Optimal Control Research Articles

Multigrid Preconditioning for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem with a Convection-Dominated State Equation

Multigrid Preconditioning for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem with a Convection-Dominated State Equation

Resource Allocation in UAV-D2D Networks: A Scalable Heterogeneous Multi-Agent Deep Reinforcement Learning Approach

In unmanned aerial vehicle (UAV)-assisted device-to-device (D2D) caching networks, the uncertainty from unpredictable content demands and variable user positions poses a significant challenge for traditional optimization methods, often making them impractical. Multi-agent deep reinforcement learning (MADRL) offers significant advantages in optimizing multi-agent system decisions and serves as an effective and practical alternative. However, its application in large-scale dynamic environments is severely limited by the curse of dimensionality and communication overhead. To resolve this problem, we develop a scalable heterogeneous multi-agent mean-field actor-critic (SH-MAMFAC) framework. The framework treats ground users (GUs) and UAVs as distinct agents and designs cooperative rewards to convert the resource allocation problem into a fully cooperative game, enhancing global network performance. We also implement a mixed-action mapping strategy to handle discrete and continuous action spaces. A mean-field MADRL framework is introduced to minimize individual agent training loads while enhancing total cache hit probability (CHP). The simulation results show that our algorithm improves CHP and reduces transmission delay. A comparative analysis with existing mainstream deep reinforcement learning (DRL) algorithms shows that SH-MAMFAC significantly reduces training time and maintains high CHP as GU count grows. Additionally, by comparing with SH-MAMFAC variants that do not include trajectory optimization or power control, the proposed joint design scheme significantly reduces transmission delay.

Research on intelligent optimal allocation control strategy for stability and braking of heavy tyre blowout vehicle

The traditional control strategy mainly compensates and corrects the driving state of heavy vehicles with a tyre blowout, and rarely considers the need for emergency braking. It is also difficult to effectively coordinate the problems of lateral yaw, slip and tailspin, and longitudinal braking performance degradation. For this, an intelligent optimization allocation control strategy combining stability control and braking control is innovatively designed in this article. The joint simulation model for heavy tyre blowout vehicles is built based on the Dugoff tyre blowout model and the TruckSim vehicle model. A linear quadratic form regulator stable control based on the particle swarm optimization algorithm optimization is used to dynamic equilibrium of the additional yaw moment generated by the vehicle tyre blowout. A logic threshold braking control based on adaptive adjustment is adopted to achieve an ideal braking effect for the vehicle. In order to simultaneously consider the stability and braking performance of vehicles with blowout tyre, a braking force distribution strategy and a fuzzy optimization allocation algorithm are proposed to achieve coordination of lateral and longitudinal control strategies. The results indicate that intelligent optimized allocation control can effectively correct the deviation trajectory of a heavy tyre blowout vehicle, enabling it to achieve rapid braking while maintaining stability.

Methodology for Determining the Optimal Support Control Distance Based on the Deformation Increment Rate of Surrounding Rock and Its Engineering Application

Methodology for Determining the Optimal Support Control Distance Based on the Deformation Increment Rate of Surrounding Rock and Its Engineering Application

Digital twinning of vertical centrifugal casting

This paper explores the transformative potential of digital twin technology in vertical centrifugal casting (VCC), a cornerstone manufacturing process for high-integrity cylindrical components. By integrating real-time data, physical models, and machine learning algorithms, digital twins unlock a new paradigm of process optimization, predictive maintenance, and quality control. Integration of digital twinning enhances the performance in different domains of work like enhancing the quality of research, production etc. Howbeit, digital twinning is nascent in the domain of manufacturing specially in the casting sub domain. A physical set up of VCC is integrated with Internet of Things (IoT) and data acquisition system to stream the collected data to the cloud-based server. Transformation of Internet of Things (IoT) enabled VCC integrated with different sensors into the digital twin helps in quality prognosis for future applications. The data is further fetched from the cloud and interconnection is established between the digital twin. Real time monitoring, controlling and operating can be done easily with the help of a digital twin to predict the quality and tentative defect locations. Further amplifying these benefits, emerging technologies like Virtual Reality (VR), Augmented Reality (AR), and the Metaverse hold immense promise for revolutionising VCC training, collaboration, and visualisation.

Optimal Periodic Control of Unmanned Aerial Vehicles Based on Fourier Integral Pseudospectral and Edge-Detection Methods

The endurance of unmanned aerial vehicles (UAVs) is a critical factor in expanding the scope of their applications. Extended flight times enable UAVs to undertake longer missions, cover larger areas and perform tasks such as persistent surveillance, data collection and search and rescue operations. Optimal trajectory planning is a cost-effective method to significantly enhance UAV endurance and performance by minimizing fuel consumption. This study introduces a novel numerical optimization framework to maximize UAV endurance. Specifically, we address the problem of determining optimal thrust and cruise angle of attack for a UAV in 2D space under specific initial, periodic and boundary conditions. By normalizing the free final time optimal control problem and employing Fourier collocation and quadrature, we transform it into a nonlinear programming problem. A key contribution of this work is accurately detecting and reconstructing the thrust history, including jump discontinuities, directly from Fourier pseudospectral data without smoothing techniques. The proposed method outperforms existing approaches in solving the periodic energy-optimal path planning problem for UAVs, as it effectively reconstructs the bang-bang thrust profile, facilitating rapid and efficient thrust adjustments essential for various flight maneuvers. Furthermore, the algorithm aligns with the UAV model, ensuring seamless integration into real-world control systems. The method’s independence from prediction horizon length, due to the use of Fourier collocation on the normalized interval [Formula: see text], is a notable advantage. This characteristic offers potential for future applications in various fields involving nonsmooth optimal control problems. This research generally provides a valuable tool for researchers and engineers working on UAV design and operation, paving the way for more efficient and effective UAV systems.

Optimal Model-Free Mean-Square Consensus for Multi-Agents with Markov Switching Topology

Due to the real applications, optimal consensus reinforcement learning with switching topology is still challenging due to the complexity of topological changes. This paper investigates the optimal consensus control problem for discrete multi-agent systems under Markov switching topologies. The goal is to design an appropriate algorithm to find the optimal control policies that minimize the performance index while achieving consensus among the agents. The concept of mean-square consensus is introduced, and the relationship between consensus error and tracking error to achieve mean-square consensus is studied. A performance function for each agent under switching topologies is established and a policy iteration algorithm using system data is proposed based on the Bellman optimality principle. The theoretical analysis shows that the consensus error realizes mean-square consensus and the performance function is optimized. The efficacy of the suggested approach is confirmed by numerical simulation using an actor–critic neural network. As a result, the value function is the optimum and the mean-square consensus can be reached using this technique.

Adaptive variable gain linear active disturbance rejection control parameter optimization in magnetic levitation

The magnetic levitation ball system is characterized by strong nonlinearity, multiple disturbances, and intrinsic instability, which has long been a thorny problem in the field of control engineering. The magnetic levitation system can be continuously and stably levitated, even in a complex environment. In this thesis, the model of the magnetic levitation ball system is firstly constructed according to the kinetic theory and simplified according to the actual situation. After that, a linear active disturbance rejection control (LADRC) controller for the magnetic levitation ball system is designed. Considering that there are many parameters in the LADRC controller and it is difficult to obtain the optimal control effect by manual tuning, an adaptive variable gain LADRC algorithm is proposed to optimize the control strategy of LADRC parameters. An adaptive iterative algorithm is used to adaptively adjust the bandwidth of the linear extended state observer (LESO) in LADRC, and the convergence of the algorithm is demonstrated by using the Lyapunov function. To solve the problem that the proportional and differential gains of the LADRC controller can only be adjusted unidirectionally and simultaneously, this paper proposes an error variable gain algorithm. The aim is to realize the non-unidirectional and more detailed adjustment of the controller parameters, and it is rigorously analyzed and demonstrated through simulation and experiment. The results show that the proposed algorithm is better than proportional–integral–derivative (PID), sliding mode control (SMC), and LADRC in terms of dynamic performance, steady-state performance, and anti-interference.

The intelligent diabetes telemonitoring using decision support to treat patients on insulin therapy (DiaTRUST) trial: study protocol for a randomized controlled trial

BackgroundDiabetes affects 10.5% of adults globally, with type 2 diabetes accounting for 90–95% of cases. Achieving optimal glycemic control is crucial yet challenging, particularly with insulin therapy, where 30–50% of patients fail to meet treatment targets. Telemedicine can improve diabetes management but generates vast amounts of data, burdening healthcare professionals. Integrating clinical decision support tools into telemonitoring systems may enhance care efficiency and glycemic control.MethodsThe trial is a multicenter 3-month, three-arm, open-label, randomized controlled trial. The trial aims to enroll 51 participants with type 2 diabetes on insulin therapy. Participants will be divided with a 3:1:1 ratio into telemonitoring with decision support, telemonitoring without decision support, and usual care groups. The study employs connected insulin pens, continuous glucose monitors (CGMs), and activity trackers to enable telemonitoring. Outcomes measured include CGM time in range, HbA1c, hypo- and hyperglycemia incidents, total daily insulin dose, body weight, treatment satisfaction, and adherence.DiscussionTelemonitoring with decision support has the potential to revolutionize diabetes management by offering personalized treatment suggestions, thereby reducing the burden on healthcare professionals, and improving patient outcomes. This study will provide valuable insights into the effectiveness of such an approach in achieving glycemic control in people with type 2 diabetes on insulin therapy. By evaluating both clinical outcomes and patient and healthcare professionals’ satisfaction, the study aims to contribute to the development of efficient, scalable telehealth solutions for diabetes care.Trial registrationClinicalTrials.gov NCT06185296. Registered on December 14, 2023.

Transmission dynamics of fractional order SVEIR model for African swine fever virus with optimal control analysis

Understanding the dynamics of the African swine fever virus during periods of intense replication is critical for effective combatting of the rapid spread. In our research, we have developed a fractional-order SVEIR model using the Caputo derivatives to investigate this behaviour. We have established the existence and uniqueness of the solution through fixed point theory and determined the basic reproduction number using the next-generation matrix method. Our study also involves an examination of the local and global stability of disease-free equilibrium points. Additionally, we have conducted optimal control analysis with two control variables to increase the number of recovered pigs while reducing the number of those infected and exposed. We have supported our findings with numerical simulations to demonstrate the effectiveness of the control strategy.

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.

The Effect of Network Delay and Contagion on Mobile Banking Users: A Dynamical Analysis

This paper analyses how network contagion affects the acceptance or rejection of mobile banking, emphasizing the risk of contagion that hinders the growth of users among bank clients. As a research method, a mathematical model based on the Susceptible, Infected, and Recovered framework is used within a nonlinear dynamic system with a distributed time delay and the optimal control strategy. The approach aims to find the behaviour dynamics of mobile banking users, non-users, and undecided ones. Our model adds value to the existing literature by employing a qualitative dynamic analysis, as opposed to other studies that study contagion empirically. The steady states and their conditions for stability are found, and the critical value for time delay causing oscillatory is determined. The optimal control strategies are identified to enlarge the number of mobile banking users and decrease the number of non-users. Numerical simulations support the theoretical findings. The research has practical implications given that the model predicts mobile banking user behaviour in assisting policy decision-making and addresses the possible policy measures that aim to increase the number of mobile banking users. The conclusions suggest that financial inclusion can contribute to the expansion of mobile banking users.

Multi-Time Scale Optimal Control of Voltage Fluctuation at PV Grids Considering Load Changes

Multi-Time Scale Optimal Control of Voltage Fluctuation at PV Grids Considering Load Changes

A Comprehensive Review of Artificial Intelligence and Machine Learning in Control Theory

Abstract: Traditional control methods, such as proportional-integral-derivative (PID) controllers and linear-quadratic regulators (LQRs), have proven effective for linear and well-modeled systems. However, these methods often perform poorly in nonlinear, complex and dynamic environments. The paper aims to investigate the modern control systems by integrating artificial intelligence (AI) techniques, such as machine learning (ML), reinforcement learning (RL), deep learning, and fuzzy logic, to enhance their adaptive, robust, and predictive capabilities. And it reviews the literature and analyzes AI integration in control systems. The proposed strategies include supervised learning for trajectory optimization and fault detection, reinforcement learning for optimal control in dynamic environments, neural networks for complex nonlinear function approximation, and fuzzy logic for handling uncertainty and imprecise inputs. AI techniques significantly enhance the ability to tackle nonlinear problems and dynamic changes, demonstrating superior performance in applications like self-driving cars adapting to various road conditions and optimal energy distribution in smart grids. Despite the challenges of computational complexity, scalability, and the safety and reliability in the implementation of interpretable AI models, this paper suggests that hybrid approaches combining traditional control and AI techniques, along with the evolution of interpretable AI and convergence with quantum control, hold great promise for advancing AI-driven control systems.

Bayesian optimization for state engineering of quantum gases

Abstract State engineering of quantum objects is a central requirement for precision sensing and quantum computing implementations. When the quantum dynamics can be described by analytical solutions or simple approximation models, optimal state preparation protocols have been theoretically proposed and experimentally realized. For more complex systems such as interacting quantum gases, simplifying assumptions do not apply anymore and the optimization techniques become computationally impractical. Here, we propose Bayesian optimization based on multi-output Gaussian processes to learn the physical properties of a Bose-Einstein condensate within few simulations only. We evaluate its performance on an optimization study case of diabatically transporting the quantum gas while keeping it in its ground state. Within a few hundred executions, we reach a competitive performance to other protocols. While restricting this benchmark to the well known Thomas-Fermi approximation for straightforward comparisons, we expect a similar performance when employing more complex theoretical models, which would be computationally more challenging, rendering standard optimal control theory protocols impractical. This paves the way for efficient state engineering of complex quantum systems including mixtures of interacting gases or cold molecules.

NECESSARY CONDITIONS FOR OPTIMALITY IN ONE NONSMOOTH OPTIMAL CONTROL PROBLEM FOR GOURSAT-DARBOUX SYSTEMS

We consider a nonsmooth optimal control problem described by a system of second-order hyperbolic equations with Goursat boundary conditions. A number of necessary optimality conditions are proved in terms of directional derivatives.

PCA-Kriging-Based Oscillating Jet Actuator Optimization and Wing Separation Flow Control

In order to improve the separation control effect of an oscillating jet, the external flow field of the actuators and the wing wake are obtained via hot-wire measurements to optimize the actuator and achieve wing separation flow control. The optimization objectives are to improve the sweeping uniformity and range of the jet. In the present study, the PCA method is used for the modal decomposition of the velocity distribution. The modal-based actuator evaluation parameters are proposed, and the kriging surrogate models of the modal coefficients (principal components) on the actuator parameters are established. The multi-objective genetic algorithm was utilized to complete the optimization of the actuator, and the effect of flow separation control on the wing was verified. The results show that three patterns exist in the time-averaged velocity distribution of the external flow field: unimodal, broad and bimodal, from unimodal to bimodal, the degree of the jet sweeping uniformity gradually decreases, and the sweeping range gradually increases. The pattern of the velocity distribution modals affects the degree of jet sweeping uniformity, while the distance of the modal peaks affects the jet sweeping range. The two evaluation parameters are negatively correlated: insufficient sweeping range or poor sweeping uniformity of the jet are not conducive to wing separation flow control, and the two must be coordinated to achieve the optimal control effect.

Improved intelligent model predictive controller for the nuclear power reactor system

Abstract Over the last two decades, extensive research has been conducted to enhance the control performance of reactor power. Various methodologies have been suggested and implemented to achieve optimal power control in nuclear reactors. However, due to the diverse characteristics and inherent uncertainties in the models, devising optimal controllers for nuclear systems remains a complex task. To address this, numerous approaches have been adopted to ensure controllability and resilience, aiming for an optimal nuclear power reactor controller. The Model Predictive Control (MPC) algorithm has garnered significant attention as a viable approach to boost operational efficiency and overall system utility. In this research, Particle Swarm Optimization (PSO) method and MPC controller are combined together to form a novel algorithm termed PSO-MPC, aiming to amplify the system’s performance and overcomes the local minima problem that basically happens when using MPC controller. First, MPC controller is applied to the nuclear reactor model, then the suggested technique PSO-MPC also is applied to the system and a comparison of the outcomes using both techniques is done. The results demonstrate enhanced system response using the innovative technique.

Variable impedance control for synchronizer position tracking based on gain scheduling

Achieving fast and stable synchronizer position tracking control can greatly improve the power and comfort of transmission shifting. In order to further improve the shift speed and stability of the synchronizer, this article takes the synchronizer control of a three-speed seamless transmission as the research object and proposes a variable impedance control method based on gain scheduling. Firstly, dynamic models of the shift actuator and synchronizer was established. Then, an impedance outer loop controller and a position inner loop controller were designed. In the impedance outer loop, adjust the synchronizer reference position based on the difference between the reference shift force and the actual shift force. At the same time, based on the actual control requirements of different motion stages of the synchronizer, the optimal impedance control parameters for each stage are selected for gain scheduling control. In the position inner loop, a prescribed performance-active disturbance rejection control is adopted, which solves the problem of system disturbance while ensuring the instantaneous performance of position tracking. Finally, simulations and bench tests were conducted on the position tracking control of synchronizer. The simulation and bench test results show that the control strategy proposed achieves fast and stable synchronizer position tracking, with superior control performance, which preliminarily verifies the effectiveness of the control strategy.

Eigenstate Thermalization Hypothesis for Wigner-Type Matrices

We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure.