Optimal Control Theory

2018 ◽  
Author(s):  
John E. Prussing
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Necessary Conditions ◽  
Minimum Principle ◽  
Minimum Cost ◽  
Initial Time ◽  
Pontryagin Minimum Principle ◽  
Final Time ◽  
Terminal Constraints

Optimal Control Theory is reviewed in detail. We consider a dynamic system that operates between a specified initial time and a final time which may be specified or unspecified. Necessary conditions for a minimum cost functional are derived. Terminal constraints are considered. Pontryagin Minimum Principle is discussed.

scholarly journals Kontrol Optimal Upaya Pengobatan Penyakit Campak Menggunakan Model Endemi SIR

2019 ◽  
Vol 9 (2) ◽  
pp. 94
Author(s):  
Ida Ayu Putu Ari Utari
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Minimum Principle ◽  
System Of Differential Equations ◽  
Pontryagin Minimum Principle ◽  
Main Target ◽  
Model Determination ◽  
Efficiency Rate

Measles is an acute highly contagious disease caused by Paramyxovirus. Measles is considered as a dangerous disease because it cause complications, brain and other organs damage, lifelong disability, paralysis and even death. In the previous studies, it was known that the spread of measles highly dependent on number of infected individuals so it is necessary to control measles through treatment. In this paper, we study about the application of the optimal control theory on the system of differential equations of the SIR endemic model. Determination of the optimal control is obtained through the application of the Pontryagin minimum principle. The main target in this paper is to find a unique optimal control where the optimal control can be described as an efficiency rate of treatment in individuals infected with measles to decrease the number of infected individuals.

scholarly journals CONSTRAINT ALGORITHM FOR EXTREMALS IN OPTIMAL CONTROL PROBLEMS

2009 ◽  
Vol 06 (07) ◽  
pp. 1221-1233 ◽  
Author(s):  
MARÍA BARBERO-LIÑÁN ◽  
MIGUEL C. MUÑOZ-LECANDA
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Theory ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Control Problems ◽  
Affine System

A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. The algorithm must be run twice so as to obtain suitable sets that once projected must be compared. Apart from the design of this general algorithm useful for any optimal control problem, it is shown how to classify the set of extremals and, in particular, how to characterize the strict abnormality. An example of strict abnormal extremal for a particular control-affine system is also given.

Intelligent energy management for hybrid fuel cell/battery system

2016 ◽  
Vol 35 (5) ◽  
pp. 1850-1864 ◽  
Author(s):  
Moussa Boukhnifer ◽  
Nadir Ouddah ◽  
Toufik Azib ◽  
Ahmed Chaibet
Keyword(s):  
Optimal Control ◽  
Fuel Cell ◽  
Control Theory ◽  
Energy Management ◽  
Optimal Control Theory ◽  
Hybrid Electric Vehicle ◽  
Minimum Principle ◽  
Management Strategies ◽  
Hybrid Architecture ◽  
Content Type

Purpose The purpose of this paper is to propose two energy management strategies (EMS) for hybrid electric vehicle, the power system is an hybrid architecture (fuel cell (FC)/battery) with two-converters parallel configuration. Design/methodology/approach First, the authors present the EMS uses a power frequency splitting to allow a natural frequency decomposition of the power loads and second the EMS uses the optimal control theory, based on the Pontryagin’s minimum principle. Findings Thanks to the optimal approach, the control objectives will be easily achieved: hydrogen consumption is minimized and FC health is protected. Originality/value The simulation results show the effectiveness of the control strategy using optimal control theory in term of improvement of the fuel consumption based on a comparison analysis between the two strategies.

scholarly journals The Derivation of Structural Properties of LM-g Splines by Necessary Condition of Optimal Control

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Xiongwei Liu ◽  
Xinjian Zhang ◽  
Lizhi Cheng
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Structural Properties ◽  
Optimal Control Theory ◽  
State Constraints ◽  
Necessary Conditions ◽  
Necessary Condition ◽  
Interpolating Splines ◽  
The Relationship ◽  
Optimization And Optimal Control

The structural properties of LM-g splines are investigated by optimization and optimal control theory. The continuity and structure of LM-g splines are derived by using a class of necessary conditions with state constraints of optimal control and the relationship between LM-g interpolating splines and the corresponding L-g interpolating splines. This work provides a new method for further exploration of LM-g interpolating splines and its applications in the optimal control.

scholarly journals Optimal controller design based on minimum principle

2018 ◽  
Vol 173 ◽  
pp. 01001
Author(s):  
Huang Da ◽  
Huang ShuCai
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Controller Design ◽  
Minimum Principle ◽  
Adaptive Controller ◽  
Control Effect ◽  
Modern Control Theory ◽  
Important Position ◽  
The Ideal

Optimal control theory is the foundation of the modern control theory, the minimum principle in optimal control theory has a very important position, using the minimum principle to design an adaptive controller, the controller integration advantages of the principle of minimum is not affected by the control system of linear or nonlinear constraints, and the end state and free time, is accused of quantity can be controlled and are free to wait for a characteristic, using the minimum controller application example and simulation, the results show that the minimum principle of the designed controller has the ideal control effect.

Maximizing Distance of the Golf Drive: An Optimal Control Study

1975 ◽  
Vol 97 (4) ◽  
pp. 362-367 ◽  
Author(s):  
M. A. Lampsa
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Variational Formulation ◽  
Necessary Conditions ◽  
Model Parameter ◽  
Steepest Ascent ◽  
Parameter Values ◽  
Control Study

Optimal control theory is used to search for the optimal control torques necessary to maximize distance of the golf drive. In the method, a mathematical model of a generalized golf swing is first developed. Film of the author’s swing serves to verify the model and to supply parameter values, constraints, and actual torques. The variational formulation of optimal control theory is utilized to establish necessary conditions for optimal control, in which constraint violations are discouraged by inclusion of penalty functions. Finally, the method of steepest ascent is used to compute optimal control torques. Also, comparison of optimal and actual torques is made, and the sensitivity of the results to small changes in model parameter values is investigated.

Optimal Control Theory Applied to a Dynamic Aquatic Ecosystem

1973 ◽  
Vol 30 (4) ◽  
pp. 576-579 ◽  
Author(s):  
N. U. Ahmed ◽  
N. D. Georganas
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Dynamic Model ◽  
Aquatic Ecosystem ◽  
Optimal Control Theory ◽  
Minimum Cost ◽  
Single Species ◽  
Pollution Reduction ◽  
Polluted Environment ◽  
Species Removal

In this report we present a dynamic model for an aquatic ecosystem consisting of a single species living in a polluted environment. Considering the dynamics of growth of the species and increase in pollution, we apply optimal control theory to obtain species removal and pollution reduction rates at minimum cost.

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