Optimal Control Research Articles

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

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.

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

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.

Optimal Control in a Mathematical Model for the Occurrence of Electronic Cheating in Certification Exams; Baccalaureate Exams in Morocco as an Example

Optimal Control in a Mathematical Model for the Occurrence of Electronic Cheating in Certification Exams; Baccalaureate Exams in Morocco as an Example

Optimal Control of Microcephaly Under Vertical Transmission of Zika

The Zika virus, known for its potential to induce neurological conditions such as microcephaly when transmitted vertically from infected mothers to infants, has sparked widespread concerns globally. Motivated by this, we propose an optimal control problem for the prevention of vertical Zika transmission. The novelty of this study lies in its consideration of time-dependent control functions, namely, insecticide spraying and personal protective measures taken to safeguard pregnant women from infected mosquitoes. New results provide a way to minimize the number of infected pregnant women through the implementation of control strategies while simultaneously reducing both the associated costs of control measures and the mosquito population, resulting in a decline in microcephaly cases.

A multi-objective optimal control approach to motor strategy changes in older people with mild cognitive impairment during obstacle crossing.

Mild cognitive impairment (MCI) may lead to difficulty maintaining postural stability and balance during locomotion. This heightened susceptibility to falls is particularly evident during tasks such as obstacle negotiation, which demands efficient motor planning and reallocation of attentional resources. This study proposed a multi-objective optimal control (MOOC) technique to assess the changes in motor control strategies during obstacle negotiation in older people affected by amnestic MCI. Motion data from 12 older adults with MCI and 12 controls when crossing obstacles were measured using a motion capture system, and used to obtain the control strategy of obstacle-crossing as the best compromise between the conflicting objectives of the MOOC problem, i.e., minimising mechanical energy expenditure and maximising foot-obstacle clearance. Comparisons of the weighting sets between groups and obstacle heights were performed using a two-way analysis of variance with a significance level of 0.05. Compared to the controls, the MCI group showed significantly lower best-compromise weightings for mechanical energy expenditure but greater best-compromise weightings for both heel- and toe-obstacle clearances. This altered strategy involved a trade-off, prioritising maximising foot-obstacle clearance at the expense of increased mechanical energy expenditure. The MCI group could successfully navigate obstacles with a normal foot-obstacle clearance but at the cost of higher mechanical energy expenditure. MCI alters the best-compromise strategy between minimising mechanical energy expenditure and maximising foot-obstacle clearances for obstacle-crossing in older people. These findings provide valuable insights into how MCI impacts motor tasks and offer potential strategies for mitigating fall risks in individuals with MCI. Moreover, this approach could serve as an assessment tool for early diagnosis and a more precise evaluation of disease progression. It may also have applications for individuals with impairments in other cognitive domains.

Global Stability and Optimal Control Analysis of COVID-19 Transmission

Global Stability and Optimal Control Analysis of COVID-19 Transmission

Distributed model predictive control for asynchronous multiagent systems with self‐triggered coordinator

AbstractThis paper investigates a distributed model predictive control strategy for asynchronous nonlinear multiagent systems (MASs) with external disturbances via self‐triggered generators and prediction horizon regulators. First, a shrinking constraint related to the error between the actual state and the predicted state is introduced into the optimal control problem to enhance the robustness of the system. Then, the triggering interval and the corresponding prediction horizon are determined by altering the expression of the Lyapunov function, thus achieving a trade‐off between control performance and energy loss. By implementing the proposed algorithm, the coordination objective of the MASs is achieved under asynchronous communication. Finally, the recursive feasibility and closed‐loop stability are proven successively. An illustrative example is conducted to demonstrate the merits of the presented approach.

Maximum principle for partially observed risk-sensitive optimal control problem of McKean–Vlasov FBSDEs involving impulse controls

Maximum principle for partially observed risk-sensitive optimal control problem of McKean–Vlasov FBSDEs involving impulse controls

Feedback Stabilization of Chain-Like MDOF Nonlinear Structural Systems Under Purely Parametric Gaussian White Noises

A feedback control method is proposed to asymptotically stabilize the chain-like multi-degree-of-freedom (MDOF) nonlinear structural system under purely parametric Gaussian white noises. First, the motion equation of a chain-like nonlinear structural system with [Formula: see text] coupled elements and an undetermined control law is derived. It is reduced to a one-dimensional partially averaged Itô stochastic differential equation of the controlled Hamiltonian by applying the stochastic averaging method, which bypasses the challenge of calculating multiple Lyapunov exponents. Next, based on the dynamical programming principle, the dynamical programming equation of the averaged system with an undetermined cost function is established and addressed to obtain the optimal control law. Then, the Lyapunov exponent of the completely averaged Itô equation is derived. For the given requirement of stabilizing the system, the Lyapunov exponent is entirely fixed and used to analyze the stability of the originally chain-like MDOF nonlinear structural system. A controlled chain-like 8-DOF nonlinear structural system is taken as an example to illustrate the application and effectiveness of the proposed procedure and the effect of control forces on stabilizing the system.