Results in Control and Optimization

Pub Date : 2026-03-01 Epub Date: 2026-02-06 DOI: 10.1016/j.rico.2026.100666

Octavian Postavaru , Savin Treanţă

This paper presents conditions that are both necessary and sufficient for optimal solutions in a new robust fractional optimization problem defined by continuous curvilinear integral derived from uncertain high-dimensional controlled Lagrangeans. We employ the concept of a convex curvilinear integral, defined through an integrable controlled Lagrangean, in conjunction with the notion of a robust weak optimal solution. This theoretical framework enables the establishment of optimality conditions necessary for identifying extreme solutions in a new category of robust optimization problems characterized by variability in both the constraints and the performance criteria. Furthermore, we present the concept of a robust Kuhn–Tucker point and offer a description result. To substantiate our theoretical contributions, we include an illustrative example.

本文给出了由不确定高维控制拉格朗日量导出的连续曲线积分所定义的一类新的鲁棒分数型优化问题的最优解的充分必要条件。我们将凸曲线积分的概念与鲁棒弱最优解的概念结合起来，通过可积控制拉格朗日函数来定义凸曲线积分。该理论框架能够建立最优性条件，以便在约束和性能标准均具有可变性的新一类鲁棒优化问题中识别极端解。在此基础上，提出了鲁棒Kuhn-Tucker点的概念，并给出了描述结果。为了证实我们的理论贡献，我们包括了一个说明性的例子。

引用次数: 0

Mathematical modeling of childhood infectious diseases using fractional derivatives and control strategies 利用分数阶导数和控制策略建立儿童传染病的数学模型

IF 3.2 Q3 Mathematics

Results in Control and Optimization

Pub Date : 2026-03-01 Epub Date: 2026-02-23 DOI: 10.1016/j.rico.2026.100665

Mostofa Kamal , Payer Ahmed , Md. Rasel Mia , Sadia Akter , Sumaya Binta Mosharraf , Mostak Ahmed , Prity Roy , Razia Sultana Ripa , Nodhi Uddin , Md. Al Amin

Childhood infectious diseases continue to pose significant global health challenges, particularly in regions with limited access to healthcare and vaccination services. To capture the memory-dependent nature of disease transmission, this study develops a fractional-order epidemiological model based on the Caputo–Fabrizio derivative. The framework incorporates two realistic intervention strategies—vaccination and isolation/treatment—and analyzes their combined effectiveness in reducing infection levels. Analytical solutions are obtained using the Laplace–Adomian Decomposition Method, while numerical approximations are generated through an Euler-based scheme. The epidemic threshold is derived, and the influence of key parameters on disease persistence is examined. Both disease-free and endemic equilibria are established, and their local and global stability properties are rigorously investigated. Additionally, the Sumudu transform is employed to further assess the system’s dynamic behavior, benefiting from its suitability for fractional operators with non-singular kernels. Fundamental mathematical properties of the model, including existence, uniqueness, positivity, and boundedness, are proven. Optimal control theory, via Pontryagin’s Maximum Principle, is applied to determine cost-effective strategies that minimize infections and maximize recovery. Computational simulations support the theoretical findings, demonstrating that integrated control measures substantially mitigate the spread of childhood infectious diseases.

儿童传染病继续对全球健康构成重大挑战，特别是在获得保健和疫苗接种服务有限的区域。为了捕捉疾病传播的记忆依赖性质，本研究开发了基于Caputo-Fabrizio衍生的分数阶流行病学模型。该框架纳入了两种现实的干预策略——疫苗接种和隔离/治疗——并分析了它们在降低感染水平方面的综合效果。利用Laplace-Adomian分解法得到解析解，并通过基于欧拉的格式生成数值逼近。推导了流行阈值，并考察了关键参数对疾病持续性的影响。建立了无病平衡和地方性平衡，并对它们的局部和全局稳定性进行了严格的研究。此外，利用Sumudu变换对非奇异核分数算子的适用性，进一步评估了系统的动态行为。证明了该模型的存在性、唯一性、正性和有界性等基本数学性质。最优控制理论，通过庞特里亚金的最大原则，被应用于确定成本效益的策略，以减少感染和最大限度地恢复。计算模拟支持理论发现，表明综合控制措施大大减轻了儿童传染病的传播。

{"title":"Mathematical modeling of childhood infectious diseases using fractional derivatives and control strategies","authors":"Mostofa Kamal , Payer Ahmed , Md. Rasel Mia , Sadia Akter , Sumaya Binta Mosharraf , Mostak Ahmed , Prity Roy , Razia Sultana Ripa , Nodhi Uddin , Md. Al Amin","doi":"10.1016/j.rico.2026.100665","DOIUrl":"10.1016/j.rico.2026.100665","url":null,"abstract":"<div><div>Childhood infectious diseases continue to pose significant global health challenges, particularly in regions with limited access to healthcare and vaccination services. To capture the memory-dependent nature of disease transmission, this study develops a fractional-order epidemiological model based on the Caputo–Fabrizio derivative. The framework incorporates two realistic intervention strategies—vaccination and isolation/treatment—and analyzes their combined effectiveness in reducing infection levels. Analytical solutions are obtained using the Laplace–Adomian Decomposition Method, while numerical approximations are generated through an Euler-based scheme. The epidemic threshold is derived, and the influence of key parameters on disease persistence is examined. Both disease-free and endemic equilibria are established, and their local and global stability properties are rigorously investigated. Additionally, the Sumudu transform is employed to further assess the system’s dynamic behavior, benefiting from its suitability for fractional operators with non-singular kernels. Fundamental mathematical properties of the model, including existence, uniqueness, positivity, and boundedness, are proven. Optimal control theory, via Pontryagin’s Maximum Principle, is applied to determine cost-effective strategies that minimize infections and maximize recovery. Computational simulations support the theoretical findings, demonstrating that integrated control measures substantially mitigate the spread of childhood infectious diseases.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"22 ","pages":"Article 100665"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147396201","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}

引用次数: 0