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In this paper, we establish a general stochastic maximum principle for optimal control for systems described by a continuous-time Markov regime-switching stochastic recursive utilities model. The control domain is postulated not to be…
In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss due to the mismatch between the true model…
In this paper, we propose a general framework for optimal control measures, which follows the evolution of COVID-19 infection counts collected by Surveillance Units on a country level. We employ an autoregressive model that allows to…
We propose and study a new mathematical model of the human immunodeficiency virus (HIV). The main novelty is to consider that the antibody growth depends not only on the virus and on the antibodies concentration but also on the uninfected…
This paper is devoted to the study of the dynamic optimization of several controlled crowd motion models in the general planar settings, which is an application of a class of optimal control problems involving a general nonconvex sweeping…
The paper is concerned with a class of optimization problems for moving sets $t\mapsto\Omega(t)\subset\mathbb{R}^2$, motivated by the control of invasive biological populations. Assuming that the initial contaminated set $\Omega_0$ is…
Tuberculosis (TB) is among the main public health challenges in Burundi. The literature lacks mathematical models for key parameter estimates of TB transmission dynamics in Burundi. In this paper, the supectible-exposed-infected-recovered…
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
We consider a class of monotone systems in which the control signal multiplies the state. Among other applications, such bilinear systems can be used to model the evolutionary dynamics of HIV in the presence of combination drug therapy. For…
We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
This article considers the optimal control of the SIR model with both transmission and treatment uncertainty. It follows the model presented in Gatto and Schellhorn (2021). We make four significant improvements on the latter paper. First,…
We study an optimal control problem for a stochastic model of tumour growth with drug application. This model consists of three stochastic hyperbolic equations describing the evolution of tumour cells. It also includes two stochastic…
After the COVID-19 pandemic, we saw an increase in demand for epidemiological mathematical models. The goal of this work is to study the optimal control for an age-structured model as a strategy of quarantine of infected people, which is…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
In this paper we propose and study a spatial diffusion model for the control of anthracnose disease in a bounded domain. The model is a generalization of the one previously developed in [14]. We use the model to simulate two different types…
In this paper, a general stochastic model with controls applied at the moments when the random process hits the boundary of a given subset of the state set is proposed and studied. The general concept of the model is formulated and its…
A system of renewal equations on a graph provides a framework to describe the exploitation of a biological resource. In this context, we formulate an optimal control problem, prove the existence of an optimal control and ensure that the…
Optimal control problems reflecting the finding of effective quarantine strategies are considered for two control SEIR~type models describing the spread of the COVID-19 virus in the human population. The properties of the corresponding…
Simple ideas, endowed from the mathematical theory of control, are used in order to analyze in general grounds the human immune system. The general principles are minimization of the pathogen load and economy of resources. They should…