Optimal Control Model Research Articles

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.

Dynamic analysis of a modified Leslie-Gower model with Michaelis-Menten prey harvesting and additive allee effect on predator population

In the current study, the dynamics of a Leslie-Gower model have been studied considering the Allee effect in the growth of the predator and the Michaelis-Menten type harvesting effect on the prey from biological and theoretical perspectives. Key findings highlight how these effects influence the existence of positive equilibria, with local stability properties and potential bifurcation behaviors examined using the center manifold theorem and linearization. Criteria for saddle-node bifurcation are established through Sotomayor’s theorem, while the direction and stability of Hopf bifurcation are explored via the first Lyapunov exponent. An optimal control model is developed to promote sustainable ecosystem development, utilizing the harvesting rate as a control parameter. Further, a few numerical simulations validate our significant findings using phase portrait diagrams.

Modeling, simulations, and Simulink developments in the analysis of optimal control of temperature and pH in a batch ethanol fermentation process

Transfer of laboratory-scale experiments to production-scale ethanol fermentation is time-consuming and involves expensive prototype systems from complex experimental designs that determine optimal operating conditions for minimal substrate and product inhibitions. The study developed and validated a Simulink-based model for optimal pH and temperature control using fuzzy logic and PID controllers respectively and taking advantage of 2D and 1D substrate and product inhibition models from which suitable ethanol fermentation reaction rates models were selected. Temperature and pH levels and substrate, product, and biomass concentrations were measured. Selected inhibition models were linear-product, linear substrate-sudden stop product, and linear substrate for cassava, maize, and sorghum, respectively. Fuzzy logic controller ascertained optimal flow rate of acid and base as 0.000196 ml/s and 0.000204 ml/s, respectively, and pH error and rate of pH error as 0.00334 and 0.00368, respectively. F-test two-sample for variances showed no significant difference between model and experimental curves (cassava: F critical = 0.9704, F calculated = 0.1905; maize: F critical 0.9704, F calculated = 0.2149; sorghum: F critical = 0.9704, F calculated = 0.2488). PID logic controller showed model curves and experimental curves with good fit. F-test two-sample for variances showed no significant difference between model and experimental curves (cassava: F critical = 0.9704, F calculated = 0.1288; maize: F critical = 0.9704, F calculated = 0.2083; sorghum: F critical = 0.9704, F calculated = 0.2016). The study provided an improved approach as solution for optimal pH and temperature conditions in order to mitigate substrate and product inhibitions during ethanol fermentation. It illustrated that the application of artificial intelligence-based controllers provides satisfactory outcomes that are desirable for implementation in the industrial space.Graphical

A trajectory optimization method for CAVs at intersections considering energy-efficiency balance

With the development of vehicle-to-everything (V2X) technology, connected automated vehicles (CAVs) will be an important part of urban road transportation. However, frequent acceleration, deceleration, and rapid stopping within intersections lead to increased energy consumption, reduced driving efficiency and balanced benefits. The study proposes an optimal control method for vehicle trajectories that considers energy-efficiency balance (OCM-EEB) based on the characteristics of V2X technology. The method first develops a vehicle trajectory control model based on the Intelligent Driver Model (IDM) by accounting for the features of V2X technology, and further, introduces the idea of balanced optimization, considering energy-efficiency balance, a vehicle trajectory optimal control model (OCM) is proposed. The proposed model was solved by design algorithms based on the non-dominated sorting genetic algorithm-II (NSGA-II). The experimental results showed that the vehicle trajectory optimization control method could increase the balanced driving efficiency of the vehicle within intersection, which is conducive to improving the robustness of the vehicle’s trajectory state, and then prove the effectiveness of the method proposed in this study. The method also provides an important technical basis for the vehicle trajectory optimization experiments under a real V2X environment in the future.

Constrained Reinforcement Learning-Based Closed-Loop Reference Model for Optimal Tracking Control of Unknown Continuous-Time Systems

Constrained Reinforcement Learning-Based Closed-Loop Reference Model for Optimal Tracking Control of Unknown Continuous-Time Systems

Koopman Modeling for Optimal Control of the Perimeter of Multi-region Urban Traffic Networks

The purpose of perimeter control is to regulate the transfer flow between the perimeters of the urban traffic network, so that the vehicle aggregation in each region is maintained at a desired level. It is regarded as one of the most important methods to solve traffic congestion in urban road networks. Accurate mathematical modeling of perimeter controlled traffic dynamics remains a challenge due to its high nonlinearity and uncertainty. Machine learning methods have been used to learn traffic dynamic models for perimeter control. However, these existing techniques lack generalization and interpretability. In this paper, we propose a Koopman modeling approach (i.e., a two-stage method) that uses a new eigenfunction of the Koopman operator based on a novel L0 norm approximation to construct an interpretable finite-dimensional approximation of the Koopman operator, which is a linear operator that describes how eigenfunctions evolve along the trajectory of a specific nonlinear dynamical system. The main advantage of utilizing the Koopman operator is that it can characterize the nonlinear system in a global linear lifted feature space. Furthermore, an algorithm based on the Koopman modeling method and model predictive control is proposed for real-time perimeter control of urban road networks. Some experiments are carried out to demonstrate the effectiveness of the proposed algorithm.

Optimal control analysis on the spread of COVID-19: Impact of contact transmission and environmental contamination

The study investigates the intricate dynamics of SARS-CoV-2 transmission, with a particular focus on both close-contact interactions and environmental factors. Using advanced mathematical modeling and epidemiological analysis, explored the effects of these transmission pathways on the spread of COVID-19. The equilibrium points for both the disease-free and endemic states calculated and evaluated their global stability. Additionally, the basic reproduction number (R0) is derived to quantify the transmission potential of the virus.To ensure model accuracy, numerical simulations are performed using MATLAB, utilizing daily COVID-19 case data from India. Parameter values are sourced from existing literature, with certain parameters estimated through fitting the model to observed data. Crucially, the model incorporates environmental transmission factors, such as surface contamination and airborne spread. The inclusion of these factors provides a more comprehensive understanding of the virus’s spread, demonstrating the importance of interventions like use of face masks, environmental sanitization, vaccine efficacy, availability of treatment resources underappreciated when focusing solely on direct human contact. A sensitivity analysis is conducted to assess the impact of different parameters on R0, with results visualized through heat maps to identify the most influential factors.Furthermore, Pontryagin’s maximum principle is employed to develop an optimal control model, enabling the formulation of effective intervention strategies. By analysing both interpersonal and environmental transmission mechanisms, this study offers a more holistic framework for understanding SARS-CoV-2 transmission. The insights gained are critical for informing public health strategies, emphasizing the necessity of addressing both direct contact and environmental sources of infection to more effectively manage current and future outbreaks.

Reinforcement Learning-Based Adaptive Optimal Control Model for Signal Light in Intelligent Transportation Systems

Day-to-day mobility among the population has increased with economic growth. Smart cities are renovated with advanced technologies to admire modern life in which intelligent transportation becomes highly focused. Because the traffic signal control systems are fixed at a constant time. They split the traffic signal into predetermined intervals and function inefficiently; they result in long wait times, waste fuel and increased carbon emissions. This research study introduces a novel technique for traffic light management to reduce the uncertainties in the system. A dynamic and intelligent traffic light adaptive optimal management system (DITLAOCS) is implemented in this research. It does this by modifying the traffic signal duration in run time and using real-time traffic data as input. Furthermore, the proposed DITLAOCS executes based on three modes: fairness mode (FM), priority mode (PM) and emergent mode (EM). In fairness mode (FM), all vehicles are prioritized equally, while vehicles in different categories receive varying priority levels. Emergency vehicles, on the other hand, receive the highest priority. Furthermore, a fuzzy inference method based on traffic data is shown to choose one mode out of three (FM, PM and EM). This model uses deep reinforcement learning to switch traffic lights in three different phases (red, green and yellow). We evaluated and accurately simulated DITLAOCS on the Shaanxi city map in China using Simulation of Urban MObility (SUMO), an open-source simulator. The simulation results illustrate the efficiency of DITLAOCS when compared to other cutting-edge algorithms on several performance measures.

Mathematical modeling and strategy for optimal control of diphtheria

This research introduces a novel approach to combating diphtheria by presenting a comprehensive optimal control strategy focused on awareness campaigns to avoid direct contact with infected individuals and promote vaccinations. These campaigns highlight the severe complications of diphtheria, such as acute respiratory issues, myocarditis, and neurological paralysis. Additionally, the campaigns emphasize the negative impacts of an unbalanced lifestyle and environmental factors, as well as the importance of timely treatment and psychological support. The model aims to improve control strategies by reducing the number of infected individuals I(t) and exposed individuals E(t), as well as asymptomatic carriers A(t), which we have integrated into the model as an aspect that has been relatively unexplored in diphtheria transmission. The optimal controls are meticulously determined using Pontryagin’s maximum principle. The resulting optimality system is solved iteratively, ensuring precision and clarity in the results. Extensive numerical simulations rigorously support and confirm the theoretical analysis using MATLAB, providing concrete evidence of the strategy’s effectiveness. The broader implications and potential applications of this optimal control strategy extend to other infectious diseases, enhancing its relevance and utility in public health.

Partially observable optimal control using exponential cost criterion

We consider a partially observable optimal control model in which the system and observation noises are correlated, and the cost criterion is in the form of an exponential of an integral. A new minimum principle criterion is derived and applied to compute the explicit solution of linear exponential Gaussian optimisation problem with correlated noises.

Cyanobacterial blooms management: A simulation-based optimization method

Controlling cyanobacterial blooms is not only an engineering and technical issue but also an optimization problem in environment management. Under budget constraints, a novel simulation-based optimization model for cyanobacterial control is constructed in this study. The simulation model is used for simulating cyanobacteria growth and diffusion processes. The optimization model is utilized to determine the optimal search and treatment path. Through the interactive coupling of simulation modeling and resource allocation optimization, this research provides decision-makers with new operational guidelines for cyanobacterial control. Our test results demonstrate that the initial invasion frequency has a greater economic impact than invasion abundance. The nearby cells to the initial invasion are affected first, and then the influence radiates outward in a diffusion pattern. Using a slow search speed and a treatment frequency of every 10 days can achieve the lowest possible economic losses in most test scenarios. Moreover, we also find that the optimal search and treatment paths revolve around the initial invasion location. This study is a typical interdisciplinary research, which can assist water resource managers in making more accurate decisions regarding cyanobacteria removal paths, removal frequencies, and treatment speeds.

Risk-Averse Optimal Control Model Under Uncertainty and Its Modified Progressive Hedging Algorithm

Risk-Averse Optimal Control Model Under Uncertainty and Its Modified Progressive Hedging Algorithm

Intelligent optimal control model of selection pressure for rapid culture of aerobic granular sludge based on machine learning and simulated annealing algorithm

Aerobic Granular Sludge (AGS) has advantages over Activated sludge (AS) but faces challenges with long granulation periods. In this study, a novel grey-box model is devised to optimize the cultivation of AGS to shorten the formation time. This model is based on an existing white-box model. The modeling process starts with the application of four sensitivity analysis methods to assess the 12 model metrics selected. Subsequently, 12 prediction models were constructed by combining the six Machine learning (ML) algorithms and integrated algorithms, with the best performance selected (R2 = 0.98). Finally, an AGS selection pressure planning model was designed in conjunction with a simulated annealing (SA) algorithm to guide AGS training. The results demonstrate that AGS formation could be achieved within four days under the model’s optimal control. Therefore, the establishment of this model provides a new technique for the cultivation of AGS.

A Control Optimization Model for a Double-Skin Facade Based on the Random Forest Algorithm

Abstract: This study addresses the current difficulties in accurately controlling the indoor temperature of double-skin facades (DSFs), and its optimization, with a focus on the window opening angles of double-skin facades. The Spearman correlation coefficient method was used to select the main meteorological factors, including outdoor temperature, dew point temperature, scattered radiation, direct radiation, and window opening angle. A modified random forest algorithm was used to construct the optimization model and 80% of the data were used for model training. In the experiments, the average accuracy of the optimization model was as high as 93.5% for all window opening angles. This study provides a data-driven method for application to double-skin facades, which can effectively determine and control the window opening angles of double-skin facades to achieve energy saving and emission reduction, reduce indoor temperature, improve comfort, and provide a practical basis for decision-making. Future research will further explore the applicability and accuracy of the model under different climatic conditions.

Modeling environmental-born melioidosis dynamics with recurrence: An application of optimal control

Melioidosis is a significant health problem in tropical and subtropical regions, especially in Southeast Asia and Northern Australia. Recurrent melioidosis is a major obstacle to eliminating the disease from the community in these nations. This work aims to propose and analyze a human melioidosis model with recurrent phenomena and an optimal control model by incorporating time-dependent control functions. The basic reproduction number (R0) of the uncontrolled model is derived using the method of the next-generation matrix. Using the construction of a Lyapunov functional, we present the global asymptotic dynamics of the autonomous model in the presence of recurrent for both disease-free and endemic equilibria. The global asymptotic stability of the model’s equilibria shows the absence of a backward bifurcation for the model in both cases, whether in the absence or presence of relapse. The sensitivity analysis aims to identify the parameters that have the most significant impact on the model’s dynamics. Furthermore, qualitative analysis of the model’s global dynamics and the changing effect of the most influential parameters on R0 are supported by numerical experiments, with the results being illustrated graphically. The model with time-dependent controls is analyzed using optimal control theory to assess the impact of various intervention strategies on the spread of the epidemic. The numerical results of the optimality system are carried out using the Forward–Backward Sweep method in Matlab. We also conducted a cost-effectiveness analysis using two approaches: the average cost-effectiveness ratio and the incremental cost-effectiveness ratio.

Stochastic optimal control model for COVID-19: mask wearing and active screening/testing

Stochastic optimal control model for COVID-19: mask wearing and active screening/testing

Dynamic control of low-carbon efforts and process innovation considering knowledge accumulation under dual-carbon policies

Governments frequently implement carbon trading (CT) and carbon subsidy (CS) policies for encouraging enterprises to engage in low-carbon efforts (LCE) and reduce emissions, ultimately aiming for sustainable development in environmental and economic realms. In response, enterprises increase their investments in process innovation (PI) to balance revenue generation and cost reduction while simultaneously accumulating knowledge. Exploring the relation between LCE and PI is crucial to guide enterprises in effectively balancing these inputs, as well as to examine the role of government regulations on carbon emissions in motivating enterprises to enhance their efforts. This study proposes a dynamic optimal control model integrating PI and LCE within the dual-carbon policy framework, considering the effect of knowledge accumulation (KA). Moreover, it evaluates changes in inputs and benefits under profit-optimal and social welfare-optimal conditions. Finally, a comparative analysis is conducted using numerical simulation and emulation. The findings indicate complementary and substitution effects between the two inputs: the KA effect enhances input stability, and the impact of social incentives consistently outweighs that of monopoly incentives. Furthermore, CT and CS policies exhibit cross-impacts on enterprise returns and the two inputs.