Optimal Control Pair Research Articles

Control of a Multivariable System Using Optimal Control Pairs: A Quadruple-Tank Process

This paper deals with one of the possible ways to control multivariable (MIMO) control loops. The suggested control design procedure uses the so-called primary controllers, auxiliary controllers, and also correction members. Parameters of the primary controllers are determined for the optimal control pairs using arbitrary single-variable synthesis methods; namely, the modulus optimum method, the balanced tuning method, and the desired model method. The optimal control pairs are determined using the so-called relative gain array tool or the relative normalized gain array tool combined with other tools, as the condition number or the Niederlinski index. The auxiliary feedback controllers serve for ensuring a control loop decoupling. Invariance to load disturbance of a control loop is realized by using the correction members. The novelty lies especially in the combination of the original inverted decoupling with disturbance rejection and provided tuning methods. The proposed control design for a MIMO loop is verified by simulation for the two-variable controlled plant of a quadruple-tank process and evaluated by using various criteria. Moreover, a numerical comparison to some other methods is given to the reader.

Optimal control strategy with delay in state and control variables of transmission of COVID-19 pandemic virus

In this work, we are interested in the study of the dynamics of transmission of COVID-19 disease, described by SIR epidemic model, with time delay in state and control variables. Our goal is to characterize the optimal control pair, which minimizes the number of susceptible and infected individuals and maximizes the number of people recovered. Pontryagin’s maximum principle with delay is used to characterize these optimal controls. The numerical resolution of the optimal system, has shown the effectiveness of our adopted strategy.

Molecular mechanism of translational stalling by inhibitory codon combinations and poly(A) tracts.

Inhibitory codon pairs and poly(A) tracts within the translated mRNA cause ribosome stalling and reduce protein output. The molecular mechanisms that drive these stalling events, however, are still unknown. Here, we use a combination of invitro biochemistry, ribosome profiling, and cryo-EM to define molecular mechanisms that lead to these ribosome stalls. First, we use an invitro reconstituted yeast translation system to demonstrate that inhibitory codon pairs slow elongation rates which are partially rescued by increased tRNA concentration or by an artificial tRNA not dependent on wobble base-pairing. Ribosome profiling data extend these observations by revealing that paused ribosomes with empty A sites are enriched on these sequences. Cryo-EM structures of stalled ribosomes provide a structural explanation for the observed effects by showing decoding-incompatible conformations of mRNA in the A sites of all studied stall- and collision-inducing sequences. Interestingly, in the case of poly(A) tracts, the inhibitory conformation of the mRNA in the A site involves a nucleotide stacking array. Together, these data demonstrate a novel mRNA-induced mechanisms of translational stalling in eukaryotic ribosomes.

Optimal control of an HIV model with CTL cells and latently infected cells

This paper deals with an optimal control problem for an human immunodeficiency virus (HIV) infection model with cytotoxic T-lymphocytes (CTL) immune response and latently infected cells. The model under consideration describes the interaction between the uninfected cells, the latently infected cells, the productively infected cells, the free viruses and the CTL cells. The two treatments represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence of the optimal control pair is established and the Pontryagin's minimum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward difference approximation. Finally, numerical simulations are performed in order to show the role of optimal therapy in controlling the infection severity.

On the control of a reaction–diffusion system: a class of SIR distributed parameter systems

In this paper, two types of distributed control functions, vaccine and treatment have been applied to a spatiotemporal SIR model with no-flux boundary conditions. The spatiotemporal SIR epidemic model is formulated from existing SIR epidemic model by including a diffusion term in his different compartments to study the impact of spatial heterogeneity of disease transmission in dense regions. Our main objective to find the optimal control pair that minimizes the number of infected individuals, the corresponding vaccination and treatment costs. The existence of the positive solution for the state system and the existence of a distributed optimal control pair are proved. Techniques of optimal control are used to characterize optimal control pair in terms of state and adjoint functions. The optimality system is solved numerically; the numerical results show that the control effect is effective if the treatment and vaccine strategies are used simultaneously.

Optimal control of a delayed smoking model with immigration

In this paper, we formulate a smoking model with delay and immigration, and the possibility of optimal controls both over the susceptible and heavy problem smoker subjects is assumed. The existence of the optimal control pair is also proved. We derive the optimality condition via the Pontryagin's maximum principle with delay and obtain the existence of the optimal solution. Numerical simulation is given. Numerical simulations are made to support the main results.

Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids.

We model the transmission of the hepatitis B virus (HBV) by six differential equations that represent the reactions between HBV with DNA-containing capsids, the hepatocytes, the antibodies and the cytotoxic T-lymphocyte (CTL) cells. The intracellular delay and treatment are integrated into the model. The existence of the optimal control pair is supported and the characterization of this pair is given by the Pontryagin’s minimum principle. Note that one of them describes the effectiveness of medical treatment in restraining viral production, while the second stands for the success of drug treatment in blocking new infections. Using the finite difference approximation, the optimality system is derived and solved numerically. Finally, the numerical simulations are illustrated in order to determine the role of optimal treatment in preventing viral replication.

Solvability and optimal controls of impulsive Hilfer fractional delay evolution inclusions with Clarke subdifferential

We study the solvability and optimal controls of an impulsive nonlinear Hilfer fractional delay evolution inclusion in Banach spaces. For the main results, we use fractional calculus, fixed point technique, semigroup theory and multivalued analysis. We introduce the notion of Clarke delay subdifferential. To continue and extend previous works in the field, we prove an existence result of optimal control pair for Lagrange problem L P under appropriate set of sufficient conditions. Finally, as application, we give an impulsive control partial differential inclusion with Hilfer fractional derivative.

Robust control of parabolic stochastic partial differential equations under model uncertainty

The present paper is devoted to the study of robust control problems of parabolic stochastic partial differential equations under model uncertainty. To be more precise, the robust control problem under investigation is expressed as a stochastic differential game in a real separable infinite dimensional Hilbert space. By resorting to the theory of mild solutions, we prove that the elliptic partial differential equation associated with the problem at hand, also known as the Hamilton-Jacobi-Bellman-Isaacs equation, admits a unique solution, which is the value function of the game. Furthermore, we investigate the problem of existence of an optimal control pair that satisfies a saddle point property. Finally, as a demonstration of the proposed approach, we apply our results to the study of a certain robust control problem arising in the spatiotemporal management of natural resources.

Optimal feedback control problems driven by fractional evolution hemivariational inequalities

This article investigates optimal feedback controls of a system driven by fractional evolution hemivariational inequalities. An existence result with respect to feasible pairs is obtained by applying the Cesari property and a fixed‐point theorem for multivalued maps. Under some suitable assumptions, it is proved that there exists at least 1 optimal feedback control pair of the Lagrange problem. An illustrating example is given.

Optimal feedback control for fractional neutral dynamical systems

In this paper, we consider feedback control systems governed by fractional neutral equations involving Riemann–Liouville derivatives. Firstly, we show the existence and uniqueness of solutions for the feedback control systems by applying Krasnoselskiis fixed point theorem. Then, we use Filippove theorem to obtain the existence of feasible pairs. Finally, an existence result of optimal control pairs for the Lagrange problem is proved.

A class of delay evolution hemivariational inequalities and optimal feedback controls

In this paper, we study the feedback optimal control for a class of evolution hemivariational inequalities with delay. First, we obtain the existence of feasible pairs by applying the Cesari property, the Filippov theorem, the properties of Clarke subdifferential and a fixed point theorem for multivalued maps. Next, the results of optimal feedback control pairs and time optimal control for delay evolution hemivariational inequalities are presented under sufficient conditions. Finally, an example is included to illustrate our main results.

Optimal control of a delayed hepatitis B viral infection model with HBV DNA‐containing capsids and CTL immune response

SummaryThis paper deals with an optimal control problem of a time‐delayed differential equation model that describes the interactions between hepatitis B virus (HBV) with HBV DNA‐containing capsids, liver cells (hepatocytes), and cytotoxic T‐lymphocyte immune response. Both the treatment and the intracellular delay are incorporated into the model. Furthermore, the existence of the optimal control pair is studied, and Pontryagin's minimum principle is used to characterize these 2 optimal controls. The first of them represents the efficiency of drug treatment in preventing new infections, whereas the second stands for the efficiency of drug treatment in inhibiting viral production. The optimality system is derived and solved numerically using the forward and backward difference approximation. Finally, numerical simulations are established to show the role of optimal therapy in controlling viral replication.

Optimal control of feedback control systems governed by systems of evolution hemivariational inequalities

In this paper, we introduce and consider a feedback control system governed by the system of evolution hemivariational inequalities. Several sufficient conditions are formulated by virtue of the properties of multimaps and partial Clarke?s subdifferentials such that the existence result of feasible pairs of the feedback control systems is guaranteed. Moreover, an existence result of optimal control pairs for an optimal control system is also established.

On Optimal Control Pair Treatment: Clinical Management of Viremia Levels In Pathogenic-Induced HIV-1 Infections

On Optimal Control Pair Treatment: Clinical Management of Viremia Levels In Pathogenic-Induced HIV-1 Infections

Optimal control of a social epidemic model with media coverage

ABSTRACTA new social epidemic model to depict alcoholism with media coverage is proposed in this paper. Some fundamental properties of the model including existence and positivity as well as boundedness of equilibria are investigated. Stability of all equilibria are studied. The existence of the optimal control pair and mathematical expressions of optimal control are obtained by Pontryagin's maximum principle. Numerical simulations are also performed to illustrate our results. Our results show that media coverage is an effective measure to quit drinking.

Optimal control strategy of HIV-1 epidemic model for recombinant virus

In this work, an optimal control strategy is developed to eliminate the spread of HIV-1. To do this, two control variables are used such as the efficaciousness of drug therapy in reducing the infection of new cells and decreasing the production of new viruses. Existence for the optimal control pair is accomplished and the Pontryagins Maximum Principle is used to characterize these optimal controls. Objective functional is constituted to minimize the densities of infected cells and free virus and to maximize the density of healthy cells. The optimality system is derived and solved numerically.

Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control

In this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. Finally, we provide an example to illustrate the obtained results.

Optimal strategy of vaccination & treatment in an SIR epidemic model

In this work, we propose a susceptible–infected–recovered (SIR) epidemic model which describes the interaction between susceptible and infected individuals in a community and analyze the SIR epidemic model through the optimal control theory and mathematical analysis. In addition, we present some possible strategies to prevent the spread of some infection causing epidemic in the society. In order to do this, we introduce an optimal control problem with an objective functional, where two control functions, vaccination and treatment have been used as control measures for susceptible and infected individuals. We show the existence of an optimal control pair for the optimal control problem and derive the optimality condition. Finally we consider a smoking epidemic model to illustrate our theoretical results with some numerical simulations, which use real data collected in April and May 2004 from 300 male students at three vocational technical high schools in Korean metropolitan areas. Our analysis suggests that two control strategies are more effective than only one control strategy in controlling the increase of male student smokers in Korean metropolitan areas.

Solvability and optimal controls of fractional delay evolution inclusions with Clarke subdifferential

This article investigates the solvability and optimal controls of systems monitored by fractional delay evolution inclusions with Clarke subdifferential type. By applying a fixed‐point theorem of condensing multivalued maps and some properties of Clarke subdifferential, an existence theorem concerned with the mild solution for the system is proved under suitable assumptions. Moreover, an existence result of optimal control pair that governed by the presented system is also obtained under some mild conditions. Finally, an example is given to illustrate our main results. Copyright © 2016 John Wiley & Sons, Ltd.