Related papers: Time-optimal control strategies in SIR epidemic mo…
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
A formalism based on Pontryagin's maximum principle is applied to determine the time-optimal protocol that drives a general initial state to a target state by a Hamiltonian with limited control, i.e., there is a single control field with…
Although modeling studies are focused on the control of SIR-based systems describing epidemic data sets (particularly the COVID-19), few of them present a formal dynamic characterization in terms of equilibrium sets and stability. Such…
One of the most important branches of nonlinear control theory is the so-called sliding-mode. Its aim is the design of a (nonlinear) feedback law that brings and maintains the state trajectory of a dynamic system on a given sliding surface.…
This article considers the minimization of the total number of infected individuals over the course of an epidemic in which the rate of infectious contacts can be reduced by time-dependent nonpharmaceutical interventions. The societal and…
This paper considers optimal control problems defined by a monotone dynamical system, a monotone cost, and monotone constraints. We identify families of such problems for which the optimal solution is bang-ride, i.e., always operates on the…
Therapeutic strategies to correct an excessive immune response to pathogenic infection is investigated as an optimal control problem. The control problem is formulated around a four dimensional mathematical model describing the inflammatory…
The spread of an epidemic is often modeled by an SIR random process on a social network graph. The MinINF problem for optimal social distancing involves minimizing the expected number of infections, when we are allowed to break at most $B$…
This article treats optimal sparse control problems with multiple constraints defined at intermediate points of the time domain. For such problems with intermediate constraints, we first establish a new Pontryagin maximum principle that…
We investigate the time-optimal solution of the selective control of two uncoupled spin 1/2 particles. Using the Pontryagin Maximum Principle, we derive the global time-optimal pulses for two spins with different offsets. We show that the…
Time optimal control problems for some non-smooth systems in general form are considered. The non-smoothness is caused by singularity. It is proved that Pontryagin's maximum principle holds for at least one optimal relaxed control. Thus,…
We improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove…
We consider the design of external inputs to achieve a control objective on the opinions, represented by scalars, in a social network. The opinion dynamics follow a variant of the discrete-time Friedkin-Johnsen model. We first consider two…
We propose a simple SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two…
Motivated by the ongoing pandemic COVID-19, we propose a closed-loop framework that combines inference from testing data, learning the parameters of the dynamics and optimal resource allocation for controlling the spread of the…
In this paper, we propose a unified stochastic optimal control framework that integrates time-optimal control problems with classical stochastic optimal control formulations. Unlike conventional deterministic time-optimal control models,…
We consider a SIR model with vaccination strategy on a sparse configuration model random graph. We show the convergence of the system when the number of nodes grows and characterize the scaling limits. Then, we prove the existence of…
In this paper we address optimal control problems in which the system parameters follow a probability distribution, and the optimization is based on average performance. These problems, known as Riemann-Stieltjes optimal control or optimal…
In this paper we give a new approach to introduce switching strategies in a special class of optimal multiprocesses. Defined as the set of partitions of the time interval, switching strategies become the character of a classical control.…