Search

Crimes are social ills that make a society unsafe to live in. Since a child is born into a family and a society is made up of different families, we develop a model to study the influence of family background on the spread of crime in the society. Five compartments are considered including: those who can commit crime (S), those who are resistant to committing crime (R), those who are committing crime alone (I), those who are committing crime in group (G) and the criminals who are under rehabilitation (J). The validity of the model was established. Crime reproductive ratio C R was computed and used to derive the necessary and sufficient conditions for crime eradication and persistence. Simulation was conducted using the computer-in-built Runge–Kutta scheme implemented in software maple and the results showed that the effectiveness of crime education together with strict security and legal system up to 70% were sufficient to eradicate criminal activities in a community. [ABSTRACT FROM AUTHOR]

In this article, we study the role of awareness and its impact on the control of infectious diseases. We analyze a susceptible-infected-recovered model with a media awareness compartment. We find the effective reproduction number R0{R}_{0}. We observe that our model exhibits transcritical forward bifurcation at R0=1{R}_{0}=1. We also performed the sensitivity analysis to determine the sensitivity of parameters of the effective reproduction number R0{R}_{0}. In addition, we study the corresponding optimal control problem by considering control in media awareness and treatment. Our studies conclude that we can reduce the rate of spread of infection in the population by increasing the treatment rate along with media awareness.

We consider a method for solving the problem of optimal control of a composite dynamic system with stochastic resource constraints. The method is based on the method of hierarchical optimization, which includes iterative solution of local problems and the coordination problem. To solve local problems, we apply the model predictive control. Taking into account stochastic resource constraints leads to the solution of one-stage problems of stochastic programming. [ABSTRACT FROM AUTHOR]

In this paper, we ameliorate the model proposed in [13], by incorporating the influence of hepatitis B e antigen (HBeAg) status of mothers on vertical transmission. We use the improved model to fit reported HBV new infections in the Zhejiang Province of China. Also to predict the course of the Hepatitis B (HBV) infection in this Chinese area, and in Tokombere, located in sub-Saharan Africa(SSA). Furthermore, we apply optimal control techniques in view to re-examine the effects of the newborn vaccination, the universal vaccination and the treatment of chronic carriers in preventing the HBV infection. Simulation results show that treatment slightly steps in the optimal strategy, while immunisation is an effective measure. On the other hand, they indicate that the control measures and immunization programs implemented in Zhejiang Province are effective. Besides, they suggest that in SSA, a package of several policies centred on birth dose vaccination should be implemented. [ABSTRACT FROM AUTHOR]

Tokamaks are the most promising devices to prove the feasibility of energy production using nuclear fusion on Earth which is foreseen as a possible source of energy for the next centuries. In large tokamaks with superconducting poloidal field (PF) coils, the problem of avoiding saturation of the currents is of paramount importance, especially for a reactor such as the European demonstration fusion power plant DEMO. Indeed, reaching the current limits during plasma operation may cause a loss of control of the plasma shape and/or current, leading to a major disruption. Therefore, a current limit avoidance (CLA) system is essential to assure safe operation. Three different algorithms to be implemented within a CLA system are proposed in this paper: two are based on online solutions of constrained optimization problems, while the third one relies on dynamic allocation. The performance assessment for all the proposed solutions is carried out by considering challenging operation scenarios for the DEMO reactor, such as the case where more than one PF current simultaneously saturates during the discharge. An evaluation of the computational burden needed to solve the allocation problem for the various proposed alternatives is also presented, which shows the compliance of the optimization-based approaches with the envisaged deadlines for real-time implementation of the DEMO plasma magnetic control system. [ABSTRACT FROM AUTHOR]

Cell-to-cell variability, born of stochastic chemical kinetics, persists even in large isogenic populations. In the study of single-cell dynamics this is typically accounted for. However, on the population level this source of heterogeneity is often sidelined to avoid the inevitable complexity it introduces. The homogeneous models used instead are more tractable but risk disagreeing with their heterogeneous counterparts and may thus lead to severely suboptimal control of bioproduction. In this work, we introduce a comprehensive mathematical framework for solving bioproduction optimal control problems in the presence of heterogeneity. We study population-level models in which such heterogeneity is retained, and propose order-reduction approximation techniques. The reduced-order models take forms typical of homogeneous bioproduction models, making them a useful benchmark by which to study the importance of heterogeneity. Moreover, the derivation from the heterogeneous setting sheds light on parameter selection in ways a direct homogeneous outlook cannot, and reveals the source of approximation error. With view to optimally controlling bioproduction in microbial communities, we ask the question: when does optimising the reduced-order models produce strategies that work well in the presence of population heterogeneity? We show that, in some cases, homogeneous approximations provide remarkably accurate surrogate models. Nevertheless, we also demonstrate that this is not uniformly true: overlooking the heterogeneity can lead to significantly suboptimal control strategies. In these cases, the heterogeneous tools and perspective are crucial to optimise bioproduction. [ABSTRACT FROM AUTHOR]

In this paper, we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems and Pontryagin maximum principle. As an important result, among others, we develop a contact Pontryagin maximum principle that permits to deal with optimal control problems with dissipation. We also consider the Herglotz optimal control problem, which is simultaneously a generalization of the Herglotz variational principle and an optimal control problem. An application to the study of a thermodynamic system is provided. [ABSTRACT FROM AUTHOR]

This article presents a cost-effective optimal control analysis of interventions applied to a S2EI2RS type deterministic compartmental model of COVID-19, considering community awareness and immunity loss. We introduce two time-dependent controls, namely, home quarantine and treatment, to the model for defining an optimal control problem (OCP). In addition to some basic qualitative properties, we obtain the reproductive threshold R0{R}_{0} by using the next-generation method and see the impact of controls on it. We also investigate the effect of community awareness and waning immunity, when no controls are applied. The existence and characterization of optimal controls is proved to establish the optimality system, and the OCP is solved using the forward–backward sweep method. The results are simulated using MATLAB. Our comparative cost-effective analysis indicates that implementing both control strategies simultaneously, along with community awareness, is the most optimal and sustainable way to flatten COVID-19 curves in a short period of time than that of implementing single controls. This article offers valuable insights that can assist policymakers and public health experts in designing targeted and effective control measures for COVID-19 and future epidemics in the post-COVID era. Therefore, this piece of work could be a valuable contribution to the existing literature.

We formulate a system of ordinary differential equations to model the contribution of antibiotic treatment and immune system to combat bacterial infections. We obtained threshold conditions that determine when the bacteria can be eliminated, which are consistent with biological phenomena. In order to minimize the bacterial population, we formulated an optimal control problem considering the action of both antibiotic and immune system. The optimal control is obtained applying the Pontryagin's Principle. The results show the relevance of the synergism between the antibiotic treatment and the immune system response. [ABSTRACT FROM AUTHOR]

We present a model which encompasses pace optimization and motor control effort for a runner on a fixed distance. We see that for long races, the long term behaviour is well approximated by a turnpike problem, that allows to define an approximate optimal velocity. We provide numerical simulations quite consistent with this approximation which leads to a simplified problem. The advantage of this simplified formulation for the velocity is that if we have velocity data of a runner on a race, and have access to his V ˙ O 2 max , then we can infer the values of all the physiological parameters. We are also able to estimate the effect of slopes and ramps. [ABSTRACT FROM AUTHOR]

The aim of this article is to understand how to apply partial or total containment to SIR epidemic model during a given finite time interval in order to minimize the epidemic final size, that is the cumulative number of cases infected during the complete course of an epidemic. The existence and uniqueness of an optimal strategy are proved for this infinite-horizon problem, and a full characterization of the solution is provided. The best policy consists in applying the maximal allowed social distancing effort until the end of the interval, starting at a date that is not always the closest date and may be found by a simple algorithm. Both theoretical results and numerical simulations demonstrate that it leads to a significant decrease in the epidemic final size. We show that in any case the optimal intervention has to begin before the number of susceptible cases has crossed the herd immunity level, and that its limit is always smaller than this threshold. This problem is also shown to be equivalent to the minimum containment time necessary to stop at a given distance after this threshold value. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of nonlinear systems driven by measures generalizing the class of impulsive systems. We use measures as control and prove existence of optimal controls (measures) and present necessary conditions of optimality. We apply the general results to derive necessary conditions of optimality for purely impulse-driven systems. These results are then applied to optimal control problems related to geosynchronous satellites with some numerical results. [ABSTRACT FROM AUTHOR]

We investigate a well-known phenomenon of variational approaches in image processing, where typically the best image quality is achieved when the gradient flow process is stopped before converging to a stationary point. This paradox originates from a tradeoff between optimization and modeling errors of the underlying variational model and holds true even if deep learning methods are used to learn highly expressive regularizers from data. In this paper, we take advantage of this paradox and introduce an optimal stopping time into the gradient flow process, which in turn is learned from data by means of an optimal control approach. After a time discretization, we obtain variational networks, which can be interpreted as a particular type of recurrent neural networks. The learned variational networks achieve competitive results for image denoising and image deblurring on a standard benchmark data set. One of the key theoretical results is the development of first- and second-order conditions to verify optimal stopping time. A nonlinear spectral analysis of the gradient of the learned regularizer gives enlightening insights into the different regularization properties. [ABSTRACT FROM AUTHOR]

In a recent paper by Bourdin and Trélat, a version of the Pontryagin maximum principle (in short, PMP) has been stated for general nonlinear finite-dimensional optimal sampled-data control problems. Unfortunately, their result is only concerned with fixed sampling times, and thus, it does not take into account the possibility of free sampling times. The present paper aims to fill this gap in the literature. Precisely, we establish a new version of the PMP that can handle free sampling times. As in the aforementioned work by Bourdin and Trélat, we obtain a first-order necessary optimality condition written as a nonpositive averaged Hamiltonian gradient condition. Furthermore, from the freedom of choosing sampling times, we get a new and additional necessary optimality condition which happens to coincide with the continuity of the Hamiltonian function. In an autonomous context, even the constancy of the Hamiltonian function can be derived. Our proof is based on the Ekeland variational principle. Finally, a linear–quadratic example is numerically solved using shooting methods, illustrating the possible discontinuity of the Hamiltonian function in the case of fixed sampling times and highlighting its continuity in the instance of optimal sampling times. [ABSTRACT FROM AUTHOR]

The present paper extends the classical second-order variational problem of Herglotz type to the more general context of the Euclidean sphere S n following variational and optimal control approaches. The relation between the Hamiltonian equations and the generalized Euler–Lagrange equations is established. This problem covers some classical variational problems posed on the Riemannian manifold S n such as the problem of finding cubic polynomials on S n . It also finds applicability on the dynamics of the simple pendulum in a resistive medium. [ABSTRACT FROM AUTHOR]

The aim of this study is to provide a feedback control, called the Chemotherapy Protocol Law, with the purpose to keep the density of tumor cells that are treated by chemotherapy below a "tolerance level" L c , while retaining the density of normal cells above a "healthy level" N c . The mathematical model is a controlled dynamical system involving three nonlinear differential equations, based on a Gompertzian law of cell growth. By evoking viability and set-valued theories, we derive sufficient conditions for the existence of a Chemotherapy Protocol Law. Thereafter, on a suitable viability domain, we build a multifunction whose selections are the required Chemotherapy Protocol Laws. Finally, we propose a design of selection that generates a Chemotherapy Protocol Law. [ABSTRACT FROM AUTHOR]

We define a new class of optimal control problems and show that this class is the largest one of control problems where every admissible process that satisfies the Extended Pontryaguin Maximum Principle is an optimal solution of nonregular optimal control problems. In this class of problems the local and global minimum coincide. A dual problem is also proposed, which may be seen as a generalization of the Mond–Weir-type dual problem, and it is shown that the 2-invexity notion is a necessary and sufficient condition to establish weak, strong, and converse duality results between a nonregular optimal control problem and its dual problem. We also present an example to illustrate our results. [ABSTRACT FROM PUBLISHER]

In this paper, a novel numerical algorithm is presented to compute the optimal time of a time optimal control problem where the governing system is a linear ordinary differential equation. By the equivalence between time optimal control problem and norm optimal control problem, computation of the optimal time can be obtained by solving a sequence of norm optimal control problems, which are transferred into their Lagrangian dual problems. The nonsmooth structure of the dual problem is approximated by the iteratively reweighted least square strategy. Several numerical tests are given to show the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In the present survey paper, we discuss applications of differential and operator inclusions to some optimization and optimal control problems. The Filippov implicit function lemma is considered and its application to the optimization of a feedback control system governed by a semilinear differential equation in a Banach space is presented. We describe the construction of the oriented coincidence degree for a compact multivalued perturbation of a nonlinear Fredholm operator and apply it to an optimal control problem induced by an ordinary differential equation with the Hopf boundary condition. We study also an optimal feedback control problem for a mathematical model of the motion of weakly concentrated water polymer solutions. [ABSTRACT FROM AUTHOR]

Optimal control theory is applied to a mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits the administration of triple HIV drug therapy. The optimal control represents a percentage effect the chemotherapy consisting of fusion inhibitors (FIs), reverse transcriptase inhibitors (RTIs), and protease inhibitors (PIs) has on the interaction of CD4+T-cells with the virus. First, we maximize the benefit based on the T-cell count and minimize the systemic cost based on the percentage of chemotherapies given and then build an objective functional to minimize the viral replication and treatment systemic costs. Our results indicate that highly toxic drugs and small dosage sizes have the potential for improving the quality of life and reducing economic costs of therapy. An optimal control strategy that seeks to maximize CD4+ T-cells has the potential to provide better treatment results over the optimal treatmet strategy that seeks to minimize the viral production. The addition of FIs to the current HIV treatment strategy of RTIs and PIs improves to relax both concentration and dose sizes of RTIs and PIs. [ABSTRACT FROM AUTHOR]