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.

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 Theory of Active Suspension Design

1995 ◽  
Vol 7 (4) ◽  
pp. 280-284
Author(s):  
Kunihiko Ichikawa ◽  
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Design Theory ◽  
Reference Signal ◽  
Low Frequency ◽  
Active Suspension ◽  
Model Matching ◽  
Frequency Range ◽  
Initial State

Active suspension design has been developed as the application of optimal control theory. However, optimal control theory is only suitable for the design of regulator, where transient responses starting from any initial state are required to converge to zero. The active suspension system is not a simple regulator because road surface unevenness acts only as disturbance in the low frequency range, while it acts not only as disturbance but also as reference signal in the high frequency range. Thus, optimal control theory is not considered suitable for active suspension design. As an alternative to optimal control theory, a new design theory based on exact model matching (EMM) with a disturbance predictor is developed in this paper. One of the peculiarities of this problem is the need to prepare a separate control law for each frequency range. The other is that the outer signal is inaccessible. The former problem is solved by introducing a weighing rational function. The latter problem is fortunately settled by the fact that disturbance and outer signal have a simple relation to each other.

scholarly journals Sub-Riemannian geometry and swimming at low Reynolds number: the Copepod case

2019 ◽  
Vol 25 ◽  
pp. 9 ◽  
Author(s):  
P. Bettiol ◽  
B. Bonnard ◽  
A. Nolot ◽  
J. Rouot
Keyword(s):  
Optimal Control ◽  
Reynolds Number ◽  
Maximum Principle ◽  
Numerical Simulations ◽  
Riemannian Geometry ◽  
Optimal Control Theory ◽  
Geometric Analysis ◽  
Optimal Solutions ◽  
The Maximum Principle ◽  
Recovery Stroke

In Takagi [Phys. Rev. E 92 (2015) 023020], based on copepod observations, Takagi proposed a model to interpret the swimming behaviour of these microorganisms using sinusoidal paddling or sequential paddling followed by a recovery stroke in unison, and compares them invoking the concept of efficiency. Our aim is to provide an interpretation of Takagi’s results in the frame of optimal control theory and sub-Riemannian geometry. The maximum principle is used to select two types of periodic control candidates as minimizers: sinusoidal up to time reparameterization and the sequential paddling, interpreted as an abnormal stroke in sub-Riemannian geometry. Geometric analysis combined with numerical simulations are decisive tools to compute the optimal solutions, refining Takagi computations. A family of simple strokes with small amplitudes emanating from a center is characterized as an invariant of SR-geometry and allows to identify the metric used by the swimmer. The notion of efficiency is discussed in detail and related with normality properties of minimizers.

scholarly journals Optimal Control of Switching Linear Systems

2004 ◽  
Vol 9 ◽  
pp. 41
Author(s):  
Ali Benmerzouga
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Linear Systems ◽  
Optimal Solution ◽  
Input Constraints ◽  
Initial State ◽  
Programming Technique ◽  
New Approach ◽  
Running Cost ◽  
Modified Algorithm

A solution to the control of switching linear systems with input constraints was given in Benmerzouga (1997) for both the conventional enumeration approach and the new approach. The solution given there turned out to be not unique. The main objective in this work is to determine the optimal control sequences {Ui(k) ,  i = 1,..., M ;  k = 0, 1, ...,  N -1} which transfer the system from a given initial state  X0  to a specific target state  XT  (or to be as close as possible) by using the same discrete time solution obtained in Benmerzouga (1997) and minimizing a running cost-to-go function. By using the dynamic programming technique, the optimal solution is found for both approaches given in Benmerzouga (1997). The computational complexity of the modified algorithm is also given.  

Application of Optimal Control in Inventory Management of Production

2010 ◽  
Vol 29-32 ◽  
pp. 2503-2508 ◽  
Author(s):  
Pei Hong Sun ◽  
Lei Tang ◽  
Li Ying Tang
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Inventory Management ◽  
Optimal Control Theory ◽  
Theoretical Foundation ◽  
Dynamic Programming Method ◽  
Management Problem ◽  
State Variables ◽  
Manufacturing Enterprise ◽  
Time Dynamic

Countering the inventory management problem of manufacturing enterprise, according to the optimal control theory, considering the numbers of products as control variables and the stocks as the state variables, this essay establishes systemic real-time dynamic model, gives the objective function, and makes use of dynamic programming method to solve the optimal control and obtains the optimal inventory, which provides a theoretical foundation for the production and inventory management of manufacturing enterprise.

scholarly journals A theoretical model for the transmission dynamics of HIV/HSV-2 co-infection in the presence of poor HSV-2 treatment adherence

2018 ◽  
Vol 3 (2) ◽  
pp. 603-626
Author(s):  
A. Mhlanga
Keyword(s):  
Optimal Control ◽  
Treatment Adherence ◽  
Optimal Control Theory ◽  
Hiv Infections ◽  
Time Dependent ◽  
Transmission Dynamics ◽  
Time Intervals ◽  
Immunodeficiency Virus ◽  
The World ◽  
Simplex Virus

AbstractHerpes simplex virus (HSV-2) triples the risk of acquiring human immunodeficiency virus (HIV) and contributes to more than 50% of HIV infections in other parts of the world. A deterministic mathematical model for the co-interaction of HIV and HSV-2 in a community, with all the relevant biological detail and poor HSV-2 treatment adherence is proposed. The threshold parameters of the model are determined and stabilities are analysed. Further, we applied optimal control theory. We proved the existence of the optimal control and characterized the controls using Pontryagin’s maximum principle. The controls represent monitoring and counselling of individuals infected with HSV-2 only and the other represent monitoring and counselling of individuals dually infected with HIV and HSV-2. Numerical results suggests that more effort should be devoted to monitoring and counselling of individuals dually infected with HIV and HSV-2 as compared to those infected with HSV-2 only. Overall, the study demonstrate that, though time dependent controls will be effective on controlling HIV cases, they may not be sustainable for certain time intervals.

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