Deterministic optimal control, given only a partial observation of the initial state

1980 ◽  
Vol 32 (3) ◽  
pp. 327-343 ◽  
Author(s):  
J. C. Allwright
Keyword(s):  
Optimal Control ◽  
Partial Observation ◽  
Initial State

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.

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 Discrete-time inverse linear quadratic optimal control over finite time-horizon under noisy output measurements

2021 ◽  
Author(s):  
Han Zhang ◽  
Yibei Li ◽  
Xiaoming Hu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Discrete Time ◽  
Finite Time ◽  
Time Horizon ◽  
Model Structure ◽  
Initial State ◽  
Quadratic Optimal Control ◽  
Initial States ◽  
Finite Time Horizon

AbstractIn this paper, the problem of inverse quadratic optimal control over finite time-horizon for discrete-time linear systems is considered. Our goal is to recover the corresponding quadratic objective function using noisy observations. First, the identifiability of the model structure for the inverse optimal control problem is analyzed under relative degree assumption and we show the model structure is strictly globally identifiable. Next, we study the inverse optimal control problem whose initial state distribution and the observation noise distribution are unknown, yet the exact observations on the initial states are available. We formulate the problem as a risk minimization problem and approximate the problem using empirical average. It is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative degrees. We then study the case where the exact observations on the initial states are not available, yet the observation noises are known to be white Gaussian distributed and the distribution of the initial state is also Gaussian (with unknown mean and covariance). EM-algorithm is used to estimate the parameters in the objective function. The effectiveness of our results are demonstrated by numerical examples.

Symmetric Control Systems

2021 ◽  
pp. 37-51
Author(s):  
A.I. Diveev ◽  
E.A. Sofronova
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Systems ◽  
Control Object ◽  
Terminal State ◽  
Initial State ◽  
Phase Constraints ◽  
The Mathematical Model

The paper focuses on the properties of symmetric control systems, whose distinctive feature is that the solution of the optimal control problem for an object, the mathematical model of which belongs to the class of symmetric control systems, leads to the solution of two problems. The first optimal control problem is the initial one; the result of its solution is a function that ensures the optimal movement of the object from the initial state to the terminal one. In the second problem, the terminal state is the initial state, and the initial state is the terminal state. The complexity of the problem being solved is due to the increase in dimension when the models of all objects of the group are included in the mathematical model of the object, as well as the emerging dynamic phase constraints. The presence of phase constraints in some cases leads to the target functional having several local extrema. A theorem is proved that under certain conditions the functional is not unimodal when controlling a group of objects belonging to the class of symmetric systems. A numerical example of solving the optimal control problem with phase constraints by the Adam gradient method and the evolutionary particle swarm method is given. In the example, a group of two symmetrical objects is used as a control object

ENSURING REACH ABILITY AND STABILITY IN THE SYNTHESIS OF ROBUST DISCRETE MODEL PREDICTIVE CONTROL IN CONDITIONS OF INCOMPLETE INFORMATION

2020 ◽  
Vol 7 (2) ◽  
pp. 29-33
Author(s):  
NGUYEN KHAC TUNG ◽  
◽  
ANTON ZHILENKOV ◽  
DANG BINH KHAC ◽  
Keyword(s):  
Optimal Control ◽  
Current Control ◽  
Initial State ◽  
Modeling And Control ◽  
Nanoscale Structures ◽  
Current State ◽  
Control Scheme ◽  
Methods Of Synthesis ◽  
And Control ◽  
Time Systems

Methods of synthesis of control of multiscale processes with predictive models for linear discrete time systems are considered. A description is given of a control scheme in which the current control action is obtained by solving at each instant of the sample the optimal control problem with a finite horizon without feedback and using the current state of the object as an initial state. An optimization problem is described that gives an optimal control sequence when the control obtained for the first step of the subsequent sequence is applied to the object. The analysis of the reachability and stability problems of synthesized controls with a predictive model under conditions of disturbances and uncertainties is given. As well as the problems of providing preset indicators of the quality of management and comparing indicators in the management of MPC in open and closed systems. The urgent issues requiring research in the framework of the considered management system are identified. The proposed solutions are extremely relevant to the problems of modeling and control of technological processes of growing nanoscale structures.

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