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The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of fractional neutral stochastic integrodifferential equations driven by Rosenblatt process and Poisson jumps in Hilbert spaces. First we establish a new set of sufficient conditions for the existence of mild solutions of the aforementioned fractional systems by using the successive approximation approach. The results are formulated and proved by using the fractional calculus, solution operator and stochastic analysis techniques. The existence of optimal control pairs of system governed by fractional neutral stochastic differential equations driven by Rosenblatt process and poisson jumps is also been presented. An example is provided to illustrate the theory. [ABSTRACT FROM AUTHOR]

Infectious diseases continue to be a significant threat to human health and civilization, and finding effective methods to combat them is crucial. In this paper, we investigate the impact of awareness campaigns and optimal control techniques on infectious diseases without proper vaccines. Specifically, we develop an SIRS-type mathematical model that incorporates awareness campaigns through media and treatment for disease transmission dynamics and control. The model displays two equilibria, a disease-free equilibrium and an endemic equilibrium, and exhibits Hopf bifurcation when the bifurcation parameter exceeds its critical value, causing a switch in the stability of the system. We also propose an optimal control problem that minimizes the cost of control measures while achieving a desired level of disease control. By applying the minimum principle to the optimal control problem, we obtain analytical and numerical results that show how the infection rate of the disease affects the stability of the system and how awareness campaigns and treatment can maintain the stability of the system. This study highlights the importance of awareness campaigns in controlling infectious diseases and demonstrates the effectiveness of optimal control theory in achieving disease control with minimal cost. [ABSTRACT FROM AUTHOR]

Uncertainty theory is a field in axiomatic mathematics committed to disposing of belief degrees. By dint of uncertain theory and Hurwicz criterion, this article mainly addresses optimal control and non-zero-sum differential game of uncertain delay dynamic systems, which are depicted as a sort of uncertain differential equation with multiple input delays. Employing the technology of dynamic programming, the optimality principle is put forward and the optimality equation is formulated simultaneously to deal with the optimal control problem. In addition, an equilibrium equation is derived to solve the Nash equilibrium for the multi-player non-zero-sum uncertain differential game on the strength of the proposed optimality equation. An example is devised to illustrate the availability of the results in the end. [ABSTRACT FROM AUTHOR]

This paper presents an application of general Tau theory to the modeling and analysis of articulatory trajectories in speech. We evaluated the model using electromagnetic articulometry data from 12 native speakers of English reading a common text, where trajectories of the following sensors were fitted: lower and upper lips, jaw, and three tongue sensors. Additionally, we analyzed trajectories of the lip aperture signal. Our experiments show that the general Tau theory model gives a better fit than existing (i) methods based on critically damped oscillators, and (ii) a method based on sequential target approximation. These findings support the hypothesis of Tau-guided movements of articulators during speech production. In the second part of the paper, our Tau theory analysis shows that articulatory movements follow similar velocity profile distributions across speakers. In particular, the value of the shape parameter κ of the Tau theory equation is identically distributed across speakers, following a unimodal distribution. The statistical mode of the distribution corresponds to the value of κ that generates a symmetric velocity profile. The analysis of the statistical distribution of κ values also reveals that its variance decreases when greater articulatory effort is required, such that produced articulatory effort remains close to that predicted by the theoretical minimal cost function based on forces acting on the moving articulator. This provides new evidence that articulatory effort is optimized during speech production. • General Tau theory is applied to articulatory movements in speech. • General Tau theory equations provide better fits to EMA data than other methods. • Evidence supporting effort minimization of articulatory movements in speech. [ABSTRACT FROM AUTHOR]

A counterexample to uniqueness of global minimizers of semilinear optimal control problems is given. The lack of uniqueness occurs for a special choice of the state-target in the cost functional. Our arguments also show that, for some state-targets, there exist local minimizers which are not global. When this occurs, gradient-type algorithms may be trapped by local minimizers, thus missing global ones. Furthermore, the issue of convexity of a quadratic functional in optimal control is analyzed in an abstract setting. As a corollary of nonuniqueness of minimizers, a nonuniqueness result for a coupled elliptic system is deduced. Numerical simulations have been performed illustrating the theoretical results. We also discuss the possible impact of the multiplicity of minimizers on the turnpike property in long time horizons. [ABSTRACT FROM AUTHOR]

The effects of habitat heterogeneity on a diffusing population are investigated here. We formulate a reaction-diffusion system of partial differential equations to analyze the effect of resource allocation in an ecosystem with resource having its own dynamics in space and time. We show a priori estimates to prove the existence of state solutions given a control. We formulate an optimal control problem of our ecosystem model such that the abundance of a single species is maximized while minimizing the cost of inflow resource allocation. In addition, we show the existence and uniqueness of the optimal control as well as the optimal control characterization. We also establish the existence of an optimal intermediate diffusion rate. Moreover, we illustrate several numerical simulations with Dirichlet and Neumann boundary conditions with the space domain in 1D and 2D. [ABSTRACT FROM AUTHOR]

We investigate 2-dimensional viscoelastic equations with a view of Lie groups. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. Reductions of similarities related to subalgebras are classified. In the end by using Bluman-Anco homotopy formula, we find local conservation laws of the viscoelastic equation. [ABSTRACT FROM AUTHOR]

This paper advances a new application of q-homotopy analysis method (q-HAM) to solve non-linear optimal control problems(NOCPs). First, the NOCP was transformed into a non-linear two-point boundary value problem by using the Pontryagins maximum principle (PMP). Then, we applied the q-HAM to solve this system. The proposed method is based on the HAM but the q-HAM, has an increased interval of convergence than the HAM. Three examples are provided to demonstrate the reliability and efficiency of the method. Next, the numerical results of the proposed method are compared with those of other methods. As can be seen from the tables, the maximum error in the second and third examples is much better than other methods. [ABSTRACT FROM AUTHOR]

We consider the optimal operating policies of a free-to-play multiplayer game with a premium subscription to maximize its lifetime operating profit. Accounting for social comparisons between free and premium players, we model the game attracting or losing players with a hybrid of the Bass diffusion model and the replicator equation in evolutionary game theory. Leveraging optimal control theory, we characterize optimal dynamic pricing and advertising policies and show that the developer should prioritize initial growth through aggressive advertising, while postponing the introduction of a premium subscription. Surprisingly, the optimal subscription price may start high and gradually decrease. We further show that the developer should strengthen social-comparison effects, that payment-based matchmaking can be an effective monetization driver, and that our main findings remain robust when allowing individual in-game item purchases/partial premium subscription. These findings are potentially instructive for game developers adopting the premium subscription model. This paper was accepted by Víctor Martínez-de-Albéniz, operations management. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.4510. [ABSTRACT FROM AUTHOR]

Most of the systems in our lives are inherently nonlinear and unstable. In control problems in the field of engineering, the aim is to define the control laws that maximize the operating efficiency of these systems under diverse security coefficients, and constraints and minimize error rates. This study aimed to model and optimally control a Double-Inverted Pendulum System on a Cart (DIPSC). A DIPSC was modeled using the Lagrange-Euler method, and classical and optimal Linear Quadratic Regulator (LQR) control methods were designed for the control of the system. The purpose of the designed controllers is to keep the arms of the double inverted pendulum on the moving cart vertically in balance and to bring the cart to the determined balance position. The critically important Q and R parameters of the LQR control technique that is one of the optimal control techniques were obtained using the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Grey Wolf Optimization (GWO) algorithms. The DIPSC system was checked using classical LQR and optimal LQR methods. All obtained results are given graphically. The proposed methods are presented and analyzed in tabular form using Settling time and Mean-Square-Error (MSE) performance criteria. [ABSTRACT FROM AUTHOR]

Some classical optimal control problems of linear systems can be characterized as finding minimum‐norm vectors from within linear varieties in appropriate dual spaces. Then, the solution to such an optimal control problem can be derived from the alignment between the optimal vector in the dual space and the optimal vector in the primal space, and the dual maximization problem of the minimum‐norm problem. This note presents a detailed introduction to this minimum‐norm in dual space approach by examples of minimum‐supremum‐norm, minimum‐energy, and minimum‐time optimal control problems of linear systems. Connections and differences between these problems in light of the introduced approach are discussed. These notes elaborate on how to characterize and solve minimum‐supremum‐norm, minimum‐energy, and minimum‐time optimal control problems of linear systems as appropriate minimum‐norm problems in dual spaces. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Beijing University of Civil Engineering & Architecture is the property of Journal of Beijing University of Civil Engineering & Architecture Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Infectious diseases drive countries to provide vaccines to individuals. Due to the limited supply of vaccines, individuals prioritize receiving vaccinations worldwide. Although, priority groups are formed based on age groupings due to the restricted decision-making time. Governments usually ordain different health protocols such as lockdown policy, mandatory use of face masks, and vaccination during the pandemics. Therefore, this study considers the case of COVID-19 with a SEQIR (susceptible–exposed–quarantined–infected–recovered) epidemic model and presents a novel prioritization technique to minimize the social and economic impacts of the lockdown policy. We use retail units as one of the affected parts to demonstrate how a vaccination plan may be more effective if individuals such as retailers were prioritized and age groups. In addition, we estimate the total required vaccine doses to control the epidemic disease and compute the number of vaccine doses supplied by various suppliers. The vaccine doses are determined using optimal control theory in the solution technique. In addition, we consider the effect of the mask using policy in the number of vaccine doses allocated to each priority group. The model's performance is evaluated using an illustrative scenario based on a real case. [ABSTRACT FROM AUTHOR]

Ultracold polar molecules have been considered as the possible candidates for quantum information processing due to their long coherence time and strong dipole-dipole interaction. In this paper, we consider three coupled polar molecules arranged in a linear chain and trapped in an electric field with gradient. By employing the pendular states of polar molecules as qubits, we successfully realize three-qubit quantum gates and quantum algorithms via the multi-target optimal control theory. Explicitly speaking, through the designs of the optimal laser pulses with multiple iterations, the triqubit Toffoli gate, the triqubit quantum adders, and the triqubit quantum Fourier transform can be achieved in only one operational step with high fidelities and large transition probabilities. Moreover, by combining the optimized Hadamard, oracle, and diffusion gate pulses, we simulate the Grover algorithm in the three-dipole system and show that the algorithm can perform well for search problems. In addition, the behaviors of the fidelity and the average transition probability with respect to iteration numbers are compared and analyzed for each gate pulse. Our findings could pave the way toward scalability for molecular quantum computing based on the pendular states and could be extended to implement multi-particle gate operation in the molecular system. [ABSTRACT FROM AUTHOR]

This document, titled "Optimal control - analysis, algorithms and applications," explores the significance of optimal control in systems and control research. It highlights key breakthroughs in the field, such as Dynamic Programming and the Maximum Principle, and emphasizes the importance of optimal control in various applications. The document includes articles that cover a range of topics, including trajectory planning for heterogeneous systems, distributed model predictive control, energy-optimal control of adaptive structures, and robust stability of moving horizon estimation. These articles provide insights into the methods and applications of optimal control, showcasing its relevance and potential for further research. [Extracted from the article]

In this work, we generalize the quantum optimal control theory (QOCT) of molecules subject to ultrashort laser pulses to the case of solvated systems, explicitly including the solvent dielectric properties in the system's quantum Hamiltonian. A reliable description of the solvent polarization is accounted for within the polarizable continuum model (PCM). The electron dynamics for the molecules in solution is coupled with the dynamics of the surrounding polarizable environment, which affects the features of the optimized laser pulse. To illustrate such effects, numerical applications of the developed method to the study of optimal population of selected excited states of two molecular solvated systems are presented and discussed. [ABSTRACT FROM AUTHOR]

We perform quantum optimal control simulations, based on the Time-Dependent Hartree (TDH) approximation, for systems of three to five dipole-dipole coupled OCS rotors. A control electric field is used to steer all of the individual rotors, arranged in chains and regular polygons in a plane, toward either identical or unique objectives. The goal is to explore the utility of the TDH approximation to model the field-induced dynamics of multiple interacting rotors in the weak dipole-dipole coupling regime. A stochastic hill climbing approach is employed to seek an optimal control field that achieves the desired objectives at a specified target time. We first show that multiple rotors in chain and polygon geometries can be identically oriented in the same direction; these cases do not significantly depend on the presence of the dipole-dipole interaction. Additionally, in particular geometrical arrangements, we demonstrate that individual rotors can be uniquely manipulated toward different objectives with the same field. Specifically, it is shown that for a three rotor chain, the two end rotors can be identically oriented in a specific direction while keeping the middle rotor in its ground state, and for an equilateral triangle, two rotors can be identically oriented in a specific direction while the third rotor is oriented in the opposite direction. These multirotor unique objective cases exploit the shape of the field in coordination with dipole-dipole coupling between the rotors. Comparisons to numerically exact calculations, utilizing the TDH-determined fields, are given for all optimal control studies involving systems of three rotors. [ABSTRACT FROM AUTHOR]

With today's worldwide competition, manufacturing companies are faced with challenges to respond to volatile market demands quickly and flexibly while maintaining a cost-effective level of production. Capacity adjustment is one of the major approaches to cope with such uncertain fluctuations, balance capacity and load and improve the effectiveness of manufacturing control. Instead of flexible staffs, working time and outsourcing, in this paper, we consider a machinery-based capacity adjustment via Reconfigurable Machine Tools (RMTs) to compensate for unpredictable events. To include these tools effectively on the operational and tactical layer, we propose a complementing feedback approach using model predictive control (MPC) to identify the potential of RMTs for a better compliance with logistics objectives and a sustainable demand oriented capacity allocation. To this end, we formulate a reconfiguration rule for the determination of the triggered RMTs and propose three strategies for resolving the integer assignment of RMTs: floor operator, genetic algorithm as well as branch and bound. Utilising simulation, we demonstrate the effectiveness of the proposed method for a four-workstation job-shop system. [ABSTRACT FROM AUTHOR]

Agility is a key characteristic in disaster relief operations. Intelligent process-aware information systems (IPAISs) can support agility in disaster relief operations through providing information and process reach and richness to manage dynamic inter-operations. In this research, based on relevant reference architectures, a conceptual overview of an IPAIS to support agility in disaster relief operations is described. This conceptual overview includes the dynamic partnering, the collaborative process composition, the collaborative ontology management, the global workflow engine, the run-time coordination, the dynamic rule management, the run-time process proposer, and the dynamic interoperability adaptor components. Based on this conceptual overview, a systematic literature review is conducted to explore emerging approaches that can be applied to realise intelligent process-centred collaborative inter-operations to respond disasters. The findings of the conducted review show the applicability of the emerging multi-agent service-oriented modelling and analysis approaches, optimal control theory based methodologies, social network analysis techniques, data-driven inductive methods, resilient-centred approaches for robustness and agility, self-organisation mechanisms based on cyber physical systems and systems of systems perspectives, simulation methods, and trust management procedures to support the realisation of the components of an IPAIS in the context of disaster relief operations. [ABSTRACT FROM AUTHOR]

Sulfuric acid decomposition is the critical reaction in sulfur-iodide thermochemical cycle to produce oxygen. Sulfuric acid can decompose spontaneously into sulfur trioxide (SO3) and water, and SO3 continues to decompose into oxygen and sulfur dioxide. The application of membrane reactor can effectively improve the conversion rate of SO3 and thermal efficiency of sulfur-iodide cycle. The decomposition of SO3 requires the absorption of a large amount of heat due to its highly endothermic properties, and there are many irreversible processes such as heat transfer, mass transfer, chemical reaction and friction flow in the SO3 membrane reactor. Therefore, it is necessary to conduct thermodynamic analysis and optimization of the decomposition process to reduce the irreversible loss of the membrane reactor system. In this paper, a finite time thermodynamic model of SO3 decomposition membrane reactor is established, and the kinetic parameters of decomposition reaction are deduced and calculated based on experimental data. Firstly, the membrane reactor heated by hot helium gas is solved and used as reference reactor. Secondly, optimal control theory is used to optimize the reference reactor under fixed reactant inlet conditions and outlet conversion rate with total entropy generation rate minimization as optimization objective. The total entropy generation rate of Opt-1 reactor is reduced by 32.7% compared with the reference value. For variable reactor length, the total entropy generation rate of Opt-2 reactor is quadratic optimum at L=0.72m, which is 34.7% less than the reference value. It is found that the reduction of total entropy generation rate in optimal reactors is mainly achieved by minimizing the entropy generation rate in heat transfer process. The distribution of local entropy generation rate is relatively uniform in the middle position, approximately consistent with the principle of equalization of entropy production rate. The conclusions obtained herein can provide guidelines for the energy-saving design of SO3 decomposition membrane reactors.

Applying optimal control theory and finite time thermodynamics, a practical Otto cycle heat engine with friction, pressure drop and heat transfer losses is studied. The maximum ecological function is taken as optimization objective, and the optimal piston motion configuration of the Otto cycle is obtained with the Newton’s heat transfer law between the working fluid and the environment. The fuel consumption and the total cycle time are fixed in the optimization. The optimal piston motion laws corresponding to the maximum ecological function configuration when the piston motion accelerations are unconstrained and constrained are obtained, respectively. By numerical examples, the piston motion optimal configurations under different optimization objectives and heat transfer laws are compared.

In this paper, a compartment model is formulated to study the transmission dynamics of avian influenza virus among birds, poultry and human population. Due to the strong coupling of the system caused by the transmission route, there are some mathematical challenges to obtain the existence of the endemic equilibrium and its global asymptotic stability. Firstly, we give the well-posedness of the model and then discuss the threshold dynamics for three sub-models. Next, we give the threshold dynamics for the whole system: the disease-free equilibrium is locally asymptotically stable with R0 < 1, and the other conditions are required for the global asymptotic stability of the disease-free equilibrium. The endemic-equilibrium is globally attractive when R0 > 1. Furthermore, the sensitivity analysis and an optimal control problem are discussed. Finally, some numerical simulations are carried out to illustrate our theoretical results and visualize the impact of various parameters on model dynamics, which suggest that decreasing the recruitment rate and increasing the death rate of poultry, can only control the disease by simultaneously cutting off the transmission from birds to poultry and humans even if the ultimate scale of the disease can be effectively controlled. In addition, enhancing public awareness of prevention to reduce the transmission from birds and poultry to humans is also effective in controlling the final scale of disease. [ABSTRACT FROM AUTHOR]

The effeteness of control intervention against monkeypox infection is threatened after the emergence of new outbreaks in many endemic and non-endemic countries. The objective of the present study is to develop a new mathematical model examining the dynamics, future prediction, and effective control intervention of this emerging disease in Nigeria. The model is parameterized using the recent monkeypox outbreak from the start (end of February 2022) to January 07, 2023, in Nigeria. The model best fit to the actual cases is presented using a standard nonlinear least square minimizing residual method and the basic reproduction number is evaluated. Further, we present future scenario of the disease using simulation of our model and dynamics of the disease through various controlling measures are analyzed based on the real data set. In this study, we also conducted mathematical analysis of the model and used a normalized sensitivity analysis to identify the most critical parameters in the system. Moreover, an optimal control problem is developed using four time-dependent control interventions. Detailed simulations of constant controls, with and without time-dependent optimal controls are shown. It is concluded that to eradicate the infection the necessary control strategies are strict personal protection coupled with effective vaccination policy should be implemented. The findings of the present study provide valuable insights for health officials to implement effective and optimal control measures to curb the outbreak.

In this study, methods for automatically controlling load transportation by a swivel crane with high speed and suppressed swing motion of suspended load at the target position are proposed. First, highly versatile trajectories for each of swivel and straight transport of load are proposed on the basis of a linearized and simplified analytical model and the optimal control theory. The proposed method has the versatility that it can be applied even with different swivel radii and swivel angles. The effectiveness and limitations of the proposed methods are shown with computer simulations and experiments with a laboratory model. Next, we propose a new method that expands the proposed method and uses the measurement data of the swing information of the load. It is shown that by using this method, even if the load swings at the start of transport, it is possible to suppress the swing of the load at the target point of transport.

In the present study, we optimize the spatio-temporal distribution of an artificial body force for reducing skin friction drag in a fully developed turbulent channel flow at a low frictional Reynolds number of 110. Specifically, by applying the optimal control theory, the optimal body force distributions for minimizing the kinetic energy at the end of a prescribed time horizon are obtained for fifty independent uncontrolled initial fields. Two different time horizons of T+ = 10.9 and 109 are considered. A comparison of the optimal control inputs for the two time horizons reveals that the optimal control input for T+ = 10.9 is smoother and applied so as to oppose the local velocity fluctuation, while the optimal control input for T+ = 109 is more intermittent and localized around low-speed streaks. The optimal body forces become maximal around y+ = 20, where near-wall turbulent structures are dominant. Using the obtained dataset of the instantaneous velocity fields and the corresponding optimal control inputs, we train a machine learning model which learns the relationship between them. It is demonstrated that the present machine learning model predicts quite well the optimal control input for the short time horizon of T+ = 10.9, while the prediction performance tends to deteriorate when the time horizon increases to T+ = 109. Nonetheless, the essential intermittent and localized features of the optimal control input are well predicted even for the longer time horizon by the present machine learning model. The present results suggest that the developed machine learning model could be used to establish an on-line feedback controller without conducting expensive forward and adjoint looping for determining the control input. Furthermore, it is also shown that employing a non-linear activation function significantly improves the prediction accuracy. This indicates that the relationship between the instantaneous flow field and the optimal control input is essentially non-linear.

The emergency collision avoidance and trajectory planning are investigated in this paper. These are considered to be essential technologies for self-driving cars, which are important in regional revitalization. The collision avoidance by braking is called AEB (Autonomous Emergency Braking), whereas collision avoidance by steering is called AES (Autonomous Emergency Steering). The present research focuses on AES and aims to develop effective control theory based on EOC (Energy Optimal Control theory) with trajectory planning. A theoretical design method for EOC's virtual physical quantities and a method for accurately specifying the target trajectory were proposed. An emergency collision avoidance problem was designed to avoid collisions with vehicles crossing the center line and bicycles encroaching on the roadway on a two-lane road, and the effectiveness of proposed control theory and trajectory planning method are examined. It is found that the present theory can track the specified target trajectory very accurately. And the trajectory planning method proposed here is very simple and can define discontinuous trajectory which is critical for the design of complicated collision avoidance trajectory.

In this manuscript, we have studied the dynamical behavior of a deadly COVID‐19 pandemic which has caused frustration in the human community. For this study, a new deterministic SEIHR fractional model is developed for the first time. The purpose is to perform a complete mathematical analysis and the design of an optimal control strategy for the proposed Caputo–Fabrizio fractional model. We have proved the existence and uniqueness of solutions by employing principle of mathematical induction. The positivity and the boundedness of solutions is proved using comprehensive mathematical techniques. Two main equilibrium points of the pandemic model are stated. The basic reproduction number for the model is computed using next generation technique to handle the future dynamics of the pandemic. We develop an optimal control problem to find the best controls for the quarantine and hospitalization strategies employed on exposed and infected humans, respectively. For numerical solution of the fractional model, we implemented the Adams–Bashforth method to prove the importance of order. A general fractional‐order optimal control problem and associated optimality conditions of Pontryagin type are discussed, with the goal to minimize the number of exposed and infected humans. The extremals are obtained numerically. [ABSTRACT FROM AUTHOR]

An online policy learning algorithm is used to solve the optimal control problem of the power battery state of charge (SOC) observer for the first time. The design of adaptive neural network (NN) optimal control is studied for the nonlinear power battery system based on a second-order (RC) equivalent circuit model. First, the unknown uncertainties of the system are approximated by NN, and a time-varying gain nonlinear state observer is designed to address the problem that the resistance capacitance voltage and SOC of the battery cannot be measured. Then, to realize the optimal control, a policy learning-based online algorithm is designed, where only the critic NN is required and the actor NN widely used in most design of the optimal control methods is removed. Finally, the effectiveness of the optimal control theory is verified by simulation. [ABSTRACT FROM AUTHOR]

Background: The continuous emergence of novel SARS-CoV-2 variants with markedly increased transmissibility presents major challenges to the zero-COVID policy in China. It is critical to adjust aspects of the policy about non-pharmaceutical interventions (NPIs) by searching for and implementing more effective ways. We use a mathematical model to mimic the epidemic pattern of the Omicron variant in Shanghai to quantitatively show the control challenges and investigate the feasibility of different control patterns in avoiding other epidemic waves. Methods: We initially construct a dynamic model with a core step-by-step release strategy to reveal its role in controlling the spread of COVID-19, including the city-based pattern and the district-based pattern. We used the least squares method and real reported case data to fit the model for Shanghai and its 16 districts, respectively. Optimal control theory was utilized to explore the quantitative and optimal solutions of the time-varying control strength (i.e., contact rate) to suppress the highly transmissible SARS-CoV-2 variants. Results: The necessary period for reaching the zero-COVID goal can be nearly 4 months, and the final epidemic size was 629,625 (95%CI: [608,049, 651,201]). By adopting the city-based pattern, 7 out of 16 strategies released the NPIs more or earlier than the baseline and ensured a zero-resurgence risk at the average cost of 10 to 129 more cases in June. By adopting the district-based pattern, a regional linked release can allow resumption of social activity to ~ 100% in the boundary-region group about 14 days earlier and allow people to flow between different districts without causing infection resurgence. Optimal solutions of the contact rate were obtained with various testing intensities, and higher diagnosis rate correlated with higher optimal contact rate while the number of daily reported cases remained almost unchanged. Conclusions: Shanghai could have been bolder and more flexible in unleashing social activity than they did. The boundary-region group should be relaxed earlier and more attention should be paid to the centre-region group. With a more intensive testing strategy, people could return to normal life as much as possible but still ensure the epidemic was maintained at a relatively low level. [ABSTRACT FROM AUTHOR]

We combined an inverse engineering technique based on Lagrange mechanics and optimal control theory to design an optimal trajectory that can transport a cartpole in a fast and stable way. For classical control, we used the relative displacement between the ball and the trolley as the controller to study the anharmonic effect of the cartpole. Under this constraint, we used the time minimization principle in optimal control theory to find the optimal trajectory, and the solution of time minimization is the bang-bang form, which ensures that the pendulum is in a vertical upward position at the initial and the final moments and oscillates in a small angle range. [ABSTRACT FROM AUTHOR]

There is a narrow but hidden link between optimal control theory and the so-called Tikhonov regularization method. In fact, the small coefficient representing the marginal cost of the control can be interpreted as the regularization parameter in a Tikhonov method as far as there exists an exact control. This strategy enables one to adjust the cost function in the optimal control model in order to define the exact control which minimizes a given functional involving both the control but also the state variables during the control process. The goal of this paper is to suggest a method which gives a simple way to characterize and compute the exact control corresponding to the minimum of a given cost functional as said above. It appears as an extension of the phase control which is a finite dimensional version of the HUM control of J.L. Lions but for partial differential equations. [ABSTRACT FROM AUTHOR]

This paper deals with a three-dimensional nonlinear mathematical model to analyze an epidemic's future course when the public healthcare facilities, specifically the number of hospital beds, are limited. The feasibility and stability of the obtained equilibria are analyzed, and the basic reproduction number ( R 0 ) is obtained. We show that the system exhibits transcritical bifurcation. To show the existence of Bogdanov–Takens bifurcation, we have derived the normal form. We have also discussed a generalized Hopf (or Bautin) bifurcation at which the first Lyapunov coefficient evanescences. To show the existence of saddle-node bifurcation, we used Sotomayor's theorem. Furthermore, we have identified an optimal layout of hospital beds in order to control the disease with minimum possible expenditure. An optimal control setting is studied analytically using optimal control theory, and numerical simulations of the optimal regimen are presented as well. [ABSTRACT FROM AUTHOR]

The self-organizing map (SOM), which is a type of artificial neural network (ANN), was formulated as an optimal control problem. Its objective function is to minimize the mean quantization error, and the state equation is the weight updating equation of SOM. Based on the objective function and the state equations, the Hamiltonian equation based on Pontryagin's minimum principle (PMP) was formed. This study presents two models of SOM formulated as an optimal control problem. In the first model, called SOMOC1, the design is based on the state equation representing the weight updating equation of the best matching units of the SOM nodes in each iteration, whereas in the second model, called SOMOC2, it considers the weight updating equation of all the nodes in the SOM as the state updating equation. The learning rate is treated as the control variable. Based on the solution of the switching function, a bang-bang control was applied with a high and low learning rate. The proposed SOMOC2 model performs better than the SOMOC1 model and conventional SOM as it considers all the nodes in the Hamiltonian equation, and the switching function obtained from it is influenced by all the states, which provides one costate variable for each. The costate determines the marginal cost of violating the constraint by the state equations, and the switching function is influenced by this, hence producing a greater improvement in terms of the mean quantization error at the final iteration. It was found that the solution leads to an infinite order singular arc. The possible solutions for the suitable learning rates during the singular arc period are discussed in this study. [ABSTRACT FROM AUTHOR]

The use of optimal control theory for motion planning is a challenging task. Cell mapping offers a way to formulate combinatorial optimization problems, allowing the inclusion of complex cost functions as well as multi-objective optimization problems. This paper presents a suboptimal solution for a trajectory planning problem in a workspace with obstacles, for a differential drive mobile robot. This method relies on the use of any linearization technique that allows the regularization of the combinatorial optimization problem. We explore some classical problems in optimal control, i.e., distance, control effort, and navigation time), as well as the multi-objective optimization problem (MOP). We also performed a comparison with two classical path planning algorithms, namely A ∗ and R R T ∗ , to validate the proposed method when the multi-objective optimization problem includes distance in the cost function, achieving a compromise of less than 2 % for the worst-case scenario for our case study. [ABSTRACT FROM AUTHOR]

In this paper, we proposed an ordinary differential equation model for the transmission of Hepatitis B virus (BHV). The model accounted for the susceptible, exposed, infected, Chronic, and removed classes. We obtained the model's disease-free and endemic equilibrium points and the effective reproductive number. Further, from a thorough sensitivity analysis of the effective reproductive number, we extended the model by incorporating five time-dependent controls to cater to the vertical transmission, vaccination, testing, and treatment of acutely and chronically infected individuals. Numerical simulation was conducted to underscore the effects of the control in combating HBV. [ABSTRACT FROM AUTHOR]

In this paper the problem of atmospheric disturbances during the UAV carrier landing operation is considered. A UAV dynamics model, and a wind gust and airwake disturbance model are introduced. A LADRC-based cascade control scheme is developed for fixed-wing UAVs. In the control scheme, three ADRC controllers are designed for attitude control, and another two ADRC controllers are designed for course and altitude tracking. Finally, a series of simulations are implemented in Simulink and the results are presented to demonstrate the performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]

A hierarchical model of a vector Nash equilibrium search under uncertainty is developed. The sufficient conditions for a vector Nash equilibrium of a noncooperative game under uncertainty are formulated, which can be used as a criterion to achieve the required degree of nonquilibrium for an acceptable solution to the problem of multi-object multicriteria systems' control optimization under conflict and uncertainty. [ABSTRACT FROM AUTHOR]

In the process of controlling an unmanned vehicle, it is practically important that under conditions of rapidly changing dynamic constraints, control laws be developed that would be optimal with respect to a given quality functional or a multicriteria functional. When static and dynamic constraints do not allow the optimal movement to be chosen to a given quality functional, the authors consider the transition to another quality functional using the predictive integral path model and the method of active simultaneous localization and mapping. In this case, the strategy for choosing the state space is more efficient than the strategy for choosing the control space. The practical question is how to achieve this. The paper presents a method and experiments using an unmanned vehicle platform at a test site in the form of a complex environment, showing the feasibility of the method. [ABSTRACT FROM AUTHOR]

This report considers optimization of aircraft maneuvers in the vertical plane based on direct control methods. It proposes an object model for longitudinal motion suitable for optimal control, algorithms for control approximation and a numerical solution to the problem via a population-based optimization algorithm. The suggested method proves its applicability by forming the control signals for basic aircraft maneuvers in the vertical plane, including climb, speed increment, descent and speed decrement. [ABSTRACT FROM AUTHOR]

The use of reinforcement learning technology for the optimal control problem solution is considered. To solve the optimal control problem an evolutionary algorithm is used that finds control to ensure the movements of a control object along different trajectories with approximately the same values of the quality criterion. Additional conditions for passing the trajectory in the neighbourhood of given areas of the state space are included in the quality criterion. To build a stabilization system for the movement of an object along a given trajectory, machine learning control by symbolic regression is used. An example of solving the optimal control problem for a quadcopter is given. [ABSTRACT FROM AUTHOR]

This paper proposes an original approach to improving the efficiency of technological processes based on collaborative robots, which differs from the existing ones by the possibility of intensifying the process of modeling the human factor when forming a control law. A structural and functional diagram of the model of a standard cobot control system in the basic industrial configuration is presented. The shortcomings of a standard solution for the formation of laws for controlling the movement of a cobot in a nondeterministic environment in the same workspace with a person are demonstrated. Structural and functional solutions are proposed to outline a strategy for increasing the degree of synergistic effect of human–machine interaction. The effect can be achieved through the introduction of an extended system of sensors and analytics and an intelligent module robot trajectory movement formation and optimization under disturbing influences. The results of the comparison between the standard control system of the cobot and the prototype of the intelligent system are presented. As an example, the operation of the implementation of collision avoidance that occurs due to the appearance of a stationary object in the working area is given. The results obtained demonstrate a significant time- and energy-saving effect (from 15% to 182% depending on the operation) in the case of using an intelligent control system. A feature of the proposed approach is to strengthen the integration links of intelligent analysis and optimization modules, which allow real-time multimodal processing of sensory data and environmental modeling to predict human actions and form cobot reactions. [ABSTRACT FROM AUTHOR]

The extended optimal control problem is considered. It is necessary to find an optimal control function, that not only provides the achievement of terminal state with optimal value of the given quality criterion, but also is implemented in the control system of a real object. It means, that the control function should depend on the state space vector, and the optimal solution should keep optimality property at small perturbations of the found solution. To solve this problem machine learning control by symbolic regression is used. In the extended optimal control problem, the problem statement of stabilization system synthesis for movement along the optimal trajectory is included. Synthesis problem is solved by the network operator method. In the synthesis problem a domain of initial conditions is considered instead of one point of initial state. It provides less sensitivity of found solution to perturbations of initial states. An example of solving the extended optimal control problem with complex phase constraints in the form of bottleneck for four quadcopters is presented. [ABSTRACT FROM AUTHOR]

Autonomous navigation is one of the key tasks in the development of control systems for real autonomous mobile objects. This paper presents the developed technology for accurately determining the position of a mobile robot in an autonomous operating mode without an external positioning system. The approach involves using a high-precision model of a real robot identified by a neural network. The robot adjusts its position, determined using odometry and video camera, according to the position of the robot, obtained using an accurate model. To train the neural network, a training set is used that takes into account the features of the movement of a wheeled robot, including wheel slip. In the experimental part, the problem of autonomous movement of a mobile robot along a given trajectory is considered. [ABSTRACT FROM AUTHOR]

This paper considers the difficulties that arise in the implementation of solutions to the optimal control problem. When implemented in real systems, as a rule, the object is subject to some perturbations, and the control obtained as a function of time as a result of solving the optimal control problem does not take into account these factors, which leads to a significant change in the trajectory and deviation of the object from the terminal goal. This paper proposes to supplement the formulation of the optimal control problem. Additional requirements are introduced for the optimal trajectory. The fulfillment of these requirements ensures that the trajectory remains close to the optimal one under perturbations and reaches the vicinity of the terminal state. To solve the problem, it is proposed to use numerical methods of machine learning based on symbolic regression. A computational experiment is presented in which the solutions of the optimal control problem in the classical formulation and with the introduced additional requirement are compared. [ABSTRACT FROM AUTHOR]

This paper considers the problem of controlling a mobile robot in the presence of circular obstacles. To solve this problem, it is proposed to use the previously suggested principle of dividing permissible trajectories into a sequence of rectilinear sections and arcs of circles that are the boundaries of circular obstacles. The conditions for the solution based on this principle of optimality are obtained. [ABSTRACT FROM AUTHOR]

The purpose of the study is to substantiate the methodological decision-making tools for the formation of a rational management structure of the dynamic capabilities of the company's personnel potential. It has been scientifically substantiated and proven that the formation of a rational management structure for the dynamic capabilities of the company's personnel potential is based on the development of a dynamic model of their assessment. The model is presented taking into account the integration of the dynamic capabilities of the enterprise, its personnel and processes business environment’s transformation. The research uses the methods of system analysis and logical generalizations, the statistical concept of dynamic capabilities, the methods of the theory of active systems, the theory of hierarchical games, financial mathematics, and the theory of optimal control of continuous and discrete systems. Updated directions of the managing formation process of a rational structure of the company's personnel potential. The proposed model for assessing the dynamic capabilities of the company's personnel potential allows for optimizing the utility function of personnel resources. Optimizing the usefulness of human resources takes place on the basis of determining the level of their dynamic capabilities to integrate, create and change the configuration of internal and external competencies to achieve sustainable competitiveness of the enterprise. The model for assessing the dynamic capabilities of the company's personnel resources determines the competencies of personnel, business systems and strategies for its development. The use of the proposed model to determine the dynamic capabilities of the enterprise regarding the reconfiguration of available human resources allows us to focus on the relevant behavioural aspects of enterprise managers and limitations, taking into account the exchange between the internal and external environment. [ABSTRACT FROM AUTHOR]