Existence of Optimal Controls for a Bi-Level Optimal Control Problem

2013 ◽  
pp. 71-84 ◽  
Author(s):  
Dean A. Carlson
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Controls ◽  
Existence Of Optimal Controls

scholarly journals On linear-quadratic optimal control of implicit difference equations

2018 ◽  
Vol 36 (3) ◽  
pp. 779-833
Author(s):  
Daniel Bankmann ◽  
Matthias Voigt
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Difference Equations ◽  
Matrix Pencil ◽  
Spectral Structure ◽  
Optimal Controls ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control

Abstract In this work we investigate explicit and implicit difference equations and the corresponding infinite time horizon linear-quadratic optimal control problem. We derive conditions for feasibility of the optimal control problem as well as existence and uniqueness of optimal controls under certain weaker assumptions compared to the standard approaches in the literature which are using algebraic Riccati equations. To this end, we introduce and analyse a discrete-time Lur’e equation and a corresponding Kalman–Yakubovich–Popov (KYP) inequality. We show that solvability of the KYP inequality can be characterized via the spectral structure of a certain palindromic matrix pencil. The deflating subspaces of this pencil are finally used to construct solutions of the Lur’e equation. The results of this work are transferred from the continuous-time case. However, many additional technical difficulties arise in this context.

Optimal feedback control of stochastic McShane differential systems

1974 ◽  
Vol 11 (2) ◽  
pp. 302-309 ◽  
Author(s):  
N. U. Ahmed ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Parabolic Type ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Optimal Controls ◽  
Necessary Conditions For Optimality ◽  
Reduced Problem

In this paper, the optimal control problem of system described by stochastic McShane differential equations is considered. It is shown that this problem can be reduced to an equivalent optimal control problem of distributed parameter systems of parabolic type with controls appearing in the coefficients of the differential operator. Further, to this reduced problem, necessary conditions for optimality and an existence theorem for optimal controls are given.

scholarly journals Free terminal time optimal control problem for the treatment of HIV infection

2016 ◽  
Vol 6 (1) ◽  
pp. 33-51 ◽  
Author(s):  
Amine Hamdache ◽  
Smahane Saadi ◽  
Ilias Elmouki
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Hiv Infection ◽  
Control Problem ◽  
Time Optimal Control ◽  
Optimal Controls ◽  
Terminal Time ◽  
Time Optimal ◽  
Time Optimal Control Problem ◽  
Free Terminal Time

In this work, an optimal control approach is presented in order to propose an optimal therapy for the treatment HIV infection using a combination of two appropriate treatment strategies. The optimal treatment duration and the optimal medications amount are considered. The main objective of this study is to be able to maximize the benet based on number of healthy CD4+ T-cells and CTL immune cells and to minimize the infection level and the overall treatment cost while optimizing the duration of therapy. The free terminal time optimal control problem is formulated and the Pontryagin's maximum principle is employedto provide the explicit formulations of the optimal controls. The corresponding optimality system with the additional transversality condition for the terminal time is derived and solved numerically using an adapted iterative method with a Runge-Kutta fourth order scheme and a gradient method routine.

scholarly journals On an optimal control problem involving second order hyperbolic systems with boundary controls

1983 ◽  
Vol 27 (1) ◽  
pp. 139-148 ◽  
Author(s):  
K.G. Choo ◽  
K.L. Teo ◽  
Z.S. Wu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hyperbolic Systems ◽  
Sufficient Conditions ◽  
Second Order ◽  
Optimal Controls ◽  
Convergence Properties ◽  
Boundary Controls ◽  
Necessary And Sufficient

In this paper, we consider an optimal control problem involving second-order hyperbolic systems with boundary controls. Necessary and sufficient conditions are derived and a result on the existence of optimal controls is obtained. Also, a computational algorithm which generated minimizing sequences of controls is devised and the convergence properties of the algorithm are investigated.

Optimal feedback control of stochastic McShane differential systems

1974 ◽  
Vol 11 (02) ◽  
pp. 302-309
Author(s):  
N. U. Ahmed ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Parabolic Type ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Optimal Controls ◽  
Necessary Conditions For Optimality ◽  
Reduced Problem

In this paper, the optimal control problem of system described by stochastic McShane differential equations is considered. It is shown that this problem can be reduced to an equivalent optimal control problem of distributed parameter systems of parabolic type with controls appearing in the coefficients of the differential operator. Further, to this reduced problem, necessary conditions for optimality and an existence theorem for optimal controls are given.

scholarly journals Optimal control for a mathematical model for chemotherapy with pharmacometrics

2020 ◽  
Vol 15 ◽  
pp. 69
Author(s):  
Maciej Leszczyński ◽  
Urszula Ledzewicz ◽  
Heinz Schättler
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Cancer Chemotherapy ◽  
Drug Effects ◽  
Optimal Controls ◽  
Angiogenic Therapy ◽  
Single Drug ◽  
Qualitative Changes

An optimal control problem for an abstract mathematical model for cancer chemotherapy is considered. The dynamics is for a single drug and includes pharmacodynamic (PD) and pharmacokinetic (PK) models. The aim is to point out qualitative changes in the structures of optimal controls that occur as these pharmacometric models are varied. This concerns (i) changes in the PD-model for the effectiveness of the drug (e.g., between a linear log-kill term and a non-linear Michaelis-Menten type Emax-model) and (ii) the question how the incorporation of a mathematical model for the pharmacokinetics of the drug effects optimal controls. The general results will be illustrated and discussed in the framework of a mathematical model for anti-angiogenic therapy.

Optimal Control of Some Class of Imperfectly Known Control Systems

1966 ◽  
Vol 88 (2) ◽  
pp. 306-310 ◽  
Author(s):  
Masanao Aoki
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Systems ◽  
State Vector ◽  
Optimal Controls ◽  
Unknown Constant ◽  
Criterion Functions

The paper discusses optimal controls of processes with unknown constant parameters, where the processes are such that no measurements on the parameters are available during control periods. The general formulation of this optimal control problem is given for such systems, and it is shown that the formulation becomes quite simple when the equation for the observed-state vector is invertible, and that the problems of estimation and optimal controls cannot be separated for the class of problems discussed in the paper even when the systems are linear with quadratic criterion functions.

scholarly journals Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays

2021 ◽  
Vol 11 (1) ◽  
pp. 75-91
Author(s):  
Mohamed Elhia ◽  
Omar Balatif ◽  
Lahoucine Boujallal ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Time Delays ◽  
Control Strategies ◽  
Multiple Time ◽  
Optimal Controls ◽  
Loss To Follow Up ◽  
Tuberculosis Model

In this paper, we formulate an optimal control problem based on a tuberculosis model with multiple infectious compartments and time delays. In order to have a more realistic model that allows highlighting the role of detection, loss to follow-up and treatment in TB transmission, we propose an extension of the classical SEIR model by dividing infectious patients in the compartment (I) into three categories: undiagnosed infected (I), diagnosed patients who are under treatment (T) and diagnosed patients who are lost to follow-up (L). We incorporate in our model delays representing the incubation period and the time needed for treatment. We also introduce three control variables in our delayed system which represent prevention, detection and the efforts that prevent the failure of treatment. The purpose of our control strategies is to minimize the number of infected individuals and the cost of intervention. The existence of the optimal controls is investigated, and a characterization of the three controls is given using the Pontryagin's maximum principle with delays. To solve numerically the optimality system with delays, we present an adapted iterative method based on the iterative Forward-Backward Sweep Method (FBSM). Numerical simulations performed using Matlab are also provided. They indicate that the prevention control is the most effective one. To the best of our knowledge, it is the first work to apply optimal control theory to a TB model which considers infectious patients diagnosis, loss to follow-up phenomenon and multiple time delays.

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