scholarly journals Optimal control to limit the spread of COVID-19 in Italy

2021 ◽  
Author(s):  
Mohamed Abdelaziz Zaitri ◽  
◽  
Mohand Ouamer Bibi ◽  
Delfim F. M. Torres ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Theory ◽  
Control Problem ◽  
Data Transmission ◽  
Optimal Control Theory ◽  
Real Data ◽  
Type Model ◽  
Social Distancing ◽  
Treatment Measures

We apply optimal control theory to a generalized SEIR-type model. The proposed system has three controls, representing social distancing, preventive means, and treatment measures to combat the spread of the COVID-19 pandemic. We analyze such optimal control problem with respect to real data transmission in Italy. Our results show the appropriateness of the model, in particular with respect to the number of quarantined/hospitalized (confirmed and infected) and recovered individuals. Considering the Pontryagin controls, we show how in a perfect world one could have drastically diminish the number of susceptible, exposed, infected, quarantined/hospitalized, and death individuals, by increasing the population of insusceptible/protected.

scholarly journals CONSTRAINT ALGORITHM FOR EXTREMALS IN OPTIMAL CONTROL PROBLEMS

2009 ◽  
Vol 06 (07) ◽  
pp. 1221-1233 ◽  
Author(s):  
MARÍA BARBERO-LIÑÁN ◽  
MIGUEL C. MUÑOZ-LECANDA
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Theory ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Control Problems ◽  
Affine System

A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. The algorithm must be run twice so as to obtain suitable sets that once projected must be compared. Apart from the design of this general algorithm useful for any optimal control problem, it is shown how to classify the set of extremals and, in particular, how to characterize the strict abnormality. An example of strict abnormal extremal for a particular control-affine system is also given.

Numerical Solution of a Hyperbolic-parabolic System by Splitting Methods and Optimal Control Approaches

2001 ◽  
Vol 7 (3) ◽  
pp. 193-207
Author(s):  
V.I. Agoshkov ◽  
E.A. Botvinovsky
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Theory ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Iterative Process ◽  
Splitting Method ◽  
Splitting Methods ◽  
New Approach ◽  
Well Posed

AbstractA new approach has been developed for solving the tide dynamics problem, based on the splitting methods and the optimal control theory. We first apply the classical splitting method for solving the problem. Then we use the optimal control theory approaches to the system of equations obtained after the splitting. An optimal control problem has been formulated for realizing a splitting method step. We prove that the optimal control problem is well-posed and we propose an iterative process of the minimization problem. The results of the numerical experiments are presented.

scholarly journals Optimal Control for a COVID-19 Model Accounting for Symptomatic and Asymptomatic

2020 ◽  
Vol 8 (1) ◽  
pp. 168-179
Author(s):  
Jead M. Macalisang ◽  
Mark L. Caay ◽  
Jayrold P. Arcede ◽  
Randy L. Caga-anan
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Medical Care ◽  
Optimal Control Theory ◽  
Comparable Result ◽  
Type Model ◽  
Hospital Beds ◽  
Transmission Reduction ◽  
Bed Capacity ◽  
The Government

AbstractBuilding on an SEIR-type model of COVID-19 where the infecteds are further divided into symptomatic and asymptomatic, a system incorporating the various possible interventions is formulated. Interventions, also referred to as controls, include transmission reduction (e.g., lockdown, social distancing, barrier gestures); testing/isolation on the exposed, symptomatic and asymptomatic compartments; and medical controls such as enhancing patients’ medical care and increasing bed capacity. By considering the government’s capacity, the best strategies for implementing the controls were obtained using optimal control theory. Results show that, if all the controls are to be used, the more able the government is, the more it should implement transmission reduction, testing, and enhancing patients’ medical care without increasing hospital beds. However, if the government finds it very difficult to implement the controls for economic reasons, the best approach is to increase the hospital beds. Moreover, among the testing/isolation controls, testing/isolation in the exposed compartment is the least needed when there is significant transmission reduction control. Surprisingly, when there is no transmission reduction control, testing/isolation in the exposed should be optimal. Testing/isolation in the exposed could seemingly replace the transmission reduction control to yield a comparable result to that when the transmission reduction control is being implemented.

Some Sufficiency Conditions for Pareto-Optimal Control

1973 ◽  
Vol 95 (4) ◽  
pp. 356-361 ◽  
Author(s):  
G. Leitmann ◽  
W. Schmitendorf
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pareto Optimality ◽  
Optimal Control Theory ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Pareto Optimal ◽  
Vector Valued ◽  
Sufficiency Conditions

We consider the optimal control problem with vector-valued criterion (including cooperative games) and seek Pareto-optimal (noninferior) solutions. Scalarization results, together with modified sufficiency theorems from optimal control theory, are used to deduce sufficient conditions for Pareto-optimality. The utilization of these conditions is illustrated by various examples.

Adjoint-Based Optimization Procedure for Active Vibration Control of Nonlinear Mechanical Systems

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Carmine M. Pappalardo ◽  
Domenico Guida
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Control Problem ◽  
Numerical Solution ◽  
Optimal Control Theory ◽  
Numerical Procedure ◽  
Nonlinear Optimal Control ◽  
Open Loop ◽  
Adjoint Equations ◽  
Loop Control

In this paper, a new computational algorithm for the numerical solution of the adjoint equations for the nonlinear optimal control problem is introduced. To this end, the main features of the optimal control theory are briefly reviewed and effectively employed to derive the adjoint equations for the active control of a mechanical system forced by external excitations. A general nonlinear formulation of the cost functional is assumed, and a feedforward (open-loop) control scheme is considered in the analytical structure of the control architecture. By doing so, the adjoint equations resulting from the optimal control theory enter into the formulation of a nonlinear differential-algebraic two-point boundary value problem, which mathematically describes the solution of the motion control problem under consideration. For the numerical solution of the problem at hand, an adjoint-based control optimization computational procedure is developed in this work to effectively and efficiently compute a nonlinear optimal control policy. A numerical example is provided in the paper to show the principal analytical aspects of the adjoint method. In particular, the feasibility and the effectiveness of the proposed adjoint-based numerical procedure are demonstrated for the reduction of the mechanical vibrations of a nonlinear two degrees-of-freedom dynamical system.

scholarly journals Optimal control theory with general constraints

1981 ◽  
Vol 23 (2) ◽  
pp. 115-126 ◽  
Author(s):  
John M. Blatt
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Time Dependent ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
General Constraints ◽  
Elementary Methods ◽  
And Control

AbstractWe consider an optimal control problem with, possibly time-dependent, constraints on state and control variables, jointly. Using only elementary methods, we derive a sufficient condition for optimality. Although phrased in terms reminiscent of the necessary condition of Pontryagin, the sufficient condition is logically independent, as can be shown by a simple example.

Optimal Control of Fractional Order COVID-19 Epidemic Spreading in Japan and India 2020

2020 ◽  
Vol 15 (04) ◽  
pp. 207-236 ◽  
Author(s):  
Meghadri Das ◽  
G. P. Samanta
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Incomplete Information ◽  
Fractional Order ◽  
Compartmental Model ◽  
Transmission Dynamics ◽  
Epidemic Spreading ◽  
Social Distancing ◽  
First Case

In Japan, the first case of Coronavirus disease 2019 (COVID-19) was reported on 15th January 2020. In India, on 30th January 2020, the first case of COVID-19 in India was reported in Kerala and the number of reported cases has increased rapidly. The main purpose of this work is to study numerically the epidemic peak for COVID-19 disease along with transmission dynamics of COVID-19 in Japan and India 2020. Taking into account the uncertainty due to the incomplete information about the coronavirus (COVID-19), we have taken the Susceptible-Asymptomatic-Infectious-Recovered (SAIR) compartmental model under fractional order framework for our study. We have also studied the effects of fractional order along with other parameters in transfer dynamics and epidemic peak control for both the countries. An optimal control problem has been studied by controlling social distancing parameter.

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