scholarly journals Optimal Control of Virus Spread under Different Conditions of Resources Limitations

Information ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 214
Author(s):  
Paolo Di Giamberardino ◽  
Daniela Iacoviello
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Virus Spread ◽  
Human Virus ◽  
Positive Diagnosis ◽  
Control Actions ◽  
The People ◽  
Different Types ◽  
The Cost ◽  
Instantaneous Control

The paper addresses the problem of human virus spread reduction when the resources for the control actions are somehow limited. This kind of problem can be successfully solved in the framework of the optimal control theory, where the best solution, which minimizes a cost function while satisfying input constraints, can be provided. The problem is formulated in this contest for the case of the HIV/AIDS virus, making use of a model that considers two classes of susceptible subjects, the wise people and the people with incautious behaviours, and three classes of infected, the ones still not aware of their status, the pre-AIDS patients and the AIDS ones; the control actions are represented by an information campaign, to reduce the category of subjects with unwise behaviour, a test campaign, to reduce the number of subjects not aware of having the virus, and the medication on patients with a positive diagnosis. The cost function considered aims at reducing patients with positive diagnosis using as less resources as possible. Four different types of resources bounds are considered, divided into two classes: limitations on the instantaneous control and fixed total budgets. The optimal solutions are numerically computed, and the results of simulations performed are illustrated and compared to put in evidence the different behaviours of the control actions.

LEARNING AND RECOGNITION OF HUMAN ACTIONS USING OPTIMAL CONTROL PRIMITIVES

2009 ◽  
Vol 06 (03) ◽  
pp. 459-479
Author(s):  
SUMITRA GANESH ◽  
RUZENA BAJCSY
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Estimation Method ◽  
Nonlinear Least Squares ◽  
Performance Criterion ◽  
Human Motion ◽  
Human Actions ◽  
Mode Estimation ◽  
Nonlinear Least Squares Problem ◽  
The Cost

We propose a unified approach for recognition and learning of human actions, based on an optimal control model of human motion. In this model, the goals and preferences of the agent engaged in a particular action are encapsulated as a cost function or performance criterion, that is optimized to yield the details of the movement. The cost function is a compact, intuitive and flexible representation of the action. A parameterized form of the cost function is considered, wherein the structure reflects the goals of the actions, and the parameters determine the relative weighting of different terms. We show how the cost function parameters can be estimated from data by solving a nonlinear least squares problem. The parameter estimation method is tested on motion capture data for two different reaching actions and six different subjects. We show that the problem of action recognition in the context of this representation is similar to that of mode estimation in a hybrid system and can be solved using a particle filter if a receding horizon formulation of the optimal controller is adopted. We use the proposed approach to recognize different reaching actions from the 3D hand trajectory of subjects.

scholarly journals An Efficient Therapy Strategy under a Novel HIV Model

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Chunming Zhang ◽  
Xiaofan Yang ◽  
Wanping Liu ◽  
Lu-Xing Yang
Keyword(s):  
Optimal Control ◽  
Human Immunodeficiency Virus ◽  
Immune System ◽  
Virus Spread ◽  
Hiv Model ◽  
Hiv Virus ◽  
Therapy Strategy ◽  
Spread Model ◽  
Immunodeficiency Virus ◽  
The Cost

By incorporating the chemotherapy into a previous model describing the interaction of the immune system with the human immunodeficiency virus (HIV), this paper proposes a novel HIV virus spread model with control variables. Our goal is to maximize the number of healthy cells and, meanwhile, to minimize the cost of chemotherapy. In this context, the existence of an optimal control is proved. Experimental results show that, under this model, the spread of HIV virus can be controlled effectively.

scholarly journals Inverse KKT: Learning cost functions of manipulation tasks from demonstrations

2017 ◽  
Vol 36 (13-14) ◽  
pp. 1474-1488 ◽  
Author(s):  
Peter Englert ◽  
Ngo Anh Vien ◽  
Marc Toussaint
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Cost Functions ◽  
Quadratic Program ◽  
Relevant Task ◽  
Kernel Hilbert Spaces ◽  
The Cost ◽  
Linear Parameterization

Inverse optimal control (IOC) assumes that demonstrations are the solution to an optimal control problem with unknown underlying costs, and extracts parameters of these underlying costs. We propose the framework of inverse Karush–Kuhn–Tucker (KKT), which assumes that the demonstrations fulfill the KKT conditions of an unknown underlying constrained optimization problem, and extracts parameters of this underlying problem. Using this we can exploit the latter to extract the relevant task spaces and parameters of a cost function for skills that involve contacts. For a typical linear parameterization of cost functions this reduces to a quadratic program, ensuring guaranteed and very efficient convergence, but we can deal also with arbitrary non-linear parameterizations of cost functions. We also present a non-parametric variant of inverse KKT that represents the cost function as a functional in reproducing kernel Hilbert spaces. The aim of our approach is to push learning from demonstration to more complex manipulation scenarios that include the interaction with objects and therefore the realization of contacts/constraints within the motion. We demonstrate the approach on manipulation tasks such as sliding a box, closing a drawer and opening a door.

scholarly journals The reserve of joint torque determines movement coordination

2021 ◽  
Author(s):  
Germain Faity ◽  
Denis Mottet ◽  
Simon Pla ◽  
Jérôme Froger
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Degrees Of Freedom ◽  
Minimum Cost ◽  
Joint Torque ◽  
Movement Coordination ◽  
Trunk Motion ◽  
Additional Load ◽  
The Cost ◽  
Healthy Participants

AbstractHumans coordinate biomechanical degrees of freedom to perform tasks at minimum cost. When reaching a target from a seated position, the trunk-arm-forearm coordination moves the hand to the well-defined spatial goal, while typically minimising hand jerk and trunk motion. However, due to fatigue or stroke, people visibly move the trunk more, and it is unclear what cost can account for this. Here we show that people recruit their trunk when the torque at the shoulder is too close to the maximum. We asked 26 healthy participants to reach a target while seated and we found that the trunk contribution to hand displacement increases from 11% to 27% when an additional load is handled. By flexing and rotating the trunk, participants spontaneously increase the reserve of anti-gravitational torque at the shoulder from 25% to 40% of maximal voluntary torque. Our findings provide hints on how to include the reserve of torque in the cost function of optimal control models of human coordination in healthy fatigued persons or in stroke victims.

New Nonlinear Observer Design With Application to Electrostatic Micro-Actuators

2005 ◽  
Author(s):  
Venkat Durbha ◽  
S. N. Balakrishnan
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Correction Term ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Optimal Feedback Control ◽  
Actuator Dynamics ◽  
One Dimensional ◽  
Practical Applications ◽  
The Cost

In many practical applications it is not possible to measure all the states required to control the system. In such instances observer/filter is used to give a good estimate of the states of the system. The objective of the observer is to estimate the states such that the error between the actual and computed measurements goes to zero and obtain the “best” estimates of the states of a given system. In the current study a new nonlinear observer structure is proposed. The development of the observer is based on optimal control theory. A cost function is defined in terms of the measurement residual and the magnitude of correction term. The observer gains are obtained by minimizing the cost function with respect to the magnitude of corrections. The proposed observer is used to estimate the states of a one-dimensional electrostatic micro-actuator. The states of the actuator dynamics are, charge on the capacitor plates, the distance between the plates and the relative velocity between the plates. The regulation of the actuator states to desired trajectories is achieved through optimal control based state feedback. However in practice it is very difficult to measure the relative position and velocity of the plates. In this paper optimal feedback control based on the state estimates provided by the observer is used to regulate the actuator states to the desired location.

scholarly journals Optimal control techniques based on infection age for the study of the COVID-19 epidemic

2020 ◽  
Vol 15 ◽  
pp. 48
Author(s):  
J. Frédéric Bonnans ◽  
Justina Gianatti
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Numerical Experiments ◽  
Age Classes ◽  
Control Techniques ◽  
Infection Age ◽  
Death Toll ◽  
Infected Population ◽  
The Future ◽  
The Cost

We propose a model for the COVID-19 epidemic where the population is partitioned into classes corresponding to ages (that remain constant during the epidemic). The main feature is to take into account the infection age of the infected population. This allows to better simulate the infection propagation that crucially depend on the infection age. We discuss how to estimate the coefficients from data available in the future, and introduce a confinement variable as control. The cost function is a compromise between a confinement term, the hospitalization peak and the death toll. Our numerical experiments allow to evaluate the interest of confinement varying with age classes.

scholarly journals OPP approach for multi degree of freedom robotic arm Based on Kinematics and Dynamics of Robot

2015 ◽  
Vol 4 (4) ◽  
pp. 284
Author(s):  
Praneet Dutta ◽  
Rashmi Ranjan Das ◽  
Rupali Mathur ◽  
Deepika Rani Sona
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Minimum Principle ◽  
Equations Of Motion ◽  
Optimal Path ◽  
Minimum Cost ◽  
Simulation Software ◽  
Degree Of Freedom ◽  
The Cost ◽  
Joint Velocity

This paper deals with the trajectory and path generation of the industrial manipulator. The trajectory is obtained using the equations of motion and also the optimal path planning (OPP) approach under kinodynamic constraints. The optimal control problem is defined for the minimum cost function and to obtain the necessary conditions. Here we have used pontrygain’s minimum principle to obtain the limiting value of joint angle and also  the joint velocity and torque. In this paper we have used the “Two degree of freedom (DOF) manipulator” for analysis and designing the optimal control for multi link and multi degree of freedom manipulator. For analysis purposes,  simulation software has been used to formulate the trajectory and minimize the cost function involved.

scholarly journals The reserve of joint torque determines movement coordination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Germain Faity ◽  
Denis Mottet ◽  
Simon Pla ◽  
Jérôme Froger
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Degrees Of Freedom ◽  
Minimum Cost ◽  
Joint Torque ◽  
Movement Coordination ◽  
Trunk Motion ◽  
Additional Load ◽  
The Cost ◽  
Healthy Participants

AbstractHumans coordinate biomechanical degrees of freedom to perform tasks at minimum cost. When reaching a target from a seated position, the trunk-arm-forearm coordination moves the hand to the well-defined spatial goal, while typically minimising hand jerk and trunk motion. However, due to fatigue or stroke, people visibly move the trunk more, and it is unclear what cost can account for this. Here we show that people recruit their trunk when the torque at the shoulder is too close to the maximum. We asked 26 healthy participants to reach a target while seated and we found that the trunk contribution to hand displacement increases from 11 to 27% when an additional load is handled. By flexing and rotating the trunk, participants spontaneously increase the reserve of anti-gravitational torque at the shoulder from 25 to 40% of maximal voluntary torque. Our findings provide hints on how to include the reserve of torque in the cost function of optimal control models of human coordination in healthy fatigued persons or in stroke victims.

On the existence of piecewise continuous optimal controls

1977 ◽  
Vol 20 (1) ◽  
pp. 31-37 ◽  
Author(s):  
E. S. Noussair
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Maximum Rate ◽  
Optimal Controls ◽  
Control Variables ◽  
Piecewise Continuous ◽  
The Cost

AbstractExistence of piecewise optimal control is proved when the cost function includes one or both of (a) a cost of sudden switching (discontinuity) of control variables, and (b) a cost associated with the maximum rate of variation of the control over segments of the path for which the control is continuous.

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