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In this paper, we investigate dynamical analysis and optimal control for human immunodeficiency virus (HIV) transmission model with age-structure. Local asymptotic stability of disease-free equilibrium is proved by applying operator theory and spectral boundary principle. And the existence of endemic equilibrium is obtained by using fixed-point theorem and monotone iterative procedure. Optimal control of an age-structure HIV model is conducted by using prevention and control education and anti-HIV treatment as control strategies. Taking a suitable objective function is to prove existences of optimal control variables which are characterized by sensitivity system and adjoint system associated with optimal state system. Finally, numerical simulations with appropriate parameters are conducted to show that comprehensive publicity and education on prevention and control for susceptible individuals and prompt treatment of HIV-infected individuals can be better to reduce HIV impact. [ABSTRACT FROM AUTHOR]

Intelligent underwater vehicles hover by way of a hovering control system. To provide design inputs and maneuver guidance, this study focused on the characteristics of intelligent underwater vehicles during hovering control with the propulsion system shut down, established a mathematical model of hovering control and determined injection and drainage functions based on optimal control theory. From analysis simulation experiments, the influence laws of control parameters, control timing and rate of injection and drainage control upon hovering control were deduced. It is proposed that, at the time of control parameter selection, the continuous injection and drainage rate at each time should be reduced as far as possible to relieve the demand on the volume of the reservoir when the requirement of depth control accuracy has been satisfied. In addition, the injection and drainage control should initiate when depth changes exceed 0.5 m. Suggestions are included on the minimum injection and drainage rate required for different initial disturbances. The proposed suggestions guide the design of hovering control systems and hovering control over intelligent underwater vehicles. [ABSTRACT FROM AUTHOR]

A new method is developed for accurately approximating the solution to state‐variable inequality path constrained optimal control problems using a multiple‐domain adaptive Legendre–Gauss–Radau collocation method. The method consists of the following parts. First, a structure detection method is developed to estimate switch times in the activation and deactivation of state‐variable inequality path constraints. Second, using the detected structure, the domain is partitioned into multiple‐domains where each domain corresponds to either a constrained or an unconstrained segment. Furthermore, additional decision variables are introduced in the multiple‐domain formulation, where these additional decision variables represent the switch times of the detected active state‐variable inequality path constraints. Within a constrained domain, the path constraint is differentiated with respect to the independent variable until the control appears explicitly, and this derivative is set to zero along the constrained arc while all preceding derivatives are set to zero at the start of the constrained arc. The time derivatives of the active state‐variable inequality path constraints are computed using automatic differentiation and the properties of the chain rule. The method is demonstrated on two problems, the first being a benchmark optimal control problem which has a known analytical solution and the second being a challenging problem from the field of aerospace engineering in which there is no known analytical solution. When compared against previously developed adaptive Legendre–Gauss–Radau methods, the results show that the method developed in this paper is capable of computing accurate solutions to problems whose solution contain active state‐variable inequality path constraints. [ABSTRACT FROM AUTHOR]

This paper concerns an optimal dividend problem for an insurance company whose uncontrolled surplus process evolves as a piecewise deterministic compound Poisson risk process (in the absence of dividend payments). With each dividend payment, there is a proportional and a fixed cost. The objective is to maximize the sum of the expected cumulative discounted dividend payments received until the time of ruin and a penalty payment at the time of ruin. We first introduce the characteristics of the Markov controls in the optimal dividend problem and the dividend strategy is an additive functional of the controlled surplus process. Under a certain assumption, we get that the dynamic programming equation (DPE) is measure-valued, and the optimal dividend strategy is a Markov control. A verification theorem is proved in the class of all admissible strategies. Furthermore, we give a short discussion on the optimal dividend problem for general distributed claim amounts, and the optimal dividend strategy has a band structure. Finally, an example with a gamma distribution for the claim amount is analyzed, in terms of a particular Gerber-Shiu function. [ABSTRACT FROM AUTHOR]

This paper addresses the stochastic linear quadratic (LQ) control problem with first‐ and second‐order moment constraints on the terminal state. The problem is a modified version of the optimal covariance control problem, where the terminal state is steered to a given probability distribution. Studying a multiplicative‐noise stochastic system rather than an additive‐noise system is a salient feature. Unlike the existing ideas in the optimal steering, by using the Lagrange multipliers method and establishing the stochastic maximum principle, our problem is converted into solving forward–backward stochastic difference equations (FBSDEs), which is a special stochastic two‐point boundary‐value problem (TPBVP). We provide the optimal closed‐loop controller and necessary and sufficient solvability conditions by developing a nonhomogeneous relationship between the optimal state and costate in FBSDEs. Finally, numerical examples are given to demonstrate our results. [ABSTRACT FROM AUTHOR]

This research article presents a mathematical model that tracks and monitors the spread of COVID-19 strains in a discrete time frame. The study incorporates two control strategies to reduce the transmission of these strains: vaccination and providing appropriate treatment and medication for each strain separately. Optimal controls were established using Pontryagin's maximum principle in discrete time, and the optimality system was solved using an iterative method. To validate the effectiveness of the theoretical findings, numerical simulations were conducted to demonstrate the impact of the implemented strategies in limiting the spread of COVID-19 mutant strains. [ABSTRACT FROM AUTHOR]

This paper introduces a paradigm shift in atomic force microscope (AFM) scan control, leveraging an artificial intelligence (AI)-based controller. In contrast to conventional control methods, which either show a limited performance, such as proportional integral differential (PID) control, or which purely focus on mathematical optimality as classical optimal control approaches, our proposed AI approach redefines the objective of control for achieving practical optimality. This presented AI controller minimizes the root-mean-square control deviations in routine scans by a factor of about 4 compared to PID control in the presented setup and also showcases a distinctive asymmetric response in complex situations, prioritizing the safety of the AFM tip and sample instead of the lowest possible control deviations. The development and testing of the AI control concept are performed on simulated AFM scans, demonstrating its huge potential. Highlights: Artificial intelligence-based asymmetric controller for the highest tip and sample safety with AFM scans. Potential to significantly outperform proportional integral derivative control in classical scan situations. Dynamic change between classically optimal and asymmetric behavior depending on the scan situation. [ABSTRACT FROM AUTHOR]

Interpolation of probability distributions can be formulated as an optimal transport problem. Positive matrix, which can be viewed as the generalization of probability distribution to higher dimension, is used in quantum theory to describe the state of a quantum system. Here, a quantum‐inspired method for the interpolation of positive matrices is proposed. Particularly, this method employs the quantum state purification of the positive matrices in an extended space. Since pure state controllability can be easily achieved using open‐loop coherent control, the continuous interpolation of positive matrices is given as a completely positive map induced by simulating the optimal control for pure state transfer. The quantum‐inspired interpolation is shape‐preserving with applications to tensor field processing. [ABSTRACT FROM AUTHOR]

Summary: In this work, a novel and model‐based artificial neural network (ANN) training method is developed supported by optimal control theory. The method augments training labels in order to robustly guarantee training loss convergence and improve training convergence rate. Dynamic label augmentation is proposed within the framework of gradient descent training where the convergence of training loss is controlled. First, we capture the training behavior with the help of empirical Neural Tangent Kernels (NTK) and borrow tools from systems and control theory to analyze both the local and global training dynamics (e.g., stability, reachability). Second, we propose to dynamically alter the gradient descent training mechanism via fictitious labels as control inputs and an optimal state feedback policy. In this way, we enforce locally ℋ2$$ {\mathscr{H}}_2 $$ optimal and convergent training behavior. The novel algorithm, Controlled Descent Training (CDT), guarantees local convergence. CDT unleashes new potentials in the analysis, interpretation, and design of ANN architectures. The applicability of the method is demonstrated on standard regression and classification problems. [ABSTRACT FROM AUTHOR]

In oil reservoir setting, an alternative for conventional wells are the smart wells having inflow control valves (ICVs). In this work, optimal control theory is implemented to investigate the performance of smart wells alongside conventional wells on an oil reservoir with permeability uncertainty and model mismatch. The performance of this scenario was compared using the Net Present Value (NPV) and Injection rates of the injector wells as perfromance indicators. The results obtained showed a better performance with smart wells irrespective of uncertainty and mismatch in the reservoir. An NPV of $4193430 was recorded for the smart well case as against its corresponding counterpart having an NPV of $3901415. Whereas for the faulted reservoir, an NPV of $314946 was obtained which is an 11% gain against the conventional well setting. This study shows that even though the rationale behind the implementation of conventional wells stems from their simple drilling process, they possess inherent limitation of sub-optimal reservoir-well contact depleting their productivity. Conversely, smart wells were shown to be better due to their enhanced monitoring and control capabilities making them suitable for reservoirs with uncertainties. [ABSTRACT FROM AUTHOR]

The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples. [ABSTRACT FROM AUTHOR]

The overall motion performance of mechatronic machines depends heavily on proper knowledge of the machine's characteristics, among which the inertia. Moreover, the inertia of most multi-body mechanisms, for example, reciprocating slider-crank mechanisms, varies as a function of the machine position, thereby challenging optimal control. Nevertheless, the inertia's variation is sometimes not known accurately enough or changes over time due to, e.g. a production process or premature wear, forcing an online control/correction of the inertia profile. Therefore, earlier, the author developed a new computational-friendly online method based on a frequency-specific magnitude response to estimate the machine's position-dependent load side inertia, assuming good knowledge of all other machine properties. Yet, to guarantee accuracy, the maximum machine speed during estimation had to be strongly reduced, resulting in an undesirable longer motion time. Therefore, in this work, the failure mechanism of the earlier proposed estimator is analysed and overcome by intelligently separating estimation and motion signals. As a result, the estimator is no longer limited by the machine's motion speed but rather by a maximum in the inertia variation per signal excitation period and, thus, time. Moreover, given this limiting variation, a guideline was established to evaluate the new method's estimation quality. Finally, both in simulation and on a physical machine, by taking advantage of the newly proposed method, the minimal required estimation time is reduced significantly (up to 50% on the machine) without diminishing the estimation accuracy. [ABSTRACT FROM AUTHOR]

We study the approximate optimal control for a class of fractional stochastic hemivariational inequalities with non-instantaneous impulses driven by Rosenblatt process in a Hilbert space. Firstly, a suitable definition of piecewise continuous mild solution is introduced, and by using stochastic analysis, properties of α -order sine and cosine family and Picard type approximate sequences, we show the existence and uniqueness of approximate mild solutions for the inequality problems of fractional order (1, 2] under the non-Lipschitz conditions. Secondly, we provide the existence conditions of approximate solutions to optimal control problems driven by the presented control systems with the help of a new minimizing sequence method. Finally, an example is provided to illustrate the theory. [ABSTRACT FROM AUTHOR]

In this paper, we study the modern mathematical theory of the optimal control problem associated with the fractional Roesser model and described by Caputo partial derivatives, where the functional is given by the Riemann-Liouville fractional integral. In the formulated problem, a new version of the increment method is applied, which uses the concept of an adjoint integral equation. Using the Banach fixed point principle, we prove the existence and uniqueness of a solution to the adjoint problem. Then the necessary and sufficient optimality condition is derived in the form of the Pontryagin's maximum principle. Finally, the result obtained is illustrated by a concrete example. [ABSTRACT FROM AUTHOR]

This study aims to explore an intelligent vehicle trajectory tracking control method based on optimal control theory. Considering the limitations of existing control strategies in dealing with signal delays and communication lags, a control strategy combining an anthropomorphic forward-looking reference path and longitudinal velocity closure is proposed to improve the accuracy and stability of intelligent vehicle trajectory tracking. Firstly, according to the vehicle dynamic error tracking model, a linear quadratic regulator (LQR) transverse controller is designed based on the optimal control principle, and a feedforward control strategy is added to reduce the system steady-state error. Secondly, an anthropomorphic look-ahead prediction model is established to mimic human driving behavior to compensate for the signal lag. The double proportional–integral–derivative (DPID) control algorithm is used to track the longitudinal speed reference value. Finally, a joint simulation is conducted based on MatLab/Simulink2021b and CarSim2019.0 software, and the effectiveness of the control strategy proposed in this paper is verified by constructing a semi-physical experimental platform and carrying out a hardware-in-the-loop test. The simulation and test results show that the control strategy can significantly improve the accuracy and stability of vehicle path tracking, which provides a new idea for future intelligent vehicle control system design. [ABSTRACT FROM AUTHOR]

In this article, we propose a mathematical approach that connects an innovative spatio-temporal model to the problem of the EG.5 variant of COVID-19 in a human population. We demonstrate the existence and uniqueness of the global positive solution for our suggested system. The implementation and analysis of an applicable optimal control issue are as follows. The methods of optimal control theory are applied in this work to demonstrate the existence of optimal control, and with necessary optimality conditions, we discover the explicit expression of optimal control that minimizes the negative impacts of this infectious disease on countries. We provide numerical simulations at the conclusion to demonstrate the efficacy of our chosen strategy. [ABSTRACT FROM AUTHOR]

This work presents the multiharmonic analysis and derivation of functional type a posteriori estimates of a distributed eddy current optimal control problem and its state equation in a time-periodic setting. The existence and uniqueness of the solution of a weak space-time variational formulation for the optimality system and the forward problem are proved by deriving inf-sup and sup-sup conditions. Using the inf-sup and sup-sup conditions, we derive guaranteed, sharp and fully computable bounds of the approximation error for the optimal control problem and the forward problem in the functional type a posteriori estimation framework. We present here the first computational results on the derived estimates. [ABSTRACT FROM AUTHOR]

An auxiliary optimal control problem is formulated that provides with its unique solution, a continuous representation of the global error of a numerical approximation to the solution of a linear quadratic optimal control problem. The resulting error functions are characterized as the unique solutions to an optimality system that is reformulated as a boundary value problem. With this formulation, reliable pointwise error estimates can be generated utilizing well-established techniques of defect control. A novel algorithm based on defect correction and defect control is presented that generates pointwise approximations to the global error of numerical optimal control solutions on a uniform grid. It is proven and numerically validated that this algorithm can generate pointwise estimates that approximate the true global error with a prescribed accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes a new highly effective method for determining the optimal control of the stress-strain state of spatially multi-connected composite bodies using a stationary temperature field. The proposed method is considered based on the example of a stationary axisymmetric thermoelastic problem for a space with a spherical inclusion and cavity. The proposed method is based on the generalized Fourier method and reduces the original problem to an equivalent problem of optimal control, in which the state of the object is determined by an infinite system of linear algebraic equations, the right-hand side of which parametrically depends on the control. At the same time, the functional of the cost of the initial problem is transformed into a quadratic functional, which depends on the state of the equivalent system and parametrically on the control. The limitation on the temperature distribution is replaced by the value of the control norm in the space of square summable sequenc es. In fact, this paper considers for the first time the problem of optimal control of an infinite system of linear algebraic equations and develops a method for its solution. The proposed method is based on presenting the solutions of infinite systems in a parametric form, which makes it possible to reduce equivalent problem to the problem of conditional extremum of a quadratic functional, which explicitly depends on the control. A further solution to this problem A further solution to this problem is found by the Lagrange method using the spectral decomposition of the quadratic functional matrix. found by the Lagrange method using the spectral decomposition of the quadratic functional matrix. The method developed in this paper is strictly justified. For all infinite systems, the Fredholm property of their operators is proved. As an important result necessary for substantiation, for the first time, an estimate from below of the module of the multi-parameter determinant of the resolving system of the boundary value problem of conjugation – space with a spherical inclusion – was obtained when solving it using the Fourier method. The theorem that establishes the conditions for the existence and uniqueness of the solution of equivalent problem or optimal control problem without restrictions in the space of square summable sequences is proved. The numerical algorithm is based on a reduction method for infinite systems of linear algebraic equations. Estimates of the practical accuracy of the numerical algorithm demo nstrated the stability of the method and sufficiently high accuracy even with close location of the boundary surfaces. Graphs showing the optimal temperature distribution for various geometric parameters of the problem and their analysis are provided. The proposed method extends to boundary value problems with different geometries. [ABSTRACT FROM AUTHOR]

The article investigates a networked optimal control problem with one remote controller and N$$ N $$ local controllers, where each local controller partially observes the local state and sends the observed information to remote controller through an unreliable channel and yet the channels from remote controller to local controllers are perfect. The objective of all the controllers is to cooperate to minimize a common cost function. In order to overcome the difficulties caused by partial observation of state, sufficient statistic of historical data is firstly investigated for a nonlinear non‐Gaussian partial observation model, which takes the same role as that of state in the full observation model. Then, a dynamic programming framework is given for solving the optimal control problem based on the sufficient statistic and common information approach. Furthermore, the explicit closed‐form solution is obtained for a linear‐quadratic‐Gaussian optimal control problem. Finally, a numerical example is given to show the effectiveness of the obtained results of this article. [ABSTRACT FROM AUTHOR]

In this paper, we consider a new approach to optimization of nonlinear control systems based on the representation of optimality conditions and improvement of the control in the form of special fixed-point problems for control operators. We propose algorithms for approximate solution of optimal control problems based on iterative methods for finding fixed points. The effectiveness of the optimization methods proposed is illustrated by model and test problems. [ABSTRACT FROM AUTHOR]

In this paper, we examine the optimal control problem for a hyperbolic system with differential constraints on the boundary, taking into account the delay. Controls are selected from the class of smooth functions that satisfy pointwise constraints. Problems of this type arise, in particular, in modeling the processes of population dynamics. The approach proposed in this paper is based on the use of "internal variations" of the control, which preserves the smoothness of the control function and ensures the fulfillment of pointwise constraints. We obtain an estimate of the state increment, prove a necessary optimality condition, and develop a scheme of an iterative method. [ABSTRACT FROM AUTHOR]

The new stochastic and deterministic hepatitis B epidemic models are established. The models consist of four types: susceptible individuals, acutely infected hepatitis B individuals, chronically infected hepatitis B individuals and recovered individuals. This study focuses on the transmission dynamics of acute and chronic hepatitis B epidemics problems and the development of optimal control strategies to control the transmission of hepatitis B in the population. To this end, we first calculate the equilibrium point and basic reproduction number of the deterministic hepatitis B model to study the stability of the above model at the equilibrium point. Secondly, we give the basic reproduction number of the stochastic model of hepatitis B virus. A suitable Lyapunov function is constructed, and the solvability of the stochastic model is confirmed using the Itô formula. By using a series of stochastic inequalities and strong number theorems, the extinction and stationary distribution of hepatitis B in this stochastic model are obtained. Finally, the optimal control theory is used to develop an optimal control strategy for eliminating hepatitis B virus transmission. The Runge–Kutta method is used to simulate the above models to verify the rationality of our main theoretical results. [ABSTRACT FROM AUTHOR]

In the modern world, where efficiency, stability, and precision play a crucial role, the development and application of optimal control strategies in oscillatory systems hold significant importance. The issues related to the numerical solution of control problems associated with damping oscillatory systems consisting of two objects are considered. To numerically solve the discussed problem, the gradient projection method, based on the formula for the first variation of the functional, and the method of successive approximations, associated with the linearity of boundary problems describing oscillatory processes, are applied. The oscillations of one object are described by a wave equation with first-order boundary conditions, while a second-order ordinary differential equation models the oscillations of the other object. Furthermore, the original and the adjoint boundary value problems are solved using direct methods at each iteration step. An algorithm for the numerical solution of the problem is proposed, and based on this algorithm, a software code for implementation is developed. The numerical results obtained in the study demonstrate that there is convergence in terms of functionality, and the approximately optimal controls found in this process are minimizing sequences in the control space. The mechanism of controlling and regulating the operation of the system according to its input constraints is provided by observed feedback, allowing systems with limited excitation to maintain stability and optimal functioning in conditions of changing external or internal circumstances. The obtained results can also be used to forecast the system's behavior in the future, resource planning, prevention of emergencies, or optimization of production processes. [ABSTRACT FROM AUTHOR]

In the dynamic realm of Unmanned Aerial Vehicles (UAVs), and, more specifically, Quadrotor drones, this study heralds a ground-breaking integrated optimal control methodology that synergizes a distributed framework, predictive control, H-infinity control techniques, and the incorporation of a Kalman filter for enhanced noise reduction. This cutting-edge strategy is ingeniously formulated to bolster the precision of Quadrotor trajectory tracking and provide a robust countermeasure to disturbances. Our comprehensive engineering of the optimal control system places a premium on the accuracy of orbital navigation while steadfastly ensuring UAV stability and diminishing error margins. The integration of the Kalman filter is pivotal in refining the noise filtration process, thereby significantly enhancing the UAV's performance under uncertain conditions. A meticulous examination has disclosed that, within miniature Quadrotors, intrinsic forces are trivial when set against the formidable influence of control signals, thus allowing for a streamlined system dynamic by judiciously minimizing non-holonomic behaviors without degrading system performance. The proposed control schema, accentuated by the Kalman filter's presence, excels in dynamic efficiency and is ingeniously crafted to rectify any in-flight model discrepancies. Through exhaustive Matlab/Simulink simulations, our findings validate the exceptional efficiency and dependability of the advanced controller. This study advances Quadrotor UAV technology by leaps and bounds, signaling a pivotal evolution for applications that demand high-precision orbital tracking and enhanced noise mitigation through sophisticated nonlinear control mechanisms. [ABSTRACT FROM AUTHOR]

In photovoltaic power plants, wind farms, and other types of renewable energy generating facilities, the usage of multilevel inverters (MLIs) is a popular and widely used choice. A unique structurally-based step-up self-balanced compact multigain switched capacitor inverter architecture (MGSCIT) is proposed in this study. The proposed MGSCIT uses two switched capacitors and nine switches to generate a seven-level (7L) output voltage with a voltage gain of three times the input. The suggested topology also includes several other important advantages, such as the minimum number of switching components, three-times voltage gain, inherent self-balancing of capacitor voltage, reduced voltage ripples, reduced voltage, and stresses. The negative voltage levels can be generated without the need for a backend H-bridge (HB). The structural design analysis of the proposed MGSCIT, self-balancing mechanism of capacitor voltages, determination of optimum values of capacitance, and control strategy are explained in detail. To demonstrate the benefits of the proposed topology, a fair comparison is offered with the most current 7-level single-source topologies, focusing on the cost function and the number of components per level. Finally, simulation results demonstrate the accuracy of the theoretical analysis, and the prototype built demonstrates the feasibility and effectiveness of the practical findings, with maximum measured efficiency reaching 95.62%. The voltage and current THD are 31.08% and 1.45%, respectively. [ABSTRACT FROM AUTHOR]

The hybrid minimum principle (HMP) is established for the optimal control of deterministic hybrid systems with both autonomous and controlled switchings and jumps where state jumps at the switching instants are permitted to be accompanied by changes in the dimension of the state space and where the dynamics, the running and switching costs as well as the switching manifolds and the jump maps are permitted to be time varying. First-order variational analysis is performed via the needle variation methodology and the necessary optimality conditions are established in the form of the HMP. A feature of special interest in this work is the explicit presentations of boundary conditions on the Hamiltonians and the adjoint processes before and after switchings and jumps. Analytic and numerical examples are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

The abort mission refers to the mission where the landing vehicle needs to terminate the landing mission when an anomaly happens and be safely guided to the desired orbit. This paper focuses on solving the time-optimal abort guidance (TOAG) problem in real-time via the feature-based learning method. First, according to the optimal control theory, the features are identified to represent the optimal solutions of TOAG using a few parameters. After that, a sufficiently large data set of time-optimal abort trajectories is generated offline by solving the TOAG problems with different initial conditions. Then, the features are extracted for all generated cases. To find the implicit relationships between the initial conditions and identified features, neural networks are constructed to map the relationships based on the generated data set. Finally, experimental flight tests are conducted to demonstrate the onboard computation capability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Controlling machine degradation enhances the accuracy of the remaining-useful-life estimation and offers the ability to control failure type and time. In order to achieve optimal degradation control, the system controller must be cognizant of the consequences of its actions by considering the degradation each action imposes on the system. This article presents a method for designing cost-aware controllers for linear systems, to increase system reliability and availability through degradation control. The proposed framework enables learning independent of the system's physical structure and working conditions, enabling controllers to choose actions that reduce system degradation while increasing system lifetime. To this end, the cost of each controller's action is calculated based on its effect on the state of health. A mathematical structure is proposed, to incorporate these costs into the cost function of the linear–quadratic controller, allowing for optimal feedback for degradation control. A simulation validates the proposed method, demonstrating that the optimal-control method based on the proposed cost function outperforms the linear–quadratic regulator in several ways. [ABSTRACT FROM AUTHOR]

In the present article, we derive optimal spatially varying control fields, which maximize the four-wave mixing efficiency in a four-subband semiconductor asymmetric double quantum well, following analogous works in atomic systems. The control fields coherently prepare the medium, where a weak probe pulse is propagated and eventually converted to a signal pulse at the output. The optimal fields, which maximize the conversion efficiency for a given propagation length, are obtained by applying optimal control theory to a simplified form of propagation equations but are tested with numerical simulations using the full set of Maxwell–Schrödinger equations, which accurately describe the propagation of light pulses in the medium. For short propagation distances, the proposed optimal scheme outperforms a simpler spatially changing control protocol that we recently studied, while for larger distances, the efficiency of both protocols approaches unity. The present work is expected to find application in frequency conversion between light beams, conversion between light beams carrying orbital angular momentum, and nonlinear optical amplification. [ABSTRACT FROM AUTHOR]

This work focuses on an exploration of the pointwise Jacobson-type necessary conditions for optimal control problems governed by differential systems with impulse at fixed times; the pointwise Jacobson-type necessary optimality conditions refer to a type of pointwise second-order necessary optimality conditions for optimal singular control in the classical sense. By introducing an impulsive linear matrix Riccati differential equation, we derive the integral representation of the functional second-order variational. Based on this, the integral form of the second-order necessary conditions and the pointwise Jacobson-type necessary conditions are obtained. Incidentally, we have established the Legendre-Clebsch condition and the pointwise Legendre-Clebsch condition. Finally, an example is provided to illustrate the effectiveness of the main result. [ABSTRACT FROM AUTHOR]

The Wigner quasi-density function allows a phase-space formulation of statistical quantum mechanics that is of fundamental importance in theoretical investigation and in applications. This work contributes to these tasks with the formulation and analysis of an optimal control problem for the Wigner equation, which describes the time evolution of the quasi-density function. For this purpose, two possible control mechanisms are considered, and, correspondingly, a detailed analysis in weighted Sobolev spaces for the controlled nonhomogeneous Wigner equation is presented. Further theoretical results are reported concerning existence of optimal controls and differentiability of the control-to-state map and of the ensemble cost functional, which allows the derivation of the optimality system that characterizes the optimal controls sought. [ABSTRACT FROM AUTHOR]

We investigate the identification problem for the one-phase Stefan problem. As the inverse Stefan problem is not well posed, an optimal control problem is considered instead. In the paper we develop a dual dynamic programming approach to derive sufficient approximate optimality conditions for that optimal control problem. As a next step we formulate and prove a verification theorem for approximate solution. The verification Theorem 4.1 is the basis for the development of a numerical algorithm. Having the verification theorem we do not need the convergence of our algorithm. [ABSTRACT FROM AUTHOR]

We consider an optimal control problem in the Mayer form with an autonomous control system, a bounded control set U, endpoint equality constraints, and one pointwise state inequality constraint. We analyze the case when the starting point of the optimal trajectory belongs to the state boundary. A nontrivial maximum principle was obtained for this case by A.Ya. Dubovitskii and V.A. Dubovitskii about 40 years ago, but the proof was written in an extremely condensed form. Here we offer a new proof of their result. [ABSTRACT FROM AUTHOR]

In this paper, infinite horizon optimal control problems subject to semilinear parabolic equations are investigated. A finite number of only time-dependent controls intervening at disjoint positions in the space domain are considered. The controls are subject to integral constraints and a term is included in the cost functional that promotes control sparsity. The existence of optimal controls is proven, first and second order optimality conditions are derived, and the approximation by finite horizon control problems is addressed. [ABSTRACT FROM AUTHOR]

In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional is considered. An explicit formula for the value functional is given, which includes a solution of a certain Fredholm integral equation. A step-by-step feedback control procedure for constructing $ \varepsilon $-optimal controls with any accuracy $ \varepsilon > 0 $ is proposed. The basis for obtaining these results is the study of a solution of the associated Hamilton–Jacobi–Bellman equation with so-called fractional coinvariant derivatives. [ABSTRACT FROM AUTHOR]

A co-infection model for onchocerciasis and Lassa fever (OLF) with periodic variational vectors and optimal control is studied and analyzed to assess the impact of controls against incidence infections. The model is qualitatively examined in order to evaluate its asymptotic behavior in relation to the equilibria. Employing a Lyapunov function, we demonstrated that the disease-free equilibrium (DFE) is globally asymptotically stable; that is, the related basic reproduction number is less than unity. When it is bigger than one, we use a suitable nonlinear Lyapunov function to demonstrate the existence of a globally asymptotically stable endemic equilibrium (EE). Furthermore, the necessary conditions for the presence of optimum control and the optimality system for the co-infection model are established using Pontryagin's maximum principle. The model is quantitatively analyzed by studying how sensitive the basic reproduction number is to the model parameters and the model simulation using Runge–Kutta technique of order 4 is also presented to study the effects of the treatments. We deduced from the quantitative analysis that, if there is an effective treatment and diagnosis of those exposed to and infected with the disease, the spread of the viral disease can be effectively managed. The results presented in this work will be useful for the proper mitigation of the disease. [ABSTRACT FROM AUTHOR]

This study investigates the automated transportation control problem of an offshore floating platform that has limited or no maneuverability. The proposed solution involves two tugboats pushing into the platform and two other tugs towing it in the opposite direction. By implementing cooperative control of these tugs, the desired planar motion of the platform is achieved. For this, the proposed control consists of the following components: (1) an observer estimates the environmental disturbances, (2) a platform motion controller acts as the supervisory control, (3) an optimal constrained allocation distributes the required actions over the tugboats, and (4) the tugboats' controller derived the control inputs of the tugs to fulfill these requirements. Simulation studies are conducted where the proposed solution is compared to one based on the robust H∞ control framework. The results prove the efficiency and robustness of the proposed system. [ABSTRACT FROM AUTHOR]

The global population has suffered extensively as an effect of the coronavirus infection, with the loss of many lives, adverse financial consequences, and increased impoverishment. In this paper, we propose an example of the non-linear mathematical modeling of the COVID-19 phenomenon. Using the fixed point theorem, we established the solution's existence and unicity. We demonstrate how, under the framework, the basic reproduction number can be redefined. The different equilibria of the model are identified, and their stability analyses are carefully examined. According to our argument, it is illustrated that there is a single optimal control that can be used to reduce the expense of the illness load and applied processes. The determination of optimal strategies is examined with the aid of Pontryagin's maximum principle. To support the analytical results, we perform comprehensive digital simulations using the Runge-Kutta 4th-order. The data simulated suggest that the effects of the recommended controls significantly impact the incidence of the disease, in contrast to the absence of control cases. Further, we calculate the incremental cost-effectiveness ratio to assess the cost and benefits of each potential combination of the two control measures. The findings indicate that public attention, personal hygiene practices, and isolating oneself will all contribute to slowing the spread of COVID-19. Furthermore, those who are infected can readily decrease their virus to become virtually non-detectable with treatment consent. [ABSTRACT FROM AUTHOR]

In this article, a fractional-order epidemic model for cholera is proposed and analyzed. Two transmission routes for cholera are considered to develop the compartmental epidemic model. The basic biological properties of the solutions of the fractional-order model are investigated. The global asymptotic stability of the equilibrium points have been established using appropriate Lyapunov functional. Moreover, a fractional-order control problem is presented, and its analytical solution is derived using Pontryagin’s maximum principle. Also, some graphical visualizations of the theoretical results are provided. It is found that the factional-order derivative only affect the time to reach the stationary states. Sensitivity analysis reveals that by reducing the rates of new recruitment and both the disease transmission rates, it may be possible to reduce the value of the basic reproduction number. [ABSTRACT FROM AUTHOR]

The next generation of low observable (LO) unmanned combat aerial vehicle (UCAV) with highly autonomy to implement a penetration mission requires advanced methods for flyable and safe route planning (i.e., respecting physical capability of vehicle and threat coverage by hostile air defense radars) at a real‐time manner. Currently, the main challenge of real‐time route planning for LO UCAV is to achieve computationally efficiency under dynamic (pop‐up/moving) threats by air defense radars. In this paper, a real‐time planning paradigm in compliance with complex penetration requirements is proposed, and a complete modeling of route planning for LO UCAV's penetration as an optimal control problem is designed. The paper at first devises a direct method to transform the optimal control problem into a nonlinear programming (NLP) problem and then solves the formulated NLP problem under a moving planning horizon. The proposed method can give computationally efficient route planning results for LO UCAV's penetration under multiple kinds of radar threats. Numerical test results based on F‐16 uninhabited platform demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: A Robust H2$$ {H}_2 $$ Nonlinear Fuzzy Decentralized Controller (H2$$ {H}_2 $$ RNFDC) is proposed to improve the overall robustness and tracking ability of a VSC‐HVDC link. The studied system is considered as composed by two overlapping nonlinear subsystems. The nonlinear interaction between the two subsystems is treated as a disturbance rejection problem by fuzzy control techniques. First, the Takagi Sugeno (TS) fuzzy model is adopted for fuzzy modeling of the uncertain nonlinear system. Next, new stability conditions for a generalized class of uncertain HVDC systems are derived from robust control techniques based on Linear Matrix Inequalities (LMIs). The design method employs the so‐called Parallel Distributed Compensation (PDC) to obtain H2$$ {H}_2 $$ RNFDC gains based on LMIs.The efficiency and robustness of the proposed controllers are analytically proven and tested through validation simulations. The main contributions of this paper are: (i) resilience: in case of failure of one converter or loss of measures or controls, the control of the other converter is not affected; (ii) robustness is improved in order to provide good responses in case of network variations and HVDC line parameters changes; (iii) fuzzy techniques are adopted to handle nonlinearities and changes of operating conditions. The proposed H2$$ {H}_2 $$ RNFDC is compared with Fuzzy H 2$$ {}_2 $$ Decentralized State Feedback Control (H2$$ {H}_2 $$ NFDC) and H∞$$ {H}_{\infty } $$ Linear Decentralized Control (H∞$$ {H}_{\infty } $$ LDC) in simulation to illustrate the control synthesis and its effectiveness. [ABSTRACT FROM AUTHOR]

This paper considers a mathematical model analysing the deterioration of system equipment and available maintenance options. Under specific conditions on costs and transition probabilities of the model, the issue of ideal maintenance of the equipment by assuming that preventive maintenance, condition-based maintenance, and the replacement times of the equipment follow known continuous probability distributions is explored. A semi-Markov decision process formulation is provided for this model and computational analysis is possible by applying well-known Markov decision algorithms. A linear programming approach is also presented with appropriate constraints established for the equipment's maintenance and repair times. Various numerical results are also presented for the validation of the model. The motivation for this paper is to develop a realistic framework for determining decisions about the type of maintenance, possible replacement, or the continuation of operation of deteriorating equipment. The above decisions are taken within a framework of time constraints for equipment maintenance and replacement. Such limitations in the implementation of these actions are very crucial for all maintenance management systems. The purpose of this paper is to make the described model a useful tool for maintenance managers who plan and implement optimal maintenance policies within an environment of variable time constraints. [ABSTRACT FROM AUTHOR]

We establish Pontryagin optimality conditions for a generalized bilevel optimal control problem in which the leader is subject to a pure state inequality constraint, while the follower is governed by a non-convex quasi-variational inequality parameterized by the final state. To simplify the problem at hand, we convert it into a single-level optimal control problem by mapping the solution set of the quasi-variational inequality to a parametric optimization problem and employing the value function reformulation. Furthermore, we introduce certain regularity conditions to ensure that the derived maximum principle remains non-degenerate. Finally, we provide an illustrative example to elucidate our research findings. [ABSTRACT FROM AUTHOR]

In this paper, the differential game model is constructed to study the coordination problem of platform supply chain by introducing the impacts of Big Data marketing and reference promotion effect on consumer conversion rate. Firstly, the optimal strategies and the profits under centralized and decentralized modes are given by applying the optimal control theory, and the comparative analyses are carried out. Subsequently, in order to coordinate the platform supply chain, a combined contract including a two-part tariff scheme and a promotion cost sharing scheme is designed. Finally, the effects of system parameters on equilibrium strategies and coordination contract are analyzed. The results show that the respective decisions of the manufacturer and the e-commerce platform as well as the total profit of the supply chain are higher under centralized mode. Moreover, within the feasible region, the combined contract not only achieves channel coordination but also improves the economic situations of channel members. It can be also observed that the coordination capacity of the proposed contract reduces with an increase in the memory parameter and improves with an increase in parameters such as the effectiveness of the Big Data marketing and the effectiveness of the reference promotion effect. [ABSTRACT FROM AUTHOR]

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In this paper, the finite horizon asymmetric information linear quadratic (LQ) control problem is investigated for a discrete-time mean field system. Different from previous works, multiple controllers with different information sets are involved in the mean field system dynamics. The coupling of different controllers makes it quite difficult in finding the optimal control strategy. Fortunately, by applying the Pontryagin's maximum principle, the corresponding decentralized control problem of the finite horizon is investigated. The contributions of this paper can be concluded as follows: For the first time, based on the solution of a group of mean-field forward and backward stochastic difference equations (MF-FBSDEs), the necessary and sufficient solvability conditions are derived for the asymmetric information LQ control for the mean field system with multiple controllers. Furthermore, by the use of an innovative orthogonal decomposition approach, the optimal decentralized control strategy is derived, which is based on the solution to a non-symmetric Riccati-type equation. [ABSTRACT FROM AUTHOR]

This paper provides a novel safe reinforcement learning (RL) control algorithm to solve safe optimal problems for fully cooperative (FC) games of discrete-time multiplayer nonlinear systems with state and input constraints. The FC game is a special case of nonzero-sum (NZS) games, where all players cooperate to accomplish a common task. The algorithm is proposed based on the policy iteration (PI) framework utilizing only the measured data along the system trajectories in the environment. Different from most works about PI, an effective method of obtaining initial safe and stable control policies is given here. In addition, control barrier functions (CBFs) and an input constraint function are introduced to augment reward functions. And the monotonically nonincreasing property of the iterative value function in the PI algorithm maintains the safe set forward invariant. Then, the neural networks are employed to approximate the system dynamics, the iterative control policies, and the iterative value function, respectively. Furthermore, the proposed algorithm is supported by theoretical proofs that guarantee both safety and convergence. Finally, the effectiveness and safety of the algorithm are illustrated by the results of the simulation. [ABSTRACT FROM AUTHOR]

The small, simple, and effective characteristics of a Supercritical CO2 (S–CO2) power system make it an ideal candidate for distributed power generation. However, the distributed power generation will be required with constant changes in the operating conditions to meet the varying demand. Thus, it is necessary for the S–CO2 power system to demonstrate that it can operate safely and efficiently under all anticipated operating conditions. One of the key issues in the S–CO2 power system is controlling the compressor inlet conditions. This paper focused on the control of the compressor inlet temperature. In this paper, a system dynamic simulation code is used to model the precooler system for the compressor inlet control first. Based on the analysis results to obtain the transfer function and the state space, a linear quadratic controller was designed using optimal control theory. Since the controller was estimated to have steady-state error, a disturbance observer was also used. To validate the designed controller, experiments were conducted. The experimental results show that the proposed controller can be used to maintain the S–CO2 compressor inlet conditions under various transient scenarios without additional tuning.

This study presents a novel approach to controlling cocoa black pod disease, caused by Phytophthora megakarya. Unlike previous methods, we employ a mathematical modeling framework based on Pontryagin’s Maximum Principle to optimize control strategies that minimize disease impact. The model incorporates the dynamics of healthy and infected pods while considering the combined effects of three key interventions: Infected pod removal, Targeted fungicide application and Promoting a healthy growing environment. Through numerical simulations, we identify the optimal timing and intensity for each intervention to minimize infected pods over time. This study highlights the following novelties: Synergistic effect of combined control which demonstrates that combining all three strategies is significantly more effective than relying on individual methods, Optimal strategies which involves dynamically adjusting control measures throughout the growing season to adapt to disease progression, Prompt action after disease detection proves crucial for successful control. These findings offer valuable data-driven recommendations for cocoa farmers and disease management professionals. By strategically implementing a combination of infected pod removal, targeted fungicide use, and environmental management, farmers can significantly reduce disease severity, enhance cocoa production, and promote a more sustainable cocoa industry.