scholarly journals Optimal Control Applied to Vaccination and Testing Policies for COVID-19

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3100
Author(s):  
Alberto Olivares ◽  
Ernesto Staffetti
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Optimal Control Problems ◽  
Vaccination Rate ◽  
Control Problems ◽  
Vaccination Programs ◽  
Infected People ◽  
Control Approach ◽  
Algebraic Constraints ◽  
The Cost

In this paper, several policies for controlling the spread of SARS-CoV-2 are determined under the assumption that a limited number of effective COVID-19 vaccines and tests are available. These policies are calculated for different vaccination scenarios representing vaccine supply and administration restrictions, plus their impacts on the disease transmission are analyzed. The policies are determined by solving optimal control problems of a compartmental epidemic model, in which the control variables are the vaccination rate and the testing rate for the detection of asymptomatic infected people. A combination of the proportion of threatened and deceased people together with the cost of vaccination of susceptible people, and detection of asymptomatic infected people, is taken as the objective functional to be minimized, whereas different types of algebraic constraints are considered to represent several vaccination scenarios. A direct transcription method is employed to solve these optimal control problems. More specifically, the Hermite–Simpson collocation technique is used. The results of the numerical experiments show that the optimal control approach offers healthcare system managers a helpful resource for designing vaccination programs and testing plans to prevent COVID-19 transmission.

High-order relaxation approaches for adjoint-based optimal control problems governed by nonlinear hyperbolic systems of conservation laws

2016 ◽  
Vol 24 (1) ◽  
Author(s):  
Elimboto M. Yohana ◽  
Mapundi K. Banda
Keyword(s):  
Optimal Control ◽  
Conservation Laws ◽  
Optimal Control Problems ◽  
Initial Conditions ◽  
Hyperbolic Systems ◽  
Control Problems ◽  
Computational Investigation ◽  
Backward Problem ◽  
Systems Of Conservation Laws ◽  
The Cost

AbstractA computational investigation of optimal control problems which are constrained by hyperbolic systems of conservation laws is presented. The general framework is to employ the adjoint-based optimization to minimize the cost functional of matching-type between the optimal and the target solution. Extension of the numerical schemes to second-order accuracy for systems for the forward and backward problem are applied. In addition a comparative study of two relaxation approaches as solvers for hyperbolic systems is undertaken. In particular optimal control of the 1-D Riemann problem of Euler equations of gas dynamics is studied. The initial values are used as control parameters. The numerical flow obtained by optimal initial conditions matches accurately with observations.

Time-optimal control of multiple unmanned aerial vehicles with human control input

2019 ◽  
Vol 12 (1) ◽  
pp. 138-152 ◽  
Author(s):  
Tao Han ◽  
Bo Xiao ◽  
Xi-Sheng Zhan ◽  
Jie Wu ◽  
Hongling Gao
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Minimum Principle ◽  
Time Optimal Control ◽  
Control Problems ◽  
Control Input ◽  
Content Type ◽  
Human Control ◽  
Time Optimal ◽  
The Cost

Purpose The purpose of this paper is to investigate time-optimal control problems for multiple unmanned aerial vehicle (UAV) systems to achieve predefined flying shape. Design/methodology/approach Two time-optimal protocols are proposed for the situations with or without human control input, respectively. Then, Pontryagin’s minimum principle approach is applied to deal with the time-optimal control problems for UAV systems, where the cost function, the initial and terminal conditions are given in advance. Moreover, necessary conditions are derived to ensure that the given performance index is optimal. Findings The effectiveness of the obtained time-optimal control protocols is verified by two contrastive numerical simulation examples. Consequently, the proposed protocols can successfully achieve the prescribed flying shape. Originality/value This paper proposes a solution to solve the time-optimal control problems for multiple UAV systems to achieve predefined flying shape.

scholarly journals Solution to Singular Optimal Control by Backward Differential Flow

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Jinghao Zhu ◽  
Shangrui Zhao ◽  
Guohua Liu
Keyword(s):  
Optimal Control ◽  
Global Optimization ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Variational Problems ◽  
Equivalent Transformation ◽  
Control Problems ◽  
Singular Optimal Control ◽  
Differential Flow ◽  
The Cost

This paper presents a backward differential flow for solving singular optimal control problems. By using Krotov equivalent transformation, the cost functional is converted to a class of global optimization problems. Some properties of the flow are given to reveal the significant relationship between the dynamic of the flow and the geometry of the feasible set. The proposed method is also used in solving a class of variational problems. Some examples are illustrated.

Parametric optimal control problems with weighted L 1-norm in the cost function

2010 ◽  
Vol 44 (4) ◽  
pp. 179-190 ◽  
Author(s):  
O. I. Kostyukova ◽  
E. A. Kostina ◽  
N. M. Fedortsova
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Parametric Optimal Control ◽  
The Cost

Numerical solution of time-delay optimal control problems by the operational matrix based on Hartley series

2021 ◽  
pp. 014233122110533
Author(s):  
Mahmood Dadkhah ◽  
Kamal Mamehrashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Numerical Technique ◽  
Operational Matrix ◽  
Main Idea ◽  
Control Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
The Cost ◽  
And Control

In this paper, a numerical technique based on the Hartley series for solving a class of time-delayed optimal control problems (TDOCPs) is introduced. The main idea is converting such TDOCPs into a system of algebraic equations. Thus, we first expand the state and control variables in terms of the Hartley series with undetermined coefficients. The delay terms in the problem under consideration are expanded in terms of the Hartley series. Applying the operational matrices of the Hartley series including integration, differentiation, dual, product, delay, and substituting the estimated functions into the cost function, the given TDOCP is reduced to a system of algebraic equations to be solved. The convergence of the proposed method is extensively investigated. At last, the precision and applicability of the proposed method is studied through different types of numerical examples.

scholarly journals Linear quadratic stochastic optimal control problems with operator coefficients: open-loop solutions

2019 ◽  
Vol 25 ◽  
pp. 17 ◽  
Author(s):  
Qingmeng Wei ◽  
Jiongmin Yong ◽  
Zhiyong Yu
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Control Problems ◽  
Linear Quadratic ◽  
Cost Functional ◽  
The Cost

An optimal control problem is considered for linear stochastic differential equations with quadratic cost functional. The coefficients of the state equation and the weights in the cost functional are bounded operators on the spaces of square integrable random variables. The main motivation of our study is linear quadratic (LQ, for short) optimal control problems for mean-field stochastic differential equations. Open-loop solvability of the problem is characterized as the solvability of a system of linear coupled forward-backward stochastic differential equations (FBSDE, for short) with operator coefficients, together with a convexity condition for the cost functional. Under proper conditions, the well-posedness of such an FBSDE, which leads to the existence of an open-loop optimal control, is established. Finally, as applications of our main results, a general mean-field LQ control problem and a concrete mean-variance portfolio selection problem in the open-loop case are solved.

Optimal control of nonlinear systems with dynamic programming

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Isaac Tawiah ◽  
Yinglei Song
Keyword(s):  
Optimal Control ◽  
Optimization Problem ◽  
Optimal Control Problems ◽  
Optimal Solution ◽  
Functional Approach ◽  
Equality Constraints ◽  
Control Problems ◽  
Iterative Approach ◽  
Simulation Results ◽  
The Cost

Abstract In this paper, a generalized technique for solving a class of nonlinear optimal control problems is proposed. The optimization problem is formulated based on the cost-to-go functional approach and the optimal solution can be obtained by Bellman’s technique. Specifically, a continuous nonlinear system is first discretized and a set of equality constraints can be obtained from the discretization. We show that, under a certain condition, the optimal solution of a problem in this class can be approximated by a solution of the set of equality constraints within any precision and the system is guaranteed to be stable under a control signal obtained from the solution. An iterative approach is then applied to numerically solve the set of equality constraints. The technique is tested on a nonlinear control problem from the class and simulation results show that the approach is not only effective but also leads to a fast convergence and accurate optimal solution.

scholarly journals Optimal control problems in transport dynamics

2017 ◽  
Vol 27 (03) ◽  
pp. 427-451 ◽  
Author(s):  
Mattia Bongini ◽  
Giuseppe Buttazzo
Keyword(s):  
Optimal Control ◽  
Population Dynamics ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Unmanned Aerial Vehicles ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Transport Dynamics ◽  
Aerial Vehicles ◽  
The Cost

In the present paper, we deal with an optimal control problem related to a model in population dynamics; more precisely, the goal is to modify the behavior of a given density of individuals via another population of agents interacting with the first. The cost functional to be minimized to determine the dynamics of the second population takes into account the desired target or configuration to be reached as well as the quantity of control agents. Several applications may fall into this framework, as for instance driving a mass of pedestrian in (or out of) a certain location; influencing the stock market by acting on a small quantity of key investors; controlling a swarm of unmanned aerial vehicles by means of few piloted drones.

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