On the local structure of time-optimal controls in R3

1985 ◽  
Author(s):  
Heinz Schaettler
Keyword(s):  
Local Structure ◽  
Optimal Controls ◽  
Time Optimal

scholarly journals Time-Optimal Control for Semilinear Stochastic Functional Differential Equations with Delays

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1956
Author(s):  
Yong Han Kang ◽  
Jin-Mun Jeong
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Time Optimal Control ◽  
Optimal Controls ◽  
Stochastic Functional Differential Equations ◽  
Time Optimal ◽  
Target Set ◽  
Functional Differential ◽  
Stochastic Functional

The purpose of this paper is to find the time-optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is to construct a fundamental solution for corresponding linear systems and establish variations of a constant formula of solutions for given stochastic equations. The existence result of time-optimal controls for one point target set governed by the given semilinear stochastic equation is also established.

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 the existence of time optimal controls for linear evolution equations

2007 ◽  
Vol 8 (4) ◽  
pp. 925-941 ◽  
Author(s):  
Kim Dang Phung ◽  
◽  
Gengsheng Wang ◽  
Xu Zhang ◽  
◽  
...  
Keyword(s):  
Evolution Equations ◽  
Optimal Controls ◽  
Linear Evolution ◽  
Time Optimal ◽  
Linear Evolution Equations

The Adjoint Gradient Method for Time-Optimal Control of a Moon Landing: Ascent, Descent, and Abort

2020 ◽  
Author(s):  
Philipp Eichmeir ◽  
Karin Nachbagauer ◽  
Wolfgang Steiner
Keyword(s):  
Optimal Solution ◽  
Initial Guess ◽  
Optimal Controls ◽  
Novel Approach ◽  
End Conditions ◽  
Time Optimal ◽  
Gradient Based ◽  
Adjoint Gradient ◽  
Moon Landing

Abstract This article illustrates a novel approach for the determination of time-optimal controls for dynamic systems under observance of end conditions. Such problems arise in robotics, e.g. if the control of a robot has to be designed such that the time for a rest-to-rest maneuver becomes a minimum. So far, such problems have been considered as two-point boundary value problems, which are hard to solve and require an initial guess close to the optimal solution. The aim of this contribution is the development of an iterative, gradient based solution strategy for solving such problems. As an example, a Moon-landing as in the Apollo program, will be considered. In detail, we discuss the ascent, descent and abort maneuvers of the Apollo Lunar Excursion Module (LEM) to and from the Moon’s surface in minimum time. The goal is to find the control of the thrust nozzle of the LEM to minimize the final time.

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