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The N–H photodissociation dynamics of the pyridinyl radical upon continuous excitation to the optically bright, first excited ππ* electronic state by an ultra-violet (UV) laser pulse has been investigated within the mathematical framework of optimal control theory. The genetic algorithm (GA) is employed as the optimization protocol. We considered a three-state and three-mode model Hamiltonian, which includes the reaction coordinate, R (a1 symmetry); the coupling coordinates (namely, out-of-plane bending coordinate of the hydrogen atom of azine group), Θ (b1 symmetry); and the wagging mode, Q9 (a2 symmetry). The three electronic states are the ground, ππ*, and πσ* states. The πσ* state crosses both the ground state and the ππ* state, and it is a repulsive state on which N–H dissociation occurs upon photoexcitation. Different vibrational wave functions along the coupling coordinates, Θ and Q9, of the ground electronic state are used as the initial condition for solving the time-dependent Schrödinger equation. The optimal UV laser pulse is designed by applying the GA, which maximizes the dissociation yield. We obtained over 95% dissociation yield through the πσ* asymptote using the optimal pulse of a time duration of ∼30 000 a.u. (∼725.66 fs). [ABSTRACT FROM AUTHOR]

Controlling molecular reactivity by shaped laser pulses is a long-standing goal in chemistry. Here, we suggest a direct optimal control approach that combines external pulse optimization with other control parameters arising in the upcoming field of vibro-polaritonic chemistry for enhanced controllability. The direct optimal control approach is characterized by a simultaneous simulation and optimization paradigm, meaning that the equations of motion are discretized and converted into a set of holonomic constraints for a nonlinear optimization problem given by the control functional. Compared with indirect optimal control, this procedure offers great flexibility, such as final time or Hamiltonian parameter optimization. A simultaneous direct optimal control theory will be applied to a model system describing H-atom transfer in a lossy Fabry–Pérot cavity under vibrational strong coupling conditions. Specifically, optimization of the cavity coupling strength and, thus, of the control landscape will be demonstrated. [ABSTRACT FROM AUTHOR]

The main burden in treating human immunodeficiency virus (HIV) infection currently, is the side effects of the antiretroviral therapy (ART) used, because each treatment is toxic to the liver. This study uses optimal control theory applied to a mathematical model that describes the dynamics of HIV infection in the liver. The optimal controls are presented as therapy efficacy of reverse transcriptase inhibitors (RTIs), integrase inhibitors (INs) and protease inhibitors (PIs). An objective function is defined with an aim to investigate the optimal control strategy that minimises toxicity, viral load and cost of first-line and second-line HIV regimen. Results indicate that, in the first-line regimen with INs, a patient has to take medication for at least 98% of the treatment time and the regimen should be close to 100% efficacious regardless of the intervention cost. For second-line regimen, the period of drug administration of PIs largely depends on the weight constants. Inclusion of INs in the first-line regimen yields better HIV DNA suppression, as they are more efficacious than NRTIs. Of all drugs studied, nevirapine is highly efficacious but most toxic. The study recommends routine transaminase tests because results indicate liver enzyme elevation even with very low viral load. Numerical results with pharmacokinetic parameters further indicate an increase in HIV load at initiation of therapy, due to viral redistribution in plasma. [ABSTRACT FROM AUTHOR]

Electrohydrodynamic fluids possess extensive applications, spanning from the formation of magnetic fields in planets and stars to oil recovery. In this paper, a variational principle for an electrohydrodynamic fluid is presented, and formulated through the semi-inverse method. The Ritz method is utilized to derive an approximate solution. Furthermore, the potential application of this principle to optimal control problems constrained by an electrohydrodynamic fluid is explored. [ABSTRACT FROM AUTHOR]

In this paper, the optimal control theory is applied to a temperature optimization problem by coupling finite element and finite volume codes. The optimality system is split into the state and adjoint system. The direct problem is solved by the widely adopted finite volume OpenFOAM code and the adjoint-control equation using a variational formulation of the problem with the in-house finite element FEMuS code. The variational formulation of the problem is the natural framework for accurately capturing the control correction while OpenFOAM guarantees the accuracy of the state solution. This coupling is facilitated through the open-source MED and MEDCoupling libraries of the SALOME platform. The code coupling is implemented with the MED libraries and additional routines added in the FEMuS and OpenFOAM codes. We demonstrate the accuracy, robustness, and performance of the proposed approach with examples targeting different objectives using distributed and boundary controls in each case. [ABSTRACT FROM AUTHOR]

Monkeypox infection is a serious illness to human health, and its outbreak has been reported in many non‐endemic regions. Various approaches have been implemented to explore the epidemiology, transmission patterns, and effective control of monkeypox. In this paper, we focus on the implementation of a mathematical modeling approach to study the dynamics of monkeypox infection with a case study of the United States, the most impacted country in 2022. The proposed mathematical model is initially constructed using a nonlinear system of differential equations with constant control measures. The human population is divided into four subgroups while the animal (non‐human) population is divided into three subclasses. An extensive theoretical analysis of the proposed monkeypox model is presented including the stability of equilibria. Further, to make the present study more visible to the literature, a real data set of the cumulative confirmed cases of monkeypox in the United States from May to October 2022 is used to estimate the proposed model parameters. Some of the demographic parameters are estimated from the population of the United States. The most important biological parameter R0$$ {\mathcal{R}}_0 $$ of the problem is investigated theoretically as well as numerically based on the reported cases. The impact of various model parameters on the dynamics of state variables and R0$$ {\mathcal{R}}_0 $$ is shown graphically. Furthermore, we analyzed the impact of various model parameters on the basic reproduction number to explore the most influential intervention strategy to curb the infection. The most crucial components of the proposed system are identified and health officials are advised. Finally, using optimization theory, the most effective optimized preventive strategies are suggested to curtail the infection in a community. We believe that the present investigation will be helpful in understanding the dynamics and prevention of monkeypox infection. [ABSTRACT FROM AUTHOR]

Abstract.This article studies a robust optimal investment problem with an ambiguity-averse manager (AAM) for a defined contribution (DC) plan with multiple risks under the mean-variance criterion. In the pension accumulation stage, the interest rate, the volatility, and the salary level are considered to be stochastic. The financial market consists of a risk-free asset, a risky asset, and a rolling bond. We assume that the term structure of interest rates is driven by an affine interest rate model, while the stock price and the salary level are modeled by the stochastic volatility model with stochastic interest rate. The goal of an AAM is to find a robust optimal strategy to maximize the expectation of terminal wealth and minimize the variance of terminal wealth in the worst-case scenario. By applying the Lagrange dual theory and the robust optimal control approach, we obtain closed-form expressions of the robust precommitment strategy and the efficient frontier, and subsequently some special cases are derived. Finally, a numerical example is given to illustrate the results obtained. [ABSTRACT FROM AUTHOR]

Heat engines transform thermal energy into useful work, operating in a cyclic manner. For centuries, they have played a key role in industrial and technological development. Historically, only gases and liquids have been used as working substances, but the technical advances achieved in recent decades allow for expanding the experimental possibilities and designing engines operating with a single particle. In this case, the system of interest cannot be addressed at a macroscopic level and their study is framed in the field of stochastic thermodynamics. In the present work, we study mesoscopic heat engines built with a Brownian particle submitted to harmonic confinement and immersed in a fluid acting as a thermal bath. We design a Stirling-like heat engine, composed of two isothermal and two isochoric branches, by controlling both the stiffness of the harmonic trap and the temperature of the bath. Specifically, we focus on the irreversible, non-quasi-static case—whose finite duration enables the engine to deliver a non-zero output power. This is a crucial aspect, which enables the optimisation of the thermodynamic cycle by maximising the delivered power—thereby addressing a key goal at the practical level. The optimal driving protocols are obtained by using both variational calculus and optimal control theory tools. Furthermore, we numerically explore the dependence of the maximum output power and the corresponding efficiency on the system parameters. [ABSTRACT FROM AUTHOR]

New product or technology innovation is always facing many uncontrollable factors, which lead to the uncertainty of the success probability of an innovation project and its developing time. Multi-agent collaboration is an effective way to improve the success probability and reduce the developing time of an innovation project. In this paper, we employ the knowledge sharing model and the success probability model to formulate a differential game for the multi-agent collaborative innovation (MACI) mechanism under uncertainty. Firstly, the equilibrium policy for each agent is obtained by applying the optimal control theory. Secondly, we observe that the derived equilibrium policy can not only effectively reduce the developing time of the innovation procedure, but also improve the success probability of the innovation project. Thirdly, we show that the optimal profit allocation contract for the collaborative mechanism can be obtained by solving a linear programming problem. Finally, this paper investigates how governments' subsidy policies affect the equilibrium of the collaborative mechanism. Numerical experiments are conducted to test the performance of different collaborative innovation mechanisms. This proposed model and its derived managerial insights provide new theoretical guidance for establishing and implementing the multi-agent collaborative mechanism of new product or technology innovations under uncertain environments. [ABSTRACT FROM AUTHOR]

The distributed optimal design of high-speed train movement is systematically investigated in this article. A distributed optimal control law is proposed, addressing the train consist of cars coupled by spring buffers, and is affected by aerodynamic drag and rolling resistance. A new distributed controller is proposed to decouple the train model by fully removing the in-train force, which greatly simplifies the complexity of calculation. Then the pending problem is redescribed to the control of cars with different mass. Grounded on the Lyapunov stability theory and optimal control theory, distributed optimal control law is proposed in line with guaranteed cost function, which enables faster updates of the real-time status of each car and adaptive vehicle mass. It ensures consistency in the tracking process of each car of the train, and further reduces the in-train force among cars. To eliminate the speed overshoot which results from the influence of acceleration change during train operation, we weigh in with the feed-forward compensator to assure the train's good acceleration performance. Ultimately, numerical simulations results are obtained to demonstrate convincingly the significance of our proposed control law. • Implement distributed control to decouple the high-speed train model into separate subsystems. • Designed controller achieves adaptivity to the mass of cars. • A feed-forward compensator has been introduced to resolve overshoot when train operating conditions change. [ABSTRACT FROM AUTHOR]

When having access to demand forecasts, a crucial question is how to effectively use this information to make better resource allocation decisions, especially during demand surges like the COVID-19 pandemic. Despite the emergence of various advanced prediction models for hospital resources, there has been a lack of prescriptive solutions for hospital managers seeking concrete decision support, for example, guidance on whether to allocate beds from other specialties to meet the surge demand from COVID-19 patients by postponing elective surgeries. In their paper "Optimal Routing under Demand Surge: the Value of Future Arrival Rate," the authors present a systematic framework to incorporate future demand into routing decisions in parallel server systems with partial flexibility and quantify the benefits of doing so. They propose a simple and interpretable two-stage index-based policy that explicitly incorporates demand forecasts into real-time routing decisions. Their analytical and numerical results demonstrate the policy's effectiveness, even in the presence of large prediction errors. Motivated by the growing availability of advanced demand forecast tools, we study how to use future demand information in designing routing strategies in queueing systems under demand surges. We consider a parallel server system operating in a nonstationary environment with general time-varying arrival rates. Servers are cross-trained to help nonprimary customer classes during demand surges. However, such flexibility comes with various operational costs, such as a loss of efficiency and inconvenience in coordination. We characterize how to incorporate the future arrival information into the routing policy to balance the tradeoff between various costs and quantify the benefit of doing so. Based on transient fluid control analysis, we develop a two-stage index-based look-ahead policy that explicitly takes the overflow costs and future arrival rates into account. The policy has an interpretable structure, is easy to implement and is adaptive when the future arrival information is inaccurate. In the special case of the N-model, we prove that this policy is asymptotically optimal even in the presence of certain prediction errors in the demand forecast. We substantiate our theoretical analysis with extensive numerical experiments, showing that our policy achieves superior performance compared with other benchmark policies (i) in complicated parallel server systems and (ii) when the demand forecast is imperfect with various forms of prediction errors. Funding: This work was supported by the National Science Foundation Civil, Mechanical, and Manufacturing Innovation [Grant 1944209]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0282. [ABSTRACT FROM AUTHOR]

This paper introduces a tontine-like annuity fund designed to provide lifelong income to its participants. Initially, each member contributes a lump-sum payment into a trust fund as a joining premium. Participants then receive benefits over time, based on their survival. As members pass away, their share of payouts is redistributed among the survivors, resulting in increased payouts for those remaining. Differing from traditional tontines, which assume a uniform mortality risk, this fund accommodates participants of various ages and allows new members to join during its operation. To accommodate these features, the authors utilize age-structured models (ASMs) to determine fair premiums for new entrants and to analyze the dynamics of benefit distribution. The core objective of this paper is to develop a pension model using ASMs, recognizing its significant potential for adaptation and expansion. The primary mathematical approach employed is the Maximum Principle from optimal control theory, which helps in deriving explicit solutions for the optimal subsidy strategy. Through numerical examples and detailed illustrations, the paper demonstrates that participants who remain in the cohort longer receive greater subsidies. Additionally, the study finds that adverse shocks lead to a smaller population and thus fewer subsidies. Conversely, starting with a larger initial cohort population tends to increase the overall population, resulting in more subsidies. However, higher costs associated with subsidies lead to their reduction. Our analysis reveals the complex interplay of factors influencing the sustainability and effectiveness of the proposed annuity model. [ABSTRACT FROM AUTHOR]

This paper examines the robust time-consistent reinsurance-investment strategy for an ambiguity-averse insurer under the 4/2 stochastic volatility model. In this model, an ambiguity-averse insurer transfers the risk generated by insurance claims through purchasing proportional reinsurance and invests the remaining capital in a financial market composed of a risk-free and a risky asset to manage the risk. The claim process is described by the classical Cramér-Lundberg process, while the price process of the risky asset is driven by the 4/2 stochastic volatility model. Under the mean-variance criterion, by employing the stochastic optimal control theory, we establish the corresponding extended Hamilton-Jacobi-Bellman (HJB) equation, and derive the robust time-consistent reinsurance-investment strategy and the corresponding equilibrium value function. In addition, we also study the reinsurance-investment problem in the case of excess-of-loss reinsurance. Finally, a sensitivity analysis is given to examine the results obtained. [ABSTRACT FROM AUTHOR]

Distributed denial of service (DDoS) is a type of cyberattack in which multiple compromised systems flood the bandwidth or resources of a single system, making the flooded system inaccessible to legitimate users. Since large-scale botnets based on the Internet of Things (IoT) have been hotbeds for launching DDoS attacks, it is crucial to defend against DDoS-capable IoT botnets effectively. In consideration of resource constraints and frequent state changes for IoT devices, they should be equipped with repair measures that are cost-effective and adaptive to mitigate the impact of DDoS attacks. From the mitigation perspective, we refer to the collection of repair costs at all times as a repair strategy. This paper is then devoted to studying the problem of developing a cost-effective and adaptive repair strategy (ARS). First, we establish an IoT botware propagation model that fully captures the state evolution of an IoT network under attack and defense interventions. On this basis, we model the ARS problem as a data-driven optimal control problem, aiming to realize both learning and prediction of propagation parameters based on network traffic data observed at multiple discrete time slots and control of IoT botware propagation to a desired infection level. By leveraging optimal control theory, we propose an iterative algorithm to solve the problem, numerically obtaining the learned time-varying parameters and a repair strategy. Finally, the performance of the learned parameters and the resulting strategy are examined through computer experiments. [ABSTRACT FROM AUTHOR]

We adapt non-linear optimal control theory (OCT) to control oscillations and network synchrony and apply it to models of neural population dynamics. OCT is a mathematical framework to compute an efficient stimulation for dynamical systems. In its standard formulation, it requires a well-defined reference trajectory as target state. This requirement, however, may be overly restrictive for oscillatory targets, where the exact trajectory shape might not be relevant. To overcome this limitation, we introduce three alternative cost functionals to target oscillations and synchrony without specification of a reference trajectory. We successfully apply these cost functionals to single-node and network models of neural populations, in which each node is described by either the Wilson-Cowan model or a biophysically realistic high-dimensional mean-field model of exponential integrate-and-fire neurons. We compute efficient control strategies for four different control tasks. First, we drive oscillations from a stable stationary state at a particular frequency. Second, we switch between stationary and oscillatory stable states and find a translational invariance of the state-switching control signals. Third, we switch between in-phase and out-of-phase oscillations in a two-node network, where all cost functionals lead to identical OC signals in the minimum-energy limit. Finally, we (de-) synchronize an (a-) synchronously oscillating six-node network. In this setup, for the desynchronization task, we find very different control strategies for the three cost functionals. The suggested methods represent a toolbox that enables to include oscillatory phenomena into the framework of non-linear OCT without specification of an exact reference trajectory. However, task-specific adjustments of the optimization parameters have to be performed to obtain informative results. [ABSTRACT FROM AUTHOR]

One of the main obstacles in rice cultivation is tungro disease, caused by Rice Tungro Spherical Virus (RTSV) and Rice Tungro Bacilliform Virus (RTBV), which are transmitted by green leafhopper vectors (Nephotettix virescens). This disease can be controlled by using pesticides and refugia plants. Excessive use of pesticides can have negative impacts and high costs, so it is necessary to control the use of pesticides. In this study, a mathematical model of the spread of tungro virus disease in rice plants was developed by considering the characteristics of the virus, the presence of green leafhoppers and natural enemies, refugia planting, and pesticide use. From this model, dynamic and sensitivity analyses were carried out, and the optimal control theory was searched using the Pontryagin minimum principle. The analysis results showed three equilibriums: two non-endemic equilibriums (when plant and vector populations exist and when plant, vector, and natural enemy populations exist) and one endemic equilibrium. The non-endemic equilibrium will be asymptotically stable locally if R 0 < 1 . At the same time, the parameters that greatly influence the spread of this disease are parameters μ ,   μ 2 , and ϕ for local sensitivity analysis and α ,   a ,   β ,   b ,   ϕ , and μ 2 for global sensitivity analysis. The results of the numerical simulation show that control using combined control is more effective in reducing the intensity of the spread of tungro disease in rice plants than control in the form of planting refugia plants as a source of food for natural enemies. The use of pesticides is sufficient for only four days, so the costs incurred are quite effective in controlling the spread of this disease. [ABSTRACT FROM AUTHOR]

In this paper, the problem of preview optimal control for second-order nonlinear systems for marine vessels is discussed on a fully actuated dynamic model. First, starting from a kinematic and dynamic model of a three-degrees-of-freedom (DOF) marine vessel, we derive a fully actuated second-order dynamic model that involves only the ship's position and yaw angle. Subsequently, through the higher-order systems methodology, the nonlinear terms in the system were eliminated, transforming the system into a one-order parameterized linear system. Next, we designed an internal model compensator for the reference signal and constructed a new augmented error system based on this compensator. Then, using optimal control theory, we designed the optimal preview controller for the parameterized linear system and the corresponding feedback parameter matrices, which led to the preview controller for the original second-order nonlinear system. Finally, a numerical simulation indicates that the controller designed in this paper is highly effective. [ABSTRACT FROM AUTHOR]

This paper examines control and cooperation mechanisms for trans-regional air pollution using differential game theory. This study focuses on analyzing pollution control pathways in regions characterized by asymmetric economic development. Three models are constructed: the Nash non-cooperative game, the pollution control cost compensation mechanism, and the collaborative cooperation mechanism. These models are used to investigate optimal pollution control strategies for various regions. The findings indicate that the collaborative cooperation model substantially reduces pollution emissions and enhances overall benefits. Additionally, the pollution control cost compensation mechanism alleviates the burden of pollution control on less developed regions. Numerical analysis confirms the effectiveness of the proposed models and offers theoretical foundations and policy recommendations for regional cooperation in pollution prevention. [ABSTRACT FROM AUTHOR]

This paper considers the problem of robust optimal tracking control of multiple autonomous underwater Vehicles (AUVs) subject to uncertain external disturbances. First, the Takagi‐Sugeno (T‐S) fuzzy based technique is utilized to convert the high‐order nonlinear multi‐AUV system into a series of linearized subsystems. Second, a novel fully distributed sliding mode control (FDSMC) strategy is proposed to attenuate the disturbances. Meanwhile, the leader‐following consensus and the nearly optimization of the energy‐cost function for the multi‐AUV system can be achieved simultaneously through the designed optimal nominal control protocol. Moreover, the proposed control strategy has more mild constraints on the communication topologies. Finally, the effectiveness of the proposed FDSMC strategy is verified by numerical simulation studies. [ABSTRACT FROM AUTHOR]

The article traces the historical development of explanations for natural phenomena, from Aristotle's four causes to modern variational principles in physics. It highlights the shift from teleological to mechanistic perspectives, with a focus on key figures like Descartes, Newton, and Fermat. The text explores the classical calculus of variations and optimal control theory, emphasizing the role of efficient and final causes in understanding physical systems. It also discusses the application of control theory in explaining the motion of controlled systems, drawing connections to Aristotle's four causes and reflecting on the limitations of technological solutions in addressing complex societal challenges. [Extracted from the article]

We propose an inverse problem to derive the stress distributions that drive the tissue flows during gastrulation in the epiblast of the chick embryo, from measurements of the tissue velocity fields at different stages of development. We assume that the embryonic tissue can be described as a highly viscous fluid, characterized by the Stokes equations. Using the theory of the optimal control, the stress distributions are determined by minimizing an objective functional, which is constructed such that it can match the numerical velocity of the flow with the experimental velocity data by choosing the stress as the control variable. The Lagrange multiplier method is utilized to derive the optimality system. The finite element method is used to approximate these partial differential equations numerically and we use the conjugate gradient algorithm to solve the optimal control problem. [ABSTRACT FROM AUTHOR]

With an increase in market competition, the association between marketing and inventory management has become more important. The commercial activities are more rapid through social media, and advertising has played a crucial role in reaching the product to the consumers before it hits the market. It has thus become normal in an oligopolistic marketing system to increase sales through advertising effort and gain more profit from potential market. It is challenging, nevertheless, to calculate demand and costs related to advertising efforts. As a result, the purpose of this study is to identify the best advertising approach and its potential impact on demand in order to optimize the firm's overall profit. In this paper, we develop an inventory model for deteriorating items to obtain an optimal advertising and inventory strategy, where the consumer demand rate depends on advertising effort and inventory of the items displayed in the store. We have formulated two optimal control problems with the assumption that the replenishment cycle is longer than the fresh product time or not. It is assumed that products do not decay within the fresh product time interval, and inventory decreases due to consumer demand. Next, items will deteriorate and inventory level decreases because of the combined effects of customer demand and deterioration. The analytical solution for the optimal dynamic advertising effort strategies obtained by applying Pontryagin's maximum principle to maximize overall profit over the planning period. The efficiency of the proposed model is demonstrated by numerical examples. A parameter sensitivity analysis is also performed, providing suggestions for enhancing the firm's profitability when dealing with deteriorating products. [ABSTRACT FROM AUTHOR]

This article explores the optimization of transaction costs in a fully invested portfolio, where all available capital is committed to risky assets. The weights assigned to these assets are fixed based on a long-term strategic allocation. Unlike a passive portfolio, a fully invested portfolio is active, necessitating regular rebalancing to maintain the desired asset mix. Transaction costs pose a significant challenge to achieving optimal portfolio performance. Financial optimization models incorporating transaction costs fall within the domain of stochastic optimal control theory. However, the lack of analytical solutions and the intricate nature of numerical solution methods pose significant obstacles in applying these models in real-world applications. To overcome these challenges, we propose a practical model that balances theoretical and numerical simplicity while maintaining practical relevance. The central idea in our approach posits that the optimal rebalancing policy within a multi-period model can be effectively approximated by a policy derived from a single-period model. Through historical simulations, we illustrate the efficiency of our model, providing empirical support for our theoretical framework. In summary, our article offers a practical and efficient approach to address the complexities of transaction cost optimization in a fully invested portfolio. [ABSTRACT FROM AUTHOR]

In pursuit–evasion scenarios, the pursuer typically possesses a lethal zone. If the evader effectively utilizes perceptual information, they can narrowly escape the lethal zone while minimizing energy consumption, thereby avoiding excessive and unnecessary maneuvers. Based on optimal control theory, we propose a guidance law for achieving critical safe miss distance evasion under bounded control. First, we establish the zero-effort miss (ZEM) state equation for the evader, while approximating disturbances from the pursuer. Next, we formulate an optimal control problem with energy consumption as the objective function and the ZEM at the terminal time as the terminal constraint. Subsequently, we design an iterative algorithm that combines the homotopy method and Newton's iteration to solve the optimal control problem, applying Pontryagin's Maximum Principle. The simulation results indicate that the designed iterative method converges effectively; through online updates, the proposed guidance law can successfully achieve critical safe miss distance evasion. Compared to programmatic maneuvering and norm differential game guidance law, this approach not only stabilizes the evader's evasion capabilities but also significantly reduces energy consumption. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

With an increase in market competition, the association between marketing and inventory management has become more important. The commercial activities are more rapid through social media, and advertising has played a crucial role in reaching the product to the consumers before it hits the market. It has thus become normal in an oligopolistic marketing system to increase sales through advertising effort and gain more profit from potential market. It is challenging, nevertheless, to calculate demand and costs related to advertising efforts. As a result, the purpose of this study is to identify the best advertising approach and its potential impact on demand in order to optimize the firm's overall profit. In this paper, we develop an inventory model for deteriorating items to obtain an optimal advertising and inventory strategy, where the consumer demand rate depends on advertising effort and inventory of the items displayed in the store. We have formulated two optimal control problems with the assumption that the replenishment cycle is longer than the fresh product time or not. It is assumed that products do not decay within the fresh product time interval, and inventory decreases due to consumer demand. Next, items will deteriorate and inventory level decreases because of the combined effects of customer demand and deterioration. The analytical solution for the optimal dynamic advertising effort strategies obtained by applying Pontryagin’s maximum principle to maximize overall profit over the planning period. The efficiency of the proposed model is demonstrated by numerical examples. A parameter sensitivity analysis is also performed, providing suggestions for enhancing the firm's profitability when dealing with deteriorating products.

Quantum walks are the quantum counterpart of classical random walks and have various applications in quantum information science. Polar molecules have rich internal energy structure and long coherence time and thus are considered as a promising candidate for quantum information processing. In this paper, we propose a theoretical scheme for implementing discrete-time quantum walks on a circle with dipole–dipole coupled SrO molecules. The states of the walker and the coin are encoded in the pendular states of polar molecules induced by an external electric field. We design the optimal microwave pulses for implementing quantum walks on a four-node circle and a three-node circle by multi-target optimal control theory. To reduce the accumulation of decoherence and improve the fidelity, we successfully realize a step of quantum walk with only one optimal pulse. Moreover, we also encode the walker into a three-level molecular qutrit and a four-level molecular ququart and design the corresponding optimal pulses for quantum walks, which can reduce the number of molecules used. It is found that all the quantum walks on a circle in our scheme can be achieved via optimal control fields with high fidelities. Our results could shed some light on the implementation of discrete-time quantum walks and high-dimensional quantum information processing with polar molecules. [ABSTRACT FROM AUTHOR]

This paper presents a method that drives key nodes with minimal control cost to influence the agents in social dilemmas to learn to cooperate. Cooperation exists widely in human society and nature. Discovering the mechanisms that promote the evolution of cooperation has always been a concern across disciplines. In this context, continuous action social dilemma games are a fitting model to explore individual interactions and the spread of cooperative behaviors in social networks. This paper proposes a novel framework that applies optimal control theory to steer the evolution of cooperation within these games. Existing research lacks a definitive method for judicious selecting critical nodes capable of guiding the entire system toward a desired state with minimal cost. To bridge this gap, our framework offers a control mechanism that influences cooperative behavior and determines the optimal number and identity of nodes to be controlled, thereby maximizing outcomes. Building upon continuous action social dilemma games in social networks, we formulate a set of coupled Hamilton-Jacobi-Bellman (HJB) equations, employ a value iteration reinforcement learning (RL) algorithm to solve for the HJB function, and demonstrate the convergence of the proposed algorithm. Furthermore, we conduct a comprehensive qualitative and quantitative investigation into the selection of controlled nodes across diverse networks, focusing on optimizing control performance while minimizing associated costs. Our research substantiates the efficacy of the proposed algorithm across a spectrum of social networks, affirming its utility and potential impact in promoting the evolution of cooperative behavior. [ABSTRACT FROM AUTHOR]

Historically, advertising allocation decisions have operated mostly at a macro level, comprising determination of the total budget followed by apportionment among media channels. Owing to the rapid and sustained rise of digital media, an additional decision now operates at a micro level, namely, which specific customers to target with advertising. In the macro case, optimal control theory provides a powerful framework for firm profit maximization, specifically allowing for ad response, cost per medium, and discount rate, all in the presence of multiple competing brands. However, optimal control theory has never been applied to the situation of microtargeting individual customers. Consequently, in this study the author shows how optimal control theory can be adapted for application to individual customers. The author estimates a multinomial logit model with individual-specific advertising response parameters. In turn, these parameters are used to determine the optimal number of exposures each customer should receive for each advertising medium. An empirical example demonstrates that using the optimal microtargeting method improves firm profits over existing ad scheduling methods by between 150% and 183%. [ABSTRACT FROM AUTHOR]

Cancer is a complex group of diseases characterized by uncontrolled cell growth that can spread throughout the body, leading to serious health issues. Traditional treatments mainly include chemotherapy, surgery, and radiotherapy. Although combining different therapies is becoming more common, predicting how these treatments will interact and what side effects they may cause, such as gastrointestinal or neurological problems, can be challenging. This research applies optimal control theory (OCT) to create precise and personalized treatment plans for cancer patients. OCT helps identify the most effective doses of chemotherapy and immunotherapy by forecasting how various treatment combinations will impact tumor growth and the immune response over time. It optimizes the integration of chemotherapy with immunotherapy to minimize side effects while maximizing therapeutic benefits. The study proposes a model for managing malignant tumors using a mix of immunotherapy, vaccines, and chemotherapy. The aim is to develop the best treatment plan that reduces new tumor growth while keeping healthy cells stable. It also takes into account individual differences among patients, including variations in tumor biology and immune responses in both younger and older individuals. To do this, we compared different optimal control strategies: interior point optimization (IPOPT), an open-source tool for nonlinear optimization; state-dependent Riccati equation (SDRE), which adapts linear control methods for nonlinear situations; and approximate sequence Riccati equation (ASRE), a globally optimal feedback control approach for nonlinear systems. The optimization criterion showed that the proposed work achieved a cost value of 52.3573 for IPOPT, compared with 52.424 for both SDRE and ASRE. For $ \mathrm{C}\mathrm{D}{8}^{+} $ T cells, the proposed method maintained a consistent value of 1.6499 for continuous (C) and dosed (D) across all techniques. Tumor cell counts had a C value of 0.0007 for IPOPT, compared with 0.0006 for ISDRE and ASRE, with D values remaining at 0 across all methods. This comparison demonstrates the successful use of control theory techniques and highlights their potential for developing personalized and effective treatment strategies for complex cancer cases. By optimizing treatment schedules and dosages, OCT can help minimize the side effects of cancer therapies, thereby enhancing patients' overall quality of life.

Abstract 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 ( $$u_{1}$$ u 1 ), quarantine ( $$u_{2}$$ u 2 ) and chemical control ( $$u_{3}$$ u 3 ). 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.

In practice, there is always competition among different pension managers. The competitive pension managers are concerned about their relative performance to make better decisions. In addition, to protect the rights of plan members who die before retirement, most of the defined contribution (DC) pension plans contain return of premiums clauses. In this article, we introduce the return of premiums clauses into two competitive DC pension plans with salary risk. Each pension manager cares about not only his own terminal wealth but also his relative wealth versus his competitor. Both the pension managers are allowed to invest the premiums in a financial market, which consists of one risk-free asset and one risky asset whose price process follows the constant elasticity of variance (CEV) model. We investigate the time-consistent investment strategies of the two pension managers under the mean-variance (MV) criterion. The aim of each pension manager is to maximize the mean and minimize the variance of his relative terminal wealth. The explicit expressions of the time-consistent strategies and the efficient frontiers are obtained via applying the extended stochastic optimal control theory. Some special cases are also discussed in detail. Finally, a numerical simulation demonstrates the results obtained. [ABSTRACT FROM AUTHOR]

Cholera is a disease of poverty affecting people with inadequate access to safe water and basic sanitation. Conflict, unplanned urbanization and climate change all increase the risk of cholera. In this article, an optimal control deterministic mathematical model of cholera disease with cost-effectiveness analysis is developed and analyzed considering both direct and indirect contact transmission pathways. The model qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction number of the model is obtained. We also performed sensitivity analysis of the basic parameters of the model. Then an optimal control problem is designed with a control functional having five controls: vaccination, treatment, environment sanitation and personal hygiene, and water quality improvement program. We examined the existence and uniqueness of the optimal controls of the system. Through the implementation of Pontryagin's maximum principle, the characterization of the optimal controls optimality system is established. The numerical simulation results the integrated control strategies demonstrated that strategy 2, 7, and 12 are effective programs to combat cholera disease from the community. Based on the local circumstances, available funds, and resources, it is recommended to the government stakeholders and policymakers to execute any one of the three integrated intervention programs. [ABSTRACT FROM AUTHOR]

High-speed aircraft capable of complex spatial maneuvers and having several technical, economic, and tactical advantages are increasingly used in aerospace warfare. In this regard, a topical problem is to optimize interception systems for such targets. The operation features of interception systems are considered based on analyzing flight path features of high-speed aircraft. Requirements for ways to optimize guidance methods are formulated. [ABSTRACT FROM AUTHOR]

In the present study, a quarter vehicle active suspension model with one degree of freedom designed considering only vertical forces were examined. LQG-based closed-loop suspension control was used to minimize the response of the system according to different road profiles. Sensor noises were added for the realistic simulations of the designed control system and a Kalman filter was used to filter these noises. The active suspension system was analyzed with the MATLAB simulation software package. The feedback signal and sensor location which used for the control system were determined using the system's Gramian matrix with the new approach. The LQG control system was compared to the conventional passive suspension system, according to the obtained results. In this study, three different road inputs were applied to active and passive suspension systems modeled according to several feedback signals. Although the LQG control was exposed to sensor noise, its damping ability against different road inputs was determined to be better than the passive suspension system. [ABSTRACT FROM AUTHOR]

The Sun–Earth Lagrange points, L1 and L2, are excellent locations for space based observatories, due to their favorable dynamical and environmental properties. Space telescopes, however, come with an extremely high price tag, and without refueling and servicing the typical lifetime is only about ten to fifteen years. The return on investment of a space telescope could be significantly increased by developing on-orbit servicing and refueling capabilities, assuming that the servicing vehicle can be launched at a fraction of the cost of the original mission and that the lifetime of the space telescope can be significantly extended to allow for continued scientific activity. In this paper we demonstrate the feasibility of this class of servicing mission from a trajectory design perspective, using novel techniques that we have developed for quick sampling of the solution space, as well as an efficient and reliable means to obtained high-fidelity, time-optimal, end-to-end transfer trajectories. As candidates for this investigation we consider Gaia and the James Webb Space Telescope. Our trajectory design methodology is, however, general enough to be applicable to future space observatories that are designed to be serviceable in space. • The lifetime of space assets at SEL2 can be greatly extended via servicing missions. • Poincare maps are leveraged to explore the design space and obtain initial guesses. • Indirect methods are used to refine the initial guesses and design optimal transfers. [ABSTRACT FROM AUTHOR]

In this paper, a Caputo fractional tumor immune model of combination therapy is established. First, the stability and biological significance of each equilibrium point are analyzed, and it is demonstrated that chaos may arise under specific conditions. Combined with the mathematical definition of Caputo fractional differentiation (CFD), it is found that there is a high correlation between the chaotic phenomenon of the patient's condition and the sensitivity of the patient to the change in the state of the day. The bifurcation threshold of each parameter is determined through numerical simulation, and the Hopf bifurcation of direct competition coefficient and inhibition coefficient between tumor cells and host healthy cells is elaborated upon in detail. Subsequently, a novel method combining optimal control theory with the particle swarm optimization (PSO) algorithm is proposed for the optimal control of the tumor immune model in combination therapy. Finally, the Adams–Bashforth–Moulton (ABM) prediction correction method is utilized in numerical simulations which demonstrate that the introduction of the CFD alters the model dynamics. Furthermore, these results indicate that fractional calculus can effectively be applied to tumor immune models better to elucidate complex chaotic dynamics of tumor cell evolution. Concurrently, the PSO can be successfully integrated with optimal control theory to address optimization challenges in cancer treatment. [ABSTRACT FROM AUTHOR]

The manipulator actuated by pneumatic artificial muscles (PAM) is a widely used type of robotic arm in industrial automation. However, its performance can be limited by non-linear dynamics and uncertainties in the system. To overcome these limitations, this paper proposes a synergetic control strategy (SACT) to improve the performance of the SACT, a social spider optimisation algorithm (SSO) has been suggested for adjusting its parameters. To verify the performance of a PAM-actuated manipulator based on an optimal SACT controller, a computer simulation study was conducted using MATLAB software. Moreover, a comparison study between the optimal synergetic algorithm control theory and the optimal sliding mode controller (SMC) has been made in terms of robustness and transient behaviour characteristics. The provided simulation results have shown that the SACT controller exhibited quicker convergence towards the desired trajectory and maintained a lower steadystate error as compared to the SMC controller. Additionally, the SACT controller demonstrated more resilience to variations in parameters and showed more robust characteristics. [ABSTRACT FROM AUTHOR]

The article focuses on a mathematical model of malaria and its control through preventive and curative measures. Topics include the formulation of the malaria model with human and mosquito classes, the introduction of optimal control for malaria prevention and treatment, and the use of Python for numerical simulations to analyze the model's effectiveness in controlling the disease.

In this article, a distributed optimal control approach is proposed for a class of affine nonlinear multi‐agent systems (MASs) with unknown nonlinear dynamics. The game theory is used to formulate the distributed optimal control problem into a differential graphical game problem with synchronized updates of all nodes. A data‐based integral reinforcement learning (IRL) algorithm is used to learn the solution of the coupled Hamilton–Jacobi (HJ) equation without prior knowledge of the drift dynamics, and the actor‐critic neural networks (A‐C NNs) are used to approximate the control law and the cost function, respectively. To update the parameters synchronously, the gradient descent algorithm is used to design the weight update laws of the A‐C NNs. Combining the IRL and the A‐C NNs, a distributed consensus optimal control method is designed. By using the Lyapunov stability theory, the developed optimal control method can show that all signals in the considered system are uniformly ultimately bounded (UUB), and the systems can achieve Nash equilibrium when all agents update their controllers simultaneously. Finally, simulation results are given to illustrate the effectiveness of the developed optimal control approach. [ABSTRACT FROM AUTHOR]

The aim of the current study is to demonstrate the feasibility of radiofrequency (RF) pulses generated via an optimal control (OC) algorithm to perform magnetic resonance elastography (MRE) and quantify the mechanical properties of materials with very short transverse relaxation times (T2 < 5 ms) for the first time. OC theory applied to MRE provides RF pulses that bring isochromats from the equilibrium state to a fixed target state, which corresponds to the phase pattern of a conventional MRE acquisition. Such RF pulses applied with a constant gradient allow to simultaneously perform slice selection and motion encoding in the slice direction. Unlike conventional MRE, no additional motion‐encoding gradients (MEGs) are needed, enabling shorter echo times. OC pulses were implemented both in turbo spin echo (OC rapid acquisition with refocused echoes [RARE]) and ultrashort echo time (OC UTE) sequences to compare their motion‐encoding efficiency with the conventional MEG encoding (classical MEG MRE). MRE experiments were carried out on agar phantoms with very short T2 values and on an ex vivo bovine tendon. Magnitude images, wave field images, phase‐to‐noise ratio (PNR), and shear storage modulus maps were compared between OC RARE, OC UTE, and classical MEG MRE in samples with different T2 values. Shear storage modulus values of the agar phantoms were in agreement with values found in the literature, and that of the bovine tendon was corroborated with rheometry measurements. Only the OC sequences could encode motion in very short T2 samples, and only OC UTE sequences yielded magnitude images enabling proper visualization of short T2 samples and tissues. The OC UTE sequence produced the best PNRs, demonstrating its ability to perform anatomical and mechanical characterization. Its success warrants in vivo confirmation in further studies. [ABSTRACT FROM AUTHOR]

Cancer is a complex group of diseases characterized by uncontrolled cell growth that can spread throughout the body, leading to serious health issues. Traditional treatments mainly include chemotherapy, surgery, and radiotherapy. Although combining different therapies is becoming more common, predicting how these treatments will interact and what side effects they may cause, such as gastrointestinal or neurological problems, can be challenging. This research applies optimal control theory (OCT) to create precise and personalized treatment plans for cancer patients. OCT helps identify the most effective doses of chemotherapy and immunotherapy by forecasting how various treatment combinations will impact tumor growth and the immune response over time. It optimizes the integration of chemotherapy with immunotherapy to minimize side effects while maximizing therapeutic benefits. The study proposes a model for managing malignant tumors using a mix of immunotherapy, vaccines, and chemotherapy. The aim is to develop the best treatment plan that reduces new tumor growth while keeping healthy cells stable. It also takes into account individual differences among patients, including variations in tumor biology and immune responses in both younger and older individuals. To do this, we compared different optimal control strategies: interior point optimization (IPOPT), an open-source tool for nonlinear optimization; state-dependent Riccati equation (SDRE), which adapts linear control methods for nonlinear situations; and approximate sequence Riccati equation (ASRE), a globally optimal feedback control approach for nonlinear systems. The optimization criterion showed that the proposed work achieved a cost value of 52.3573 for IPOPT, compared with 52.424 for both SDRE and ASRE. For C D 8 + T cells, the proposed method maintained a consistent value of 1.6499 for continuous (C) and dosed (D) across all techniques. Tumor cell counts had a C value of 0.0007 for IPOPT, compared with 0.0006 for ISDRE and ASRE, with D values remaining at 0 across all methods. This comparison demonstrates the successful use of control theory techniques and highlights their potential for developing personalized and effective treatment strategies for complex cancer cases. By optimizing treatment schedules and dosages, OCT can help minimize the side effects of cancer therapies, thereby enhancing patients' overall quality of life. [ABSTRACT FROM AUTHOR]