Optimal Control Model Research Articles

An optimal control model with sensitivity analysis for COVID-19 transmission using logistic recruitment rate

An optimal control model with sensitivity analysis for COVID-19 transmission using logistic recruitment rate

A mathematical model of corruption dynamics and optimal control

A mathematical model of corruption dynamics and optimal control

Cooperative Low-Carbon Trajectory Planning of Multi-Arrival Aircraft for Continuous Descent Operation

To address the technical challenges of implementing Continuous Descent Operations (CDO) in high-traffic-density terminal control areas, we propose a cooperative low-carbon trajectory planning method for multiple arriving aircraft. Firstly, this study analyzes the CDO phases of aircraft in the terminal area, establishes a multi-phase optimal control model for the vertical profile, and introduces a novel vertical profile optimization method for CDO based on a genetic algorithm. Secondly, to tackle the challenges of CDO in busy terminal areas, a T-shaped arrival route structure is designed to provide alternative paths and to generate a set of four-dimensional (4D) alternative trajectories. A Mixed Integer Programming (MIP) model is constructed for the 4D trajectory planning of multiple aircraft, aiming to maximize the efficiency of arrival traffic flow while considering conflict constraints. The complex constrained MIP problem is transformed into an unconstrained problem using a penalty function method. Finally, experiments were conducted to evaluate the implementation of CDO in busy terminal areas. The results show that, compared to actual operations, the proposed optimization model significantly reduces the total aircraft operating time, fuel consumption, CO2 emissions, SO2 emissions, and NOx emissions. Specifically, with the optimization objective of minimizing total cost, the proposed method reduces the total operation time by 22.4%; fuel consumption, CO2 emissions, SO2 emissions by 22.9%, and NOx emissions by 23.7%. The method proposed in this paper not only produces efficient aircraft sequencing results, but also provides a feasible low-carbon trajectory for achieving optimal sequencing.

Co-infection mathematical model for HIV/AIDS and tuberculosis with optimal control in Ethiopia.

The co-epidemics of HIV/AIDS and Tuberculosis (TB) outbreak is one of a serious disease in Ethiopia that demands integrative approaches to combat its transmission. In contrast, epidemiological co-infection models often considered a single latent case and recovered individuals with TB. To bridge this gap, we presented a new optimal HIV-TB co-infection model that considers both high risk and low risk latent TB cases with taking into account preventive efforts of both HIV and TB diseases, case finding for TB and HIV/AIDS treatment. This study aimed to develop optimal HIV/AIDS-TB co-infection mathematical model to explore the best cost-effective measure to mitigate the disease burden. The model is analysed analytically by firstly segregating TB and HIV only sub models followed by the full TB-HIV co-infection model. The Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) points are found and the basic reproduction number R0 is obtained using the next generation matrix method (NGM). Based on the threshold value R0, the stabilities of equilibria for each sub-model are analysed. The DFE point is locally asymptotically stable when R0 < 1 and unstable when R0 > 1. The EE point is also asymptotically stable when R0 > 1 and does not exist otherwise. At R0 = 1, the existence of backward bifurcation phenomena is discussed. To curtail the cost and disease fatality, an optimal control model is formulated via time based controlling efforts. The optimal mathematical model is analysed both analytically and numerically. The numerical results are presented for two or more control measures at a time. In addition, the Incremental Cost-Effectiveness Ratio(ICER) has identified the best strategy which is crucial in limited resource. Hence, the model outcomes illustrated that applying HIV/AIDS prevention efforts and TB case finding concurrently is the most cost-effective strategy to offer substantial relief from the burden of the pandemic in the community. All results found in this study have significant public health lessons. We anticipated that the results will notify evidence based approaches to control the disease. Thus, this study will aids in the fight against HIV/AIDS, TB, and their co-infection policy-makers and other concerned organizations.

Synergistic Impact of Active Case Detection and Early Hospitalization for Controlling the Spread of Yellow Fever Outbreak in Nigeria: An Epidemiological Modeling and Optimal Control Analysis

Capturing the factors influencing yellow fever (YF) outbreaks is essential for effective public health interventions, especially in regions like Nigeria, where the disease poses significant health risks. This study explores the synergistic effects of active case detection (ACD) and early hospitalization on controlling YF transmission dynamics. We develop a dynamic model that integrates vaccination, active case detection, and hospitalization to enhance our understanding of disease spread and inform prevention strategies. Our methodology encompasses mechanistic dynamic modeling, optimal control analysis, parameter estimation, model fitting, and sensitivity analyses to study YF transmission dynamics, ensuring the robustness of control measures. We employ advanced mathematical techniques, including next-generation matrix methods, to accurately compute the reproduction number and assess outbreak transmissibility. Rigorous qualitative analysis of the model reveals two equilibria: disease-free and endemic, demonstrating global asymptotic stability and its impact on overall YF transmission dynamics, significantly affecting control and prevention mechanisms. Furthermore, through sensitivity analysis, we identify crucial parameters of the model that require urgent attention for more effective YF control. Moreover, our results highlight the critical roles of ACD and early hospitalization in reducing YF transmission. These insights provide a foundation for informed decision making and resource allocation in epidemic control efforts, ultimately contributing to the enhancement of public health strategies aimed at mitigating the impact of YF outbreaks.

The Integration of Macroscopic Traffic Optimization Control and Microscopic Traffic Flow Model for Mixed Traffic: A Cyber-Physical System Perspective

The Integration of Macroscopic Traffic Optimization Control and Microscopic Traffic Flow Model for Mixed Traffic: A Cyber-Physical System Perspective

CONTROL MODEL OF THE NATURAL GAS PURIFICATION PROCESS

The equipment used in the processes of cleaning and drying natural gas for transportation and consumption and the methods applied for drying gas were comparatively analyzed, it was noted that the absorption method is more widespread among these methods due to its simplicity and efficiency, it was shown that drying gas should be carried out immediately after its cleaning from mechanical and other impurities so that during the transportation and use of gas, there are no blockages in pipelines, malfunctions in measuring devices and other gas equipment. Drying gas prevents the formation of hydrates in pipes due to condensation during transportation and increases the heat-generating capacity of gas by burning it well. The characteristics of the liquid absorbent used to dry gas in the absorption process - the absorbent, being regenerated and returned to the gas drying process were investigated, and the parameters and quality indicators affecting the technological process were determined for optimal control of the gas drying technological process at normal temperature and pressure for that process, as well as the output parameters of the gas drying unit. It was noted that although the pneumatic control system is considered morally obsolete, some elements and devices of this system, in particular, pneumatic actuators, are distinguished by their reliability in mining and field conditions. Therefore, it is advisable to use them in modern control systems with controllers. For this purpose, the structure of the general control system of the process, the information model of the control object was built, the input and output parameters, the limiting conditions for reflecting the exciting and controlling effects in the structure of the mathematical model were determined, and the limit ranges containing the minimum and maximum values of each parameter were determined. The control problem can also be formulated and solved as a problem of stabilizing productivity or another parameter. An optimal control model of the gas drying process was built, and the optimization criterion was selected. In the problem of optimizing the technological process of gas drying, the maximum productivity of the plant was adopted as the main criterion, and the humidity of the gas was adopted as the limiting condition. Several recommendations are given for solving this problem. Keywords: gas drying, absorbent, control system, optimal control, model.

Co-contraction embodies uncertainty: An optimal feedforward strategy for robust motor control.

Despite our environment often being uncertain, we generally manage to generate stable motor behaviors. While reactive control plays a major role in this achievement, proactive control is critical to cope with the substantial noise and delays that affect neuromusculoskeletal systems. In particular, muscle co-contraction is exploited to robustify feedforward motor commands against internal sensorimotor noise as was revealed by stochastic optimal open-loop control modeling. Here, we extend this framework to neuromusculoskeletal systems subjected to random disturbances originating from the environment. The analytical derivation and numerical simulations predict a characteristic relationship between the degree of uncertainty in the task at hand and the optimal level of anticipatory co-contraction. This prediction is confirmed through a single-joint pointing task experiment where an external torque is applied to the wrist near the end of the reaching movement with varying probabilities across blocks of trials. We conclude that uncertainty calls for impedance control via proactive muscle co-contraction to stabilize behaviors when reactive control is insufficient for task success.

Evaluate Multi-Objective Optimization Model for Product Supply Chain Inventory Control Based on Grey Wolf Algorithm

Enterprise supply chain inventory control plays a critical role in modern enterprise management. Yet achieving multi-objective optimization remains challenging. This paper proposes a deep learning integrated model based on grey wolf optimization (GWO-DLIM) aimed at optimizing inventory holding costs, stockout costs, and order costs. The model integrates multi-layer perceptron (MLP), DeBERTa, and GWO, leveraging the powerful predictive and feature extraction capabilities of deep learning models, combined with the global optimization ability of the grey wolf algorithm, to achieve multi-objective optimization. These results demonstrate that the GWO-DLIM model significantly outperforms other comparative models across all metrics, exhibiting lower prediction errors and root mean square errors, as well as higher service levels. This study provides an effective multi-objective optimization solution for supply chain inventory management, holding significant theoretical and practical implications.

Dissociable Effects of Urgency and Evidence Accumulation during Reaching Revealed by Dynamic Multisensory Integration.

When making perceptual decisions, humans combine information across sensory modalities dependent on their respective uncertainties. However, it remains unknown how the brain integrates multisensory feedback during movement and which factors besides sensory uncertainty influence sensory contributions. We performed two reaching experiments on healthy adults to investigate whether movement corrections to combined visual and mechanical perturbations scale with visual uncertainty. To describe the dynamics of multimodal feedback responses, we further varied movement time and visual feedback duration during the movement. The results of our first experiment show that the contribution of visual feedback decreased with uncertainty. Additionally, we observed a transient phase during which visual feedback responses were stronger during faster movements. In a follow-up experiment, we found that the contribution of vision increased more quickly during slow movements when we presented the visual feedback for a longer time. Muscle activity corresponding to these visual responses exhibited modulations with sensory uncertainty and movement speed ca. 100 ms following the onset of the visual feedback. Using an optimal feedback control model, we show that the increased response to visual feedback during fast movements can be explained by an urgency-dependent increase in control gains. Further, the fact that a longer viewing duration increased the visual contributions suggests that the brain accumulates sensory information over time to estimate the state of the arm during reaching. Our results provide additional evidence concerning the link between reaching control and decision-making, both of which appear to be influenced by sensory evidence accumulation and response urgency.

Single-Phase Multilevel Inverter Design with Low Voltage Stress and Optimized Control Model

The research explicitly examines the power control of a single-phase renewable energy sources battery energy storage system (RES-BESS)mixed-distributing network designed for domestic usage. The system utilizes a cascaded H-bridge (CHB) conversion architecture as its grid connection. The CHB uses a hierarchical power management design consisting of a single centralized regulator for the top layer and several dispersed regulators for the bottom layer. The higher stratum produces the reference signals that need to be monitored. Under optimal circumstances, the CHB should operate efficiently with all solar panels at their Maximum Power Point (MPP) and with an electrical factor of 1. However, several functional limitations prevent this from always being feasible, such as limits related to voltage and current, biased shadowing, and State of Charge (SOC) incompatibilities. Hence, a novel optimization technique is introduced to take into account these impacts directly and calculate a collection of reference parameters to be monitored. This approach aims to maximize the long-term viability of the structure while ensuring compliance with the given limitations. The optimization method in this structure incorporates many functional needs, prioritizing them based on the specific operating circumstances. The decentralized management layer utilizes traditional feedback-controlling methods to monitor the best referencing. Experimental findings are conducted to verify the best method under normal conditions for operation and evaluate the efficacy of the suggested CHB arrangement with the complete control technique.

Collaborative control framework at isolated signalized intersections under the mixed connected automated vehicles environment

AbstractThis study proposes a collaborative control framework under the mixed traffic environment of connected and automated vehicles and connected human‐driven vehicles, which can simultaneously optimize the signal timing, lane settings, and vehicle trajectories at isolated intersections. Initially, considering the dynamics of traffic demand and incompatible signals, we analyze the vehicle delay of each lane. Based on the delay analysis, the spatiotemporal resource collaborative optimization model of lane setting and signal timing is established to minimize the average delay. Subsequently, in the buffer zone, a graph‐theoretic‐based sorting and platooning model provides a clear and concise representation of the transformation process from the initial state to the target state of vehicles, enabling the platoon formation. Additionally, trajectory optimization is integrated into the collaborative control framework by the optimal control model and car‐following model in the passing zone. Simulation experiments and sensitivity analyses demonstrate the effectiveness of the proposed framework in reducing average vehicle delay, improving fuel consumption, and coping with changing traffic demand at intersections.

Machine learning-based optimal temperature management model for safety and quality control of perishable food supply chain

The management of a food supply chain is difficult and complex because of the product's short shelf-life, time-sensitivity, and perishable nature which must be carefully considered to minimize food waste. Temperature-controlled perishable food supply chain provides the highly crucial facilities necessary to maintain the quality and safety of the product. The storage temperature is the most vital factor in maintaining both the quality and shelf-life of a perishable food. Adequate storage temperature control ensures that perishable foods are transported to the end-users in good quality and safe to consume. This paper presents perishable food storage temperature control through mathematical optimal control model where the storage temperature is regarded as the control variable and the deterioration of the perishable food’s quality follows the first-order reaction. The optimal storage temperature for a single perishable food is determined by applying the Pontryagin's maximum principle to solve the optimal control model problem. For multi-temperature commodities supply chain, an unsupervised machine learning (ML) method, called k-means clustering technique is used to determine the temperature clusters for a range of perishables. Based on descriptive analysis, it is observed that the k-means clustering technique is effective in identifying the best suitable storage temperature clusters for quality control of multi-commodity supply chain.

Dynamic pricing and inventory model for perishable products with reference price and reference quality

Reference price (quality) is a benchmark point used by consumers to make price (quality) judgements. Combining reference price and reference quality with dynamic pricing and inventory management, this paper applies differential equations theory to construct a optimal control model for perishable products when the quality of products declines exponentially. The demand of products depends on price, quality, reference price and reference quality, among which reference price and reference quality are influenced by consumers’ past memory. The aim is to maximize the retailer’s profit during the period. The conclusions are as follows. Firstly, a optimal dynamic pricing and inventory model for perishable products with reference price and reference quality is constructed, and the model is extended to dual decision variables, stochastic demand, time-dependent effects, competitive and infinite planing horizon setups. Secondly, through the Pontryagin maximum principle, the analytical expression of the optimal dynamic price is derived. Thirdly, a linear search method to solve the optimal static price is proposed. Finally, the sensitivity of the main parameters is analyzed and the corresponding management enlightenments are given. By comparison of dynamic and static pricing, we find that dynamic pricing can achieve more profits and take a shorter selling period. In addition, for the sales problem of perishable products affected by both reference price and reference quality, retailers should adopt skimming pricing strategy (the optimal price decreases with time). Furthermore, to obtain more profit, retails should strive to increase the sensitivity coefficients of two types of reference, and the reference quality memory coefficient, while to decrease the reference price memory coefficient.

Developing PDE-constrained optimal control of multicomponent contamination flows in porous media

This paper develops a robust and efficient PDE-constrained optimal control model for multicomponent pollutions in porous media, which takes into account nonlinear multi-component contamination flows of groundwater. The objective of the pollution optimal control is to identify the optimal injection rates from the top part boundary of domain, which can minimize the least squares error between the concentrations that are simulated and the allowable observed concentrations at observation sites, combining with the affection of costs associated with reducing emissions at injection locations. To discrete the constrained governing system of nonlinear multi-component flows, the splitting improved upwind finite difference scheme is developed for multicomponent PDEs system involving nonlinear chemical reactions of multicomponent pollutants and the pollutant injected rates on the upper part boundary. We employ the differential evolution (DE) optimization algorithm to solve the optimization. We numerically demonstrate the effectiveness of our model by analyzing the flow simulation on a simple geometric aquifer and identifying the optimal injection rates by minimizing the concentration derivation and the abatement costs. We also investigate the simulation of the contamination flow in a more realistic-shaped aquifer, which further validates our model's robustness and efficacy. The developed PDE-constrained control model and algorithm can be applied to applications of groundwater pollution control.

A zoning-based distributed control method for medium-low voltage AC/DC distribution networks

Abstract With the increasing percentage of renewable energy sources and new types of power equipment, the medium-low voltage AC/DC distribution network structure improves the source-load carrying capacity and is considered a prevailing trend. Traditional centralized voltage optimization and control methods face challenges due to computational inefficiencies arising from the numerous control devices involved. In this paper, a distributed optimal control strategy based on distribution network zoning is proposed. Firstly, a network decoupling and multi-agent deployment method based on zoning is introduced. Secondly, a distributed optimal control model for medium-low voltage AC/DC distribution networks is developed to minimize network losses within the region. Subsequently, the optimization model is transformed into a Markov process, and the multi-agent proximal policy optimization (MAPPO) algorithm is used to solve this Markov process, facilitating the distributed control of medium-low voltage AC/DC distribution network based on zoning. Simulation examples are analyzed to prove the effectiveness of the proposed method.

Research on trajectory planning based on optimal control modeling

With the advancement of autonomous driving technology, trajectory planning has emerged as one of the core technologies to achieve safe and efficient vehicle driving. An algorithm for single-vehicle trajectory planning based on the Optimal Control Problem (OCP) is proposed in this paper, which can not only plan a safe and efficient path for autonomous vehicles, but also realize the obstacle avoidance function. Firstly, the OCP is modeled for the cycle trajectory planning problem. Secondly, this paper transforms it into a Nonlinear Programming (NLP) with all discrete methods, and uses the interior point method to solve it. Then, the Y-type intersection is selected as the verification scene, and through a series of simulation experiments, the efficiency and safety of the algorithm in different driving environments are verified. The model and algorithm proposed in this paper are not only applicable to Y-type intersections, but also can be extended to other complex traffic roads, providing a new idea and method for trajectory planning in intelligent transportation systems.

Fuzzy Multi-Agent Simulation for Collective Energy Management of Autonomous Industrial Vehicle Fleets

This paper presents a multi-agent simulation implemented in Python, using fuzzy logic to explore collective battery recharge management for autonomous industrial vehicles (AIVs) in an airport environment. This approach offers adaptability and resilience through a distributed system, taking into account variations in AIV battery capacity. Simulation scenarios were based on a proposed charging/discharging model for an AIV battery. The results highlight the effectiveness of adaptive fuzzy multi-agent models in optimizing charging strategies, improving operational efficiency, and reducing energy consumption. Dynamic factors such as workload variations and AIV-infrastructure communication are taken into account in the form of heuristics, underlining the importance of flexible and collaborative approaches in autonomous systems. In particular, an infrastructure capable of optimizing charging according to energy tariffs can significantly reduce consumption during peak hours, highlighting the importance of such strategies in dynamic environments. An optimal control model is established to improve the energy consumption of each AIV during its mission. The energy consumption depends on the speed, as demonstrated via numerical simulations using realistic data. The speed profile of each AIV is adjusted according to the various constraints within an airport. Overall, the study highlights the potential of incorporating adaptive fuzzy multi-agent models for AIV energy management to boost efficiency and sustainability in industrial operations.

Cost-effective and optimal control analysis for mitigation strategy to chocolate spot disease of faba bean

Faba bean is one of the most important grown plants worldwide for human and animal. Despite its various importance, the productivity of faba bean has been constrained by several biotic and abiotic factors. Many faba bean pathogens have been reported so far, of which the most important yield limiting disease is Chocolate Spot Disease (Botrytis fabae). The dynamics of disease transmission and decision-making processes for intervention programs for disease control are now better understood through the use of mathematical modeling. In this paper a deterministic mathematical model for Chocolate Spot disease (CSD) on faba bean plant with an optimal control model was developed and analyzed to examine the best strategy in controlling CSD. The optimal control model is developed with three control interventions, namely prevention (u1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{1}$$\\end{document}), quarantine (u2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{2}$$\\end{document}) and chemical control (u3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{3}$$\\end{document}). The Pontryagin’€™s maximum principle isused to derive the Hamiltonian, the adjoint variables, the characterization of the controls and the optimality system. A cost-effective approach is chosen from a set of possible integrated strategies using the incremental cost-effectiveness ratio (ICER). The forward-backward sweep iterative approach is used to run numerical simulations. We obtained the Hamiltonian, the adjoint variables, the characterization of the controls and the optimality system. The numerical results demonstrate that each integrated strategy can reduce the diseases within the specified period. However due to limited resources, an integrated strategy prevention and uprooting was found to be a best cost-effective strategy to combat CSD. Therefore, attention should be given for the integrated cost-effective and environmentally eco-friendly strategy by stake holders and policy makers to control CSD and disseminate the integrated intervention to the farmers in order to fight the spread of CSD in the Faba bean population and produce the expected yield from the field.

A comparative analysis of intelligent energy modelling approaches for a grid-tied PVT system application

Renewable energy resources are a long-term answer to the current chronic energy dilemma. Solar photovoltaic (PV) systems are the most often used form of a practical solution for power supply and energy management in buildings. A PV-thermal (PVT) system is essential to lowering the demand for grid energy by capturing electrical and thermal energy from sunlight, optimising energy usage and encouraging sustainable energy practices. The most significant difficulty faced by developing countries, such as South Africa, is a lack of power supply to meet demand while limiting grid overload. An alternative source of energy is a critical component. This research compares two intelligent energy modelling methodologies: optimal control scheme-based open loop and model predictive control (MPC) in a PVT application. The primary goal of the modelling is to limit the electricity required from the grid while stressing the system’s energy efficiency and cost-effectiveness. The open loop approach uses mathematical optimisation techniques to establish the best control strategy for the PVT system. The ideal set-points for various system parameters are found by presenting the problem as an optimisation task to reduce grid power usage. The optimal control technique delivers a global optimisation solution based on the system dynamics and constraints. The MPC technique employs a predictive control technique of the PVT system to create optimal control actions in a receding horizon manner. The MPC algorithm anticipates future system behaviour and generates control actions that minimise grid power drawn by iteratively solving an optimisation problem at each time step. This robust online control scheme enables real-time modifications and responses to system disruptions that effectively and dynamically coordinate system behaviour.