Optimal control with initial state not a priort given and boundary condition involving a delay

2006 ◽  
pp. 94-108 ◽  
Author(s):  
Adam Kowalewski
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Initial State

scholarly journals Optimal control of a viscous generalized θ-type dispersive equation with weak dissipation

2020 ◽  
Vol 18 (1) ◽  
pp. 1302-1316
Author(s):  
Guobing Fan ◽  
Zhifeng Yang
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Weak Solution ◽  
Existence And Uniqueness ◽  
Optimal Solution ◽  
Dispersive Equation ◽  
Weak Dissipation ◽  
Formula Type

Abstract In this paper, we investigate the problem for optimal control of a viscous generalized \theta -type dispersive equation (VG \theta -type DE) with weak dissipation. First, we prove the existence and uniqueness of weak solution to the equation. Then, we present the optimal control of a VG \theta -type DE with weak dissipation under boundary condition and prove the existence of optimal solution to the problem.

On the optimality of optical pumping for a closed Λ-system with large decay rates of the intermediate excited state

2021 ◽  
Author(s):  
Dionisis Stefanatos ◽  
Emmanuel Paspalakis
Keyword(s):  
Optimal Control ◽  
Excited State ◽  
Decay Rate ◽  
Optimal Control Theory ◽  
Optical Pumping ◽  
Quantum Information Processing ◽  
Decay Rates ◽  
Population Transfer ◽  
Initial State ◽  
Weakly Coupled

Abstract We use optimal control theory to show that for a closed Λ-system where the excited intermediate level decays to the lower levels with a common large rate, the optimal scheme for population transfer between the lower levels is actually optical pumping. In order to obtain this result we exploit the large decay rate to eliminate adiabatically the weakly coupled excited state, then perform a transformation to the basis comprised of the dark and bright states, and finally apply optimal control to this transformed system. Subsequently, we confirm the optimality of the optical pumping scheme for the original closed Λ-system using numerical optimal control. We also demonstrate numerically that optical pumping remains optimal when the decay rate to the target state is larger than that to the initial state or the two rates are not very different from each other. The present work is expected to find application in various tasks of quantum information processing, where such systems are encountered

scholarly journals Direct Method for Resolution of Optimal Control Problem with Free Initial Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Louadj Kahina ◽  
Aidene Mohamed
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Optimal Control Theory ◽  
World Literature ◽  
Direct Method ◽  
Initial Condition ◽  
Initial State ◽  
The Maximum Principle ◽  
Constructive Methods ◽  
The World

The theory of control analyzes the proprieties of commanded systems. Problems of optimal control (OC) have been intensively investigated in the world literature for over forty years. During this period, series of fundamental results have been obtained, among which should be noted the maximum principle (Pontryagin et al., 1962) and dynamic programming (Bellman, 1963). For many of the problems of the optimal control theory (OCT), adequate solutions are found (Bryson and Yu-chi, 1969, Lee and Markus, 1967, Gabasov and Kirillova, 1977, 1978, 1980). Results of the theory were taken up in various fields of science, engineering, and economics. The present paper aims at extending the constructive methods of Balashevich et al., (2000) that were developed for the problems of optimal control with the bounded initial state is not fixed are considered.

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