Conditions For Optimal Control Research Articles

Analysis of the influence of temperature error on the procedure for measuring the geometric parameters of vehicles using laser meters

The purpose of the research was to study the effect of temperature error and temperature conditions on the measurement of the linear dimensions of vehicles, as well as to identify the optimal control conditions that ensure the reduction of errors in measuring the geometric parameters of vehicles. The goal was achieved by solving an urgent problem related to the use of laser-containing equipment, as well as determining the requirements and recommendations for the conditions for measuring the geometric parameters of vehicles. Keywords road transport, geometric parameters, environment, temperature, measurement accuracy

A modified optimal control for the mathematical model of dengue virus with vaccination

<abstract> <p>The dengue viruses (of which there are four strains) are the causes of three illnesses of increasing severity; dengue fever (DF), dengue hemorrhagic fever (DHF) and dengue shock syndrome (DSS). Recently, dengue fever has reached epidemic proportion in several countries. Strategies or preventative methods have to be developed to combat these epidemics. This can be done by development of vaccines or by preventing the transmission of the virus. The latter approach could involve the use of mosquito nets or insecticide spraying. To determine which strategy would work, we test the strategy using mathematical modeling to simulate the effects of the strategy on the dynamics of the transmission. We have chosen the Susceptible-Exposed-Infected-Recovered (SEIR) model and the SusceptibleExposed-Infected (SEI) model to describe the human and mosquito populations, repectively. We use the Pontryagin's maximum principle to find the optimal control conditions. A sensitivity analysis revealed that the transmission rate $ ({\gamma }_{h}, {\gamma }_{v}) $, the birth rate of human population ($ {\mu }_{h} $), the constant recruitment rate of the vector population ($ A $) and the total human population ($ {N}_{h} $) are the most influential factors affecting the disease transmission. Numerical simulations show that the optimal controlled infective responses, when implemented, cause the convergence to zero to be faster than that in uncontrolled cases.</p> </abstract>

A mathematical model and optimal control analysis for scholar Drop out

In this paper, we proposed and analyzed a non-linear mathematical model for scholar Drop out and we advanced an optimal control policy for this model by considering three variables namely the numbers of school-age children who are in school, school-age children who are out of school, and school-age children in non-formal education. The model is examined using the stability theory of differential equations. The optimal control analysis for the proposed scholar Drop out model is performed using Pontryagin's maximum principle. The conditions for optimal control of the problem with effective use of implemented policies to counter this scourge are derived and analyzed.

Optimal Control Problems for Hilfer Fractional Neutral Stochastic Evolution Hemivariational Inequalities

In this paper, we concentrate on a control system with a non-local condition that is governed by a Hilfer fractional neutral stochastic evolution hemivariational inequality (HFNSEHVI). By using concepts of the generalized Clarke sub-differential and a fixed point theorem for multivalued maps, we first demonstrate adequate requirements for the existence of mild solutions to the concerned control system. Then, using limited Lagrange optimal systems, we demonstrate the existence of optimal state-control pairs that are regulated by an HFNSEHVI with a non-local condition. In order to demonstrate the existence of fixed points, the symmetric structure of the spaces and operators that we create is essential. Without considering the uniqueness of the control system’s solutions, the best control results are established. Lastly, an illustration is used to demonstrate the major result.

Second-order necessary conditions in optimal control of evolution systems

Second-order necessary conditions in optimal control of evolution systems

Ergodic risk-sensitive control for regime-switching diffusions

In this article, we study the ergodic risk-sensitive control problem for controlled regime-switching diffusions. Under a blanket stability hypothesis, we solve the associated nonlinear eigenvalue problem for weakly coupled systems and characterize the optimal stationary Markov controls via a suitable verification theorem. We also consider the near-monotone case and obtain the existence of principal eigenfunction and optimal stationary Markov controls.

Using a Reduced Order Robust Control Approach to Damp Subsynchronous Resonance in Power Systems

his work focuses on the use of the Linear Quadratic Gaussian (LQG) technique to construct a reliable Static VAr Compensator (SVC), Thyristor Controlled Series Compensator (TCSC), and Excitation System controller for damping Subsynchronous Resonance ( SSR ) in a power system. There is only one quantifiable feedback signal used by the controller (generator speed deviation). It is also possible to purchase this controller in a reduced-order form. The findings of the robust control are contrasted with those of the “idealistic” full state optimal control. The LQG damping controller’s regulator robustness is then strengthened by the application of Loop Transfer Recovery (LTR). Nonlinear power system simulation is used to confirm the resilience of the planned controller and demonstrates how well the regulator dampens power system oscillations. The approach dampens all torsional oscillatory modes quickly while maintaining appropriate control actions, according to simulation results.

Generating Nesterov’s accelerated gradient algorithm by using optimal control theory for optimization

Nesterov’s accelerated gradient algorithm is derived from first principles. The first principles are founded on the recently-developed optimal control theory for optimization. This theory frames a generic optimization problem as an optimal control problem. The necessary conditions for optimal control produce a controllable dynamical system. Stabilizing this system by dissipating a simple, quadratic “control” Lyapunov function generates an equation that produces Nesterov’s algorithm. In this context, the proposed theory solves the long-standing mystery surrounding the algorithm.

Determination of Optimal Line-Heating Conditions for Flatness Control of Wind Tower Blocks Using Strain as Direct Boundary Method.

The wind tower block is welded with the flange to assemble the wind tower. The inherent strain due to local heating and cooling of the weld affects the flatness of the flange. Therefore, line heating is performed to satisfy the design criteria of the flange flatness, but the work variables depend on the operator's empirical judgment. This study proposed a method to determine the optimum linear heating conditions to control the welded flatness of wind tower blocks and flanges. A proposed method uses the inherent strain method, a simple analysis method, and the optimization is performed based on the deformation superposition method. The changes in flange flatness due to welding and single-point heating were calculated. Then, the flatness change due to single-point heating is superimposed with a scale factor, which represents the magnitude of line heating, and is added to the flatness change due to welding. Using the optimization procedure, the line heating conditions used to derive the flatness that satisfies the design criteria were derived and applied to the analytical model for verification.

Dynamics of a stochastic delayed chemostat model with nutrient storage and Lévy jumps

In this paper, a stochastic delayed chemostat model with nutrient storage and Lévy jumps is proposed. Firstly, the existence and uniqueness of the positive global solution of the model are discussed. Then, the threshold λ̄ and optimal control conditions for the persistence in the mean and extinction of the microorganism x are obtained. Besides, the ergodic stationary distribution of the SDDE model under a low-level intensity of stochastic noise is deduced. Finally, some numerical examples are given to support the theoretical analysis results. The simulation results show that stochastic noise and time delay play a vital role in controlling the persistence and extinction of microorganisms, respectively. On the one hand, high-intensity noise can inhibit the growth of microorganisms. On the other hand, if τ>τ∗, the corresponding deterministic model will become unstable and produce a Hopf bifurcation. Moreover, the solutions of the SDDE model will oscillate around the non-constant T−periodic solution of the corresponding deterministic model.

Vaccination’s Role in Combating the Omicron Variant Outbreak in Thailand: An Optimal Control Approach

COVID-19 is the name of the new infectious disease which has reached the pandemic stage and is named after the coronavirus (COVs) which causes it. COV is a single-stranded RNA virus which in humans leads to respiratory tract symptoms which can lead to death in those with low immunities, particularly older people. In this study, a standard dynamic model for COVID-19 was proposed by comparing a simple model and the optimal control model to reduce the number of infected people and become a guideline to control the outbreak. Control strategies are the vaccination rate and vaccine-induced immunity. An analysis was performed to find an equilibrium point, the basic reproduction number (R0), and conditions that generate stability by using Lyapunov functions to prove the stability of the solution at the equilibrium point. Pontryagin’s maximum principle was used to find the optimal control condition. Moreover, sensitivity analysis of the parameters was performed to learn about the parameters that might affect the outbreak in order to be able to control the outbreak. According to the analysis, it is seen that the efficacy of vaccines (b) and the infection rate (βan,βsn,βav,βsv) will affect the increased (decreased) incidence of the outbreak. Numerical analyses were performed on the Omicron variant outbreak data collected from the Thailand Ministry of Health, whose analyses then indicated that the optimal control strategy could lead to planning management and policy setting to control the COVID-19 outbreak.

Dynamics of Stochastic Zika Virus with Treatment Class in Human Population via Spectral Method

The Zika virus model (ZIKV) is mathematically modeled to create the perfect control strategies. The main characteristics of the model without control strategies, in particular reproduction number, are specified. Based on the basic reproduction number, if R0<0, then ZIKV satisfies the disease-free equilibrium. If R0>1, then ZIKV satisfies the endemic equilibrium. We use the maximum principle from Pontryagin’s. This describes the critical conditions for optimal control of ZIKV. Notwithstanding, due to the prevention and treatment of mosquito populations without spraying, people infected with the disease have decreased dramatically. Be that as it may, there has been no critical decline in mosquitoes contaminated with the disease. The usage of preventive treatments and insecticide procedures to mitigate the spread of the proposed virus showed a more noticeable centrality in the decrease in contaminated people and mosquitoes. The application of preventive measures including treatment and insecticides has emerged as the most ideal way to reduce the spread of ZIKV. Best of all, to decrease the spread of ZIKV is to use avoidance, treatment and bug spraying simultaneously as control methods. Moreover, for the numerical solution of such stochastic models, we apply the spectral technique. The stochastic or random phenomenons are more realistic and make the model more informative with the additive information. Throughout this paper, the additive term is assumed as additive white noise. The Legendre polynomials and applications are implemented to transform the proposed system into a nonlinear algebraic system.

Swarm Intelligence Based Model Predictive Control Strategy for Optimal State Control of Discrete Time-varying MIMO Linear Systems

Swarm Intelligence Based Model Predictive Control Strategy for Optimal State Control of Discrete Time-varying MIMO Linear Systems

A NOTE ON CONTROLLABILITY OF NONINSTANTANEOUS IMPULSIVE ATANGANA–BALEANU–CAPUTO NEUTRAL FRACTIONAL INTEGRODIFFERENTIAL SYSTEMS

This paper describes the required and adequate conditions for controllability and optimal controls of Atangana–Baleanu–Caputo (ABC) neutral fractional integrodifferential equations (NFIE) with noninstantaneous impulses. Measure of noncompactness, semigroup theory, fractional calculus and fixed point techniques act as the main tools in deriving the results. An illustration is offered to enhance our theoretical outcomes.

Optimal production of microalgae in the presence of grazers

Zooplankton contamination represents a major constraint in large-scale microalgal cultivation systems. While zooplankton contamination cannot be avoided, their development can be controlled by regulating the dilution rate. However, it is not straightforward to find the best control strategy for the dilution rate. Low dilution rates (or long retention times) favor grazer development and high dilution rates avoid their establishment at the risk of reducing microalgal productivity. Furthermore, the presence of periodic regimes arising from the interaction predator–prey makes it unclear if the presence of grazers must be completely avoided. In this paper, we study the role of the dilution rate in the control of zooplankton populations and in the optimization of biomass productivity. We show that in the long-term operation (static optimal control problem or SOCP), the optimal constant dilution rate must ensure the eradication of the zooplankton population. In the case of time-varying dilution rate, we numerically solve an optimal control problem (OCP) over a finite interval of time. We find that the optimal solution approaches the solution for the SOCP most of the time, except when zooplankton actively avoid the pond outflow. Based on these results, we propose a simple sub-optimal feedback control that approximately matches the solution of the OCP when the initial concentration of grazers is low.

Time-energy suboptimal control of nonlinear input-affine systems

In this paper, we derive the necessary conditions for time-energy optimal control of input-affine nonlinear systems using Hamilton–Jacobi–Bellman equation. The objective function is chosen as a weighted combination of control effort and time-horizon minimisation. The necessary conditions of optimality are transformed such that the resultant conditions are structurally similar to a differential matrix Riccati equation. A closed-form approximate solution to these necessary conditions is derived such that the resulting closed-loop dynamics is locally exponentially stable around the origin. Furthermore, it is also shown that the states converge within a ball of an arbitrarily small radius around the origin within a finite time. Finally, the performance of the proposed controller is tested using numerical simulations for Vander Pol's oscillator as well as spacecraft detumbling problem. Furthermore, the performance of the proposed controller is also tested in comparison to the infinite-horizon state-dependent Riccati equation controller.

Optimal Control of the Logistics Automation Transmission System Based on Partial Differential Equation

In this paper, the finite difference scheme of the spatiotemporal fractional convection-diffusion equation is established, and its stability and convergence are proved. Furthermore, this discrete technique is extended to solve nonlinear spatiotemporal fractional convection-diffusion equations. By using the Krylov subspace method to solve the discrete system, the numerical solution of the spatiotemporal fractional convection-diffusion equation can be obtained quickly. In this paper, an efficient optimal control algorithm is proposed to solve the free control problem of a class of nonlinear time-delay systems. We obtained the optimal control law of the system through the Bellman optimality principle, obtained the asymptotic stability criterion of the system in the form of LMI under the optimal control input by using the Lyapunov stability theory, and discussed the effect of the delay parameter on the system stability. Using the principle of intelligent neural network approximation function, the evaluation neural network and the execution neural network are used to approximate the optimal performance index function and optimal control input, respectively, the optimal control strategy of the system is obtained, and the convergence of the weight estimation error is proved to be optimal. On the basis of optimal state adjustment, the optimal tracking control problem is further solved. Numerical example results verify the effectiveness of the proposed method in terms of stability analysis, optimal state control, and optimal tracking control for the nonlinear time-delay system proposed in this paper. We calculate the parameters of the conveyor and select a reasonable transmission and sorting mechanism to realize the speed regulation of the driving motor of each mechanism. Through the work of each part, the design scheme of the automatic transmission system is formed, and the reliability, practicability, and economy of the system are guaranteed.

Optimal control analysis of a multigroup SEAIHRD model for COVID-19 epidemic.

The COVID‐19 pandemic has threatened public health and caused substantial economic loss to most countries worldwide. A multigroup susceptible–exposed–asymptomatic–infectious–hospitalized–recovered–dead (SEAIHRD) compartment model is first constructed to model the spread of the disease by dividing the population into three age groups: young (aged 0–19), prime (aged 20–64), and elderly (aged 65 and over). Then, we develop a free terminal time, partially fixed terminal state optimal control problem to minimize deaths and costs associated with hospitalization and the implementation of different control strategies. And the optimal strategies are derived under different assumptions about medical resources and vaccination. Specifically, we explore optimal control strategies for reaching herd immunity in the COVID‐19 outbreak in a free terminal time situation to evaluate the effect of nonpharmaceutical interventions (NPIs) and vaccination as control measures. The transmission rate of SARS‐CoV‐2 is calibrated by using real data in the United States at the early stage of the epidemic. Through numerical simulation, we conclude that the outbreak of COVID‐19 can be contained by implementing appropriate control of the prime age population and relatively strict control measures for young and elderly populations. Within a specific period, strict control measures should be implemented before the vaccine is marketed.

Stability Analysis and Optimal Control of Endemic Malaria Disease Transmission Model with Cost-Effective Strategies

In this study, a non-linear system of ordinary differential equation model that describes the dynamics of malaria disease transmission is formulated and analyzed. Conditions are derived from the existence of disease-free and endemic equilibria. The basic reproduction number R0 of the model is obtained, and we investigated that it is the threshold parameter between the extinction and persistence of the disease. If R0 is less than unity, then the disease-free equilibrium point is both locally and globally asymptotically stable resulting in the disease removing out of the host populations. The disease can persist whenever R0 is greater than unity and the conditions for the existence of both forward and backward bifurcation at R0 is equal to unity are derived. Sensitivity analysis is also performed and the important parameter that derive the disease dynamics is identified. Furthermore, optimal combinations of time dependent control measures are incorporated to the model, and we derived the necessary conditions of optimal control using Pontryagins’s maximum principal theory. Numerical simulations were conducted using MATLAB to confirm our analytical results. Our findings were that, malaria may be controlled by reducing the requirement rate of mosquito populations and the use of a combination of vaccination, insecticide treated net ITN, indoor residual spray IRS and active treatment or strategy d can also help to reduce the number of populations with malaria symptoms to zero. We also find that the same strategy that is, strategy d proves to be efficacious and cost-effective.

State and Control Path-Dependent Stochastic Optimal Control With Jumps

We consider the state and control path-dependent stochastic optimal control problem for jump-diffusion models, where the dynamics and the objective functional are dependent on (current and past) paths of state and control processes. We prove the dynamic programming principle of the value functional, for which, unlike the existing literature, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Skorohod metric</i> is necessary to maintain the separability of càdlàg (state and control) spaces. We introduce the state and control path-dependent integro-type Hamilton–Jacobi–Bellman (PIHJB) equation, which includes the Lévy measure in the corresponding nonlocal path-dependent integral operator. Then, by using the functional Itô calculus of a càdlàg path, we show the verification theorem, which constitutes the sufficient condition for optimality in terms of the solution to the PIHJB equation. We finally apply our verification theorem to the linear-quadratic optimal control problem of jump-diffusion models with delay and the control path-dependent problem, for which the explicit optimal solutions are obtained by solving the corresponding PIHJB equation.