scholarly journals Time-optimal control of infinite order hyperbolic systems with time delays

2009 ◽  
Vol 19 (4) ◽  
pp. 597-608 ◽  
Author(s):  
Adam Kowalewski
Keyword(s):  
Optimal Control ◽  
Time Delays ◽  
Infinite Order ◽  
Hyperbolic Systems ◽  
Integral Form ◽  
Adjoint System ◽  
Time Optimal Control ◽  
Optimal Controls ◽  
State Equations ◽  
Time Optimal

Time-optimal control of infinite order hyperbolic systems with time delaysIn this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular properties of optimal control are discussed.

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 Optimality Conditions for Infinite Order Distributed Parabolic Systems with Multiple Time Delays Given in Integral Form

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Bahaa G. M.
Keyword(s):  
Optimality Conditions ◽  
Time Delays ◽  
Infinite Order ◽  
Neumann Boundary ◽  
Integral Form ◽  
Parabolic Systems ◽  
Multiple Time ◽  
State Equations ◽  
Multiple Time Delays ◽  
Performance Functional

The optimal boundary control problem for (n×n) infinite order distributed parabolic systems with multiple time delays given in the integral form both in the state equations and in the Neumann boundary conditions is considered. Constraints on controls are imposed. Necessary and suffacient optimality conditions for the Neumann problem with the quadratic performance functional are derived.

Discrete-time optimal control of systems with unilateral time-delays

Automatica ◽  
1987 ◽  
Vol 23 (6) ◽  
pp. 763-765 ◽  
Author(s):  
Toru Fujinaka ◽  
Mituhiko Araki
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Time Delays ◽  
Time Optimal Control ◽  
Time Optimal
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