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Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to economics. However, the inherent complexity of such systems poses serious difficulties to control design, when control objectives depart from the standard ones investigated in the current literature, e.g. stabilization, regulation, and etc. In this paper we propose one approach to control design, which is based on the construction of symbolic models, where each symbolic state and each symbolic label correspond to an aggregate of continuous states and to an aggregate of input signals in the original system. The use of symbolic models offers a systematic methodology for control design in which constraints coming from software and hardware, interacting with the physical world, can be integrated. The main contribution of this paper is in showing that incrementally input-to-state stable time-delay systems do admit symbolic models that are approximately bisimilar to the original system, with a precision that can be rendered as small as desired. An algorithm is also presented which computes the proposed symbolic models. When the state and input spaces of time-delay systems are bounded, which is the case in many realistic situations, the proposed algorithm is shown to terminate in a finite number of steps., 12 pages

A mathematical model for the transmission of buruli ulcer disease is proposed in this paper, incorporating three control strategies. Using the stability theory of differential equations, optimal control, and computer simulation, a nonlinear mathematical model for the problem is developed and qualitatively analyzed. Buruli ulcer free equilibrium and buruli ulcer present equilibrium were established. Using the next-generation operator method, the basic reproduction number of the model is obtained. It is found that the buruli ulcer-free equilibrium point is asymptotically stable locally and globally when R 0 1 and otherwise when R 0 > 1 . The bifurcation analysis performed in this study indicates that the buruli ulcer model exhibits backward bifurcation. To investigate the parameters that influence the basic reproduction number R 0 , sensitivity analysis is performed. To minimize the transmission dynamics of buruli ulcer in humans and water bugs populations respectively, the buruli ulcer model is updated to include control measures attached to the parameters that affect the R 0 . In particular, the prevention measures covered are health education on the use of protective clothing, treatment of infected humans, and spraying of insecticides. The Pontryagin’s maximum principle is used to characterize the controls’ optimal levels. Using forward and backward sweep techniques in MATLAB, the optimality system was solved numerically. The results of the simulations show that, relative to the case of no control, there is a substantial decrease in the population of infected humans and the total population of water bugs when control measures are implemented. A study of cost-effectiveness shows that the most cost-effective approach is strategy G with the smallest ICER of 33442.44. To mitigate or eliminate buruli ulcer in the population, we conclude that the government should invest in health education on the use of protective clothing, treatment of infected humans, and the use of insecticide spray.

Switched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems, the constant evolution of technology demands that we make similar progress with respect to different, and perhaps more complex, objectives. This paper describes one particular approach to address these different objectives based on the construction of approximately equivalent (bisimilar) symbolic models for switched systems. The main contribution of this paper consists in showing that under standard assumptions ensuring incremental stability of a switched system (i.e. existence of a common Lyapunov function, or multiple Lyapunov functions with dwell time), it is possible to construct a finite symbolic model that is approximately bisimilar to the original switched system with a precision that can be chosen a priori. To support the computational merits of the proposed approach, we use symbolic models to synthesize controllers for two examples of switched systems, including the boost DC-DC converter., Comment: 17 pages

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.

The decision by the United Kingdom (UK) government in 2007 that the country should build a 33GW wind fleet, capable of generating 25 percent of the UK electricity requirement, was controversial. Proponents argued that it was the most attractive means of lowering the UK greenhouse gas emissions, whereas opponents noted that it would result in an unnecessary and burdensome additional expense to industry and households. Subsequently there have been calls for the wind fleet target to be further increased to perhaps 50 percent of demand. Although the National Grid has had little difficulty in accommodating the current output of about 10 percent of the total demand on the grid, this will not be the case for a substantially larger wind fleet. When the wind blows strongly, turbines shed wind which is surplus to demand, leading to significant reductions in generating efficiency. The purpose of the research described in this paper has been to develop a method for investigating the likely performance of future large wind fleets. The method relies on the use of mathematical models based on National Grid records for 2013 to 2015, each year being separately analysed. It was found that the incremental load factor of the wind fleet will be reduced to 63 percent of its current level should the wind fleet increase from its current size of 14GW to 35GW, assuming a base load of 15GW, 24 pages, 15 figures, 4 tables

Diabetes is a disease which caused by socio-environmental and / or genetic factors. The negative effect of socio-environmental or lifestyle leads a susceptible individual to become a diabetic. On the one hand, social interaction wields a great deal of influence over lifestyle. On the other hand, genetic factors are the main cause of the birth diabetes genetic disorder. Considering these above mentioned factors. In the present paper, we study a discrete age continuous mathematical model that describes the dynamics of diabetics. We highlight the negative impact of socio-environmental on diabetic patients according to age groups. We also suggest an optimal strategy to implement the best campaigns of rising awareness that aims at protecting diabetic patients from the negative impact of a lifestyle that leads them to complications. In addition to psychological treatment and follow-up of diabetic patients with complications, an awareness campaign will also be carried out for people with potential diabetes that aims at educating them about the dangerous of diabetes and its complications. Pontryagin’s maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. The numerical simulation is carried out using MATLAB.

The rapid and surprised emergence of COVID-19, having infected three million and killed two hundred thousand people worldwide in less than five months, has led many experts to focus on simulating its propagation dynamics in order to have an estimated outlook for the not too distante future and so supporting the local and national governments in making decisions. In this paper, we apply the SIR model to simulating the propagation dynamics of COVID-19 on the Cape Verde Islands. It will be done firstly for Santiago and Boavista Islands, ant then for Cape Verde in general. The choice of Santiago rests on the fact that it is the largest island, with more than 50% of the Population of the country, whereas Boavista was chosen because it is the island where the first case of COVID-19 in Cape Verde was diagnosed. Observations made after the date of the simulations were carried out corroborates our projections., Comment: 23 pages, 8 figures and 6 tables

Highlights • We give a model of dynamical behavior of COVID-19 in Tunisia. • We study the qualitative properties of the considered model. • We establish the stability of equilibrium point via R 0. • We prove theoretically and by numerical simulations the effect of quarantine strategy on the spread of the disease., Corona virus disease (COVID-19) is an extremely serious infection with an extremely high death rate worldwide. In March, the disease was declared a ”global pandemic” by the World Health Organization (WHO). Until now, there is no known vaccine or drug, since the unknown things related to the disease are more important than our theoretical and empirical knowledge. However, mathematical modeling and the estimation of the basic number of reproductions can provide clarifications in order to determine the potential and severity of this epidemic and therefore provide essential information to identify the type of measures and interventions to be taken to control the intensity of the spread of the disease. Hence, in this paper, we propose a new deterministic compartmental model based on the clinical progression of the disease, the epidemiological state of the individuals and the intervention for the dynamics of COVID-19 infections. Our approach consists of seven phenotypes: the susceptible humans, exposed humans, infectious humans, the recovered humans, the quarantine population, there recovered-exposed and deceased population. We proved first through mathematical approach the positivity, boundness and existence of a solution to the considered model. We also studied the existence of the disease free equilibrium and corresponding stability. Our work shows, in particular, that the disease will decrease if the number of reproduction R0 was less than one. Moreover, the impact of the quarantine strategies to reduce the spread of this disease is discussed. The theoretical results are validated by some numerical simulations of the system of the epidemic’s differential equations. It should be mentioned that, the error between the considered model and the official data curve is quite small.

emir/0000-0001-7220-0042 WOS: 000386878300001 Necessary and sufficiently conditions are derived for the decomposition of a second order linear time-varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation of the system itself. Scientific and Technological Research Council of TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [115E952] This paper has been supported by the Scientific and Technological Research Council of Turkey under the project no. 115E952.

The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model’s parameters are calculated. In the time-dependent constant control case, Pontryagin’s Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.

International audience; This paper presents a general review on hybrid modelling which is about to become ubiquitous in biological and medical modelling. Hybrid modelling is classically defined as the coupling of a continuous approach with a discrete one, in order to model a complex phenomenon that cannot be described in a standard homogeneous way mainly due to its inherent multiscale nature. In fact, hybrid modelling can be more than that since any types of coupled formalisms qualify as being hybrid. This review first presents the evolution and current context of this modelling approach. It then proposes a classification of the models through three different types that relate to the nature and level of coupling of the formalisms used.

Some twenty years ago we introduced a nonstandard matrix Riccati equation to solve the partial stochastic realization problem. In this paper we provide a new derivation of this equation in the context of system identification. This allows us to show that the nonstandard matrix Riccati equation is universal in the sense that it can be used to solve more general analytic interpolation problems by only changing certain parameters. Such interpolation problems are ubiquitous in systems and control. In this context we also discuss a question posed by R.E. Kalman in beginning of the 1970s.

Social balance theory describes allowable and forbidden configurations of the topologies of signed directed social appraisal networks. In this paper, we propose two discrete-time dynamical systems that explain how an appraisal network \textcolor{blue}{converges to} social balance from an initially unbalanced configuration. These two models are based on two different socio-psychological mechanisms respectively: the homophily mechanism and the influence mechanism. Our main theoretical contribution is a comprehensive analysis for both models in three steps. First, we establish the well-posedness and bounded evolution of the interpersonal appraisals. Second, we fully characterize the set of equilibrium points; for both models, each equilibrium network is composed by an arbitrary number of complete subgraphs satisfying structural balance. Third, we establish the equivalence among three distinct properties: non-vanishing appraisals, convergence to all-to-all appraisal networks, and finite-time achievement of social balance. In addition to theoretical analysis, Monte Carlo validations illustrates how the non-vanishing appraisal condition holds for generic initial conditions in both models. Moreover, numerical comparison between the two models indicate that the homophily-based model might be a more universal explanation for the formation of social balance. Finally, adopting the homophily-based model, we present numerical results on the mediation and globalization of local conflicts, the competition for allies, and the asymptotic formation of a single versus two factions.

This paper proposes models of learning process in teams of individuals who collectively execute a sequence of tasks and whose actions are determined by individual skill levels and networks of interpersonal appraisals and influence. The closely-related proposed models have increasing complexity, starting with a centralized manager-based assignment and learning model, and finishing with a social model of interpersonal appraisal, assignments, learning, and influences. We show how rational optimal behavior arises along the task sequence for each model, and discuss conditions of suboptimality. Our models are grounded in replicator dynamics from evolutionary games, influence networks from mathematical sociology, and transactive memory systems from organization science., Comment: A preliminary version has been accepted by the 53rd IEEE Conference on Decision and Control. The journal version has been submitted to IEEE Transactions on Automatic Control

This paper proposes models of learning process in teams of individuals who collectively execute a sequence of tasks and whose actions are determined by individual skill levels and networks of interpersonal appraisals and influence. The closely-related proposed models have increasing complexity, starting with a centralized manager-based assignment and learning model, and finishing with a social model of interpersonal appraisal, assignments, learning, and influences. We show how rational optimal behavior arises along the task sequence for each model, and discuss conditions of suboptimality. Our models are grounded in replicator dynamics from evolutionary games, influence networks from mathematical sociology, and transactive memory systems from organization science.

Although diseases such as influenza, tuberculosis and SARS are transmitted through an environmentally mediated mechanism, most modeling work on these topics is based on the concepts of infectious contact and direct transmission. In this paper we use a paradigm model to show that environmental transmission appears like direct transmission in the case where the pathogen persists little time in the environment. Furthermore, we formulate conditions for the validity of this modeling approximation and we illustrate them numerically for the cases of cholera and influenza. According to our results based on recently published parameter estimates, the direct transmission approximation fails for both cholera and influenza. While environmental transmission is typically chosen over direct transmission in modeling cholera, this is not the case for influenza.

It is anticipated that penetration of renewable energy sources (RESs) in power systems will increase further in the next decades mainly due to environmental issues. In the long term of several decades, which we refer to in terms of the future grid (FG), balancing between supply and demand will become dependent on demand actions including demand response (DR) and energy storage. So far, FG feasibility studies have not considered these new demand-side developments for modelling future demand. In Australia, installed rooftop photovoltaic (PV) generation has been increasing significantly in recent years, and this is increasingly influence the nett load profile for FG feasibility studies. This paper proposes an aggregate nett load or demand model to be used at higher voltage levels considering the effect of rooftop PV, energy storage and DR for FG scenarios, which is inspired by the smart home concept. The proposed model is formulated as an optimization problem aiming at minimizing the electricity cost. As a case study, the effect of the load model is studied on the load profile, balancing and loadability of the Australian National Electricity Market in 2020 with the increased penetration of wind and solar generation., Comment: 11 pages, 6 figures, 3 Tables, submitted to IET Generation, Transmission & Distribution

This paper deals with the development of a new mathematical model that characterizes the structure-process interaction for a complex milling system. The structure is divided into a work piece and a machine part, which are represented by different models. While the machine dynamics is characterized by a standard multi-body system, the work piece is described as a linear thermo-elastic continuum. The coupling of both parts is carried out by an empirical process model permitting an estimate of heat and coupling forces occurring during milling. This work reports the derivation of the governing equations emphasizing the coupling and summarizes the numerical algorithms being applied to solve the coupled equation system. The results of numerical simulations that show the dynamics of the complex thermo-mechanical system are presented at the end.