Related papers: Reliable optimal controls for SEIR models in epide…
In this paper, we derive a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. Our framework is actually much more general, and we treat optimal control problems for…
We consider optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. Using the sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems.…
The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…
We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…
Mathematical models are instrumental to forecast the spread of pathogens and to evaluate the effectiveness of non-pharmaceutical measures. A plethora of optimal strategies has been recently developed to minimize either the infected peak…
In this paper, we present a framework for solving continuous optimal control problems when the true system dynamics are approximated through an imperfect model. We derive a control strategy by applying Pontryagin's Minimum Principle to the…
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…
We develop a general theoretical framework for optimal probability density control on standard measure spaces, aimed at addressing large-scale multi-agent control problems. In particular, we establish a maximum principle (MP) for control…
Exact solutions of the SEIR epidemic model are derived, and various properties of solutions are obtained directly from the exact solution. In this paper Abel differential equations play an important role in establishing the exact solution…
In this article, the feasibility of using optimal control theory will be studied to develop control theoretic methods for personalized treatment of HCV patients. The mathematical model for HCV progression includes compartments for healthy…
We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
This paper revisits a longstanding problem of interest concerning the distributed control of an epidemic process on human contact networks. Due to the stochastic nature and combinatorial complexity of the problem, finding optimal policies…
Nowadays, epidemic models provide an appropriate tool for describing the propagation of biological viruses in human or animal populations, or rumours and other kinds of information in social networks and malware in both computer and ad hoc…
In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…
This paper is a survey on some recent aspects and developments in stochastic control. We discuss the two main historical approaches, Bellman's optimality principle and Pontryagin's maximum principle, and their modern exposition with…
We adapt a SEIRD differential model with asymptomatic population and Covid deaths, which we call SEAIRD, to simulate the evolution of COVID-19, and add a control function affecting both the diffusion of the virus and GDP, featuring all…
We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals,…
We study the impact of model parameter uncertainty on optimally mitigating the spread of epidemics. We capture the epidemic spreading process using a susceptible-infected-removed (SIR) epidemic model and consider testing for isolation as…
The relationship between epidemiology, mathematical modeling and computational tools allows to build and test theories on the development and battling of a disease. This PhD thesis is motivated by the study of epidemiological models applied…