An extremal shift method for control of HIV infection dynamics

AbstractOptimal control problems for mathematical models describing HIV infection dynamics in a human body are considered in the paper. An overview of current approaches to solution of control problems for models of HIV dynamics is presented for techniques related to construction of optimal programme (open loop) or positional (feedback) controls for various criteria of control process quality and is based on the Pontryagin’s maximum principle and the Bellman’s theory of dynamic programming, respectively. In the framework of the theory of positional differential games of Krasovskii, there are constructive and efficient methods of synthesis of controls for different classes of dynamical systems. In this paper we present a formalization of a control problem for HIV infection considered as a corresponding positional differential game. The control algorithm based on the method of extremal shift is applied to the ODEs model of HIV infection. The numerical implementation of the extremal shift method is developed to construct the control taking the system to a neighbourhood of a given trajectory using the information on the dynamics of the guides or leaders.

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Stochastic Model for Langerhans Cells and HIV Dynamics In Vivo

ISRN Applied Mathematics ◽

10.1155/2014/594617 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Waema R. Mbogo ◽

Livingstone S. Luboobi ◽

John W. Odhiambo

Keyword(s):

Hiv Infection ◽

Stochastic Model ◽

Langerhans Cells ◽

Sensitivity Analyses ◽

Viral Dynamics ◽

Human Immune System ◽

Hiv Dynamics ◽

Infection Dynamics ◽

Human Immune

Many aspects of the complex interaction between HIV and the human immune system remain elusive. Our objective is to study these interactions, focusing on the specific roles of Langerhans cells (LCs) in HIV infection. In patients infected with HIV, a large amount of virus is associated with LCs in lymphoid tissue. To assess the influence of LCs on HIV viral dynamics during antiretroviral therapy, we present and analyse a stochastic model describing the dynamics of HIV, CD4+ T cells, and LCs interactions under therapeutic intervention in vivo and show that LCs play an important role in enhancing and spreading initial HIV infection. We perform sensitivity analyses on the model to determine which parameters and/or which interaction mechanisms strongly affect infection dynamics.

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On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2019057 ◽

2020 ◽

Vol 26 ◽

pp. 41

Author(s):

Tianxiao Wang

Keyword(s):

Optimal Control ◽

Closed Loop ◽

Optimal Control Problems ◽

Mean Field ◽

Open Loop ◽

Time Inconsistency ◽

Control Problems ◽

Linear Quadratic ◽

Linear Quadratic Optimal Control ◽

Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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Design and control of 2-DoF joystick using MR-fluid rotary actuator

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x211063947 ◽

2021 ◽

pp. 1045389X2110639

Author(s):

Bao Tri Diep ◽

Quoc Hung Nguyen ◽

Thanh Danh Le

Keyword(s):

Pid Controller ◽

Force Feedback ◽

Control Method ◽

Open Loop ◽

Friction Torque ◽

Feedback Controls ◽

Loop Control ◽

Fuzzy Logic Algorithm ◽

Experimental Apparatus ◽

Close Loop Control

The purpose of this paper is to design a control algorithm for a 2-DoF rotary joystick model. Firstly, the structure of the joystick, which composes of two magneto-rheological fluid actuators (shorten MRFA) with optimal configuration coupled perpendicularly by the gimbal mechanism to generate the friction torque for each independent rotary movement, is introduced. The control strategy of the designed joystick is then suggested. Really, because of two independent rotary movements, it is necessary to design two corresponding controllers. Due to hysteresis and nonlinear dynamic characteristics of the MRFA, controllers based an accurate dynamic model are difficult to realize. Hence, to release this issue, the proposed controller (named self-turning fuzzy controllers-STFC) will be built through the fuzzy logic algorithm in which the parameters of controllers are learned and trained online by Levenberg-Marquardt training algorithm. Finally, an experimental apparatus will be constructed to assess the effectiveness of the force feedback controls. Herein, three experimental cases are performed to compare the control performance of open-loop and close-loop control method, where the former is done through relationship between the force at the knob and the current supplied to coil while the latter is realized based on the proposed controller and PID controller. The experimental results provide strongly the ability of the proposed controller, meaning that the STFC is robust and tracks well the desirable force with high accuracy compared with both the PID controller and the open-loop control method.

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Numerical Algorithms For State-Linear Optimal Impulsive Control Problems Based On Feedback Necessary Optimality Conditions

Cybernetics and Physics ◽

10.35470/2226-4116-2020-9-3-152-158 ◽

2020 ◽

pp. 152-158

Author(s):

Stepan Sorokin ◽

Maxim Staritsyn

Keyword(s):

Optimality Conditions ◽

Impulsive Control ◽

Numerical Algorithms ◽

Necessary Optimality Conditions ◽

Maximum Principles ◽

Control Problems ◽

Impulsive Systems ◽

Feedback Controls ◽

Non Local ◽

Optimal Impulsive Control

We propose and compare three numeric algorithms for optimal control of state-linear impulsive systems. The algorithms rely on the standard transformation of impulsive control problems through the discontinuous time rescaling, and the so-called “feedback”, direct and dual, maximum principles. The feedback maximum principles are variational necessary optimality conditions operating with feedback controls, which are designed through the usual constructions of the Pontryagin’s Maximum Principle (PMP); though these optimality conditions are formulated completely in the formalism of PMP, they essentially strengthen it. All the algorithms are non-local in the sense that they are aimed at improving non-optimal extrema of PMP (local minima), and, therefore, show the potential of global optimization.

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