Optimal control of dynamic pulse power loads in naval power systems using the Pontryagin minimum principle and Dynamic Programming

2012 ◽  
Author(s):  
D. F. Opila ◽  
L. Solomon
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Power Systems ◽  
Minimum Principle ◽  
Pulse Power ◽  
Pontryagin Minimum Principle ◽  
Naval Power ◽  
Dynamic Pulse

scholarly journals Application and benchmarking of a direct method to optimize the fuel consumption of a diesel electric locomotive

2018 ◽  
Vol 232 (9) ◽  
pp. 2272-2289 ◽  
Author(s):  
V Macian ◽  
C Guardiola ◽  
B Pla ◽  
A Reig
Keyword(s):  
Optimal Control ◽  
Direct Method ◽  
Minimum Principle ◽  
Optimization Technique ◽  
Direct Methods ◽  
Optimization Methods ◽  
Computational Time ◽  
Electric Locomotive ◽  
Pontryagin Minimum Principle ◽  
A Direct Method

This paper addresses the optimal control of a long-haul passenger train to deliver minimum-fuel operations. Contrary to the common Pontryagin minimum principle approach in railroad-related literature, this work addresses this optimal control problem with a direct method of optimization, the use of which is still marginal in this field. The implementation of a particular direct method based on the Euler collocation scheme and its transcription into a nonlinear problem are described in detail. In this paper, this optimization technique is benchmarked with well-known optimization methods in the literature, namely dynamic programming and the Pontryagin minimum principle, by simulating a real route. The results showed that the direct methods are on the same level of optimality compared with other algorithms while requiring reduced computational time and memory and being able to handle very complex dynamic systems. The performance of the direct method is also compared to the real trajectory followed by the train operator and exhibits up to 20% of fuel saving in the example route.

scholarly journals Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics

2021 ◽  
Author(s):  
Etienne Bertin ◽  
Elliot Brendel ◽  
Bruno Hérissé ◽  
Julien Alexandre dit Sandretto ◽  
Alexandre Chapoutot
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Closed Loop ◽  
Minimum Principle ◽  
Open Loop ◽  
Pontryagin Minimum Principle ◽  
Interval Method ◽  
Bounded Uncertainties ◽  
The Given

An interval method based on the Pontryagin Minimum Principle is proposed to enclose the solutions of an optimal control problem with embedded bounded uncertainties. This method is used to compute an enclosure of all optimal trajectories of the problem, as well as open loop and closed loop enclosures meant to enclose a concrete system using an optimal control regulator with inaccurate knowledge of the parameters. The differences in geometry of these enclosures are exposed, as well as some applications. For instance guaranteeing that the given optimal control problem will yield a satisfactory trajectory for any realization of the uncertainties or on the contrary that the problem is unsuitable and needs to be adjusted.

An Optimal Control Problem of Knowledge Dissemination

2020 ◽  
pp. 461-482
Author(s):  
Pantry Elastic ◽  
Toni Bakhtiar ◽  
Jaharuddin
Keyword(s):  
Optimal Control ◽  
Information Dissemination ◽  
Control Strategies ◽  
Minimum Principle ◽  
Control Model ◽  
Technical Training ◽  
Knowledge Dissemination ◽  
Transfer System ◽  
Pontryagin Minimum Principle

In this chapter, the authors develop an optimal control model of knowledge dissemination among people in the society. The knowledge transfer system is formulated in term of compartmental model, where the society members are categorized into four classes based on knowledge acquisition and their willingness to disseminate. The model is equipped with a set of control variables for process intervening, namely technical training for ignorant-immigrants, information dissemination through social media for solitariants and enthusiants, and technical training for solitariants. Optimality conditions in terms of differential equations system was derived by using Pontryagin minimum principle leading to the characterization of optimal control strategies that minimizing the number of solitariants, enthusiants, and ignorants simultaneously with the control efforts. The sweep method and the fourth order Runge-Kutta algorithm was implemented to numerically solve the equation systems. The effectiveness of the control strategies toward a set of control scenarios was evaluated through examples.

scholarly journals Optimal Control of Mathematical Models on The Dynamics Spread of Drug Abuse

2021 ◽  
Vol 17 (3) ◽  
pp. 339-348
Author(s):  
Nita Anggriani ◽  
Syamsuddin Toaha ◽  
Kasbawati Kasbawati
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Drug Abuse ◽  
Mathematical Models ◽  
Minimum Principle ◽  
Self Psychology ◽  
Sweep Method ◽  
Pontryagin Minimum Principle ◽  
Counseling Needs ◽  
Forward Backward Sweep Method

This article examines the optimal control of a mathematical model of the spread of drug abuse. This model consists of five population classes, namely susceptible to using drugs (S), light-grade drugs (A), heavy-grade drugs (H), medicated drugs (T), and Recovery from drugs (R). The system is solved using the Pontryagin minimum principle and numerically by the forward-backward sweep method. Numerical simulations of the optimal problem show that with the implementation of anti-drug campaigns and strengthening of self-psychology through counseling, the spread of drug abuse can be eradicated more quickly. The implementation of campaigns and strengthening of self-psychology through large amounts of counseling needs to be done from the beginning then the proportion can be reduced until a certain time does not need to be given anymore. The use of control in the form of strengthening efforts to self-psychology through counseling means that it needs to be done in a longer time to prevent the spread of drug abuse.

scholarly journals KONTROL OPTIMAL MODEL PENYEBARAN VIRUS KOMPUTER DENGAN PENGARUH KOMPUTER EKSTERNAL YANG TERINFEKSI DAN REMOVABLE STORAGE MEDIA

2017 ◽  
Vol 9 (1) ◽  
pp. 113
Author(s):  
Dewi Erla Mahmudah ◽  
Muhammad Zidny Naf’an ◽  
Muh. Sofi’i ◽  
Wika Wika
Keyword(s):  
Optimal Control ◽  
Optimality Condition ◽  
Minimum Principle ◽  
Prevention Strategies ◽  
Optimal Model ◽  
Pontryagin Minimum Principle ◽  
Computer Viruses ◽  
Storage Media ◽  
The Cost

.  In this paper, we discuss an optimal control on the spread of computer viruses under the effects of infected external computers and removable storage media. Prevention Strategies do with ascertaining control prevention to minimize the number of infective computers (Latent and Breakingout) and installing effective antivirus programs in each sub-population. The aim are to derive optimal prevention strategies and minimize the cost associated with the control. The characterization of optimal control is perform analitically by applying Pontryagin Minimum Principle. The obtained optimality system of Hamilton fuction is satistfy the optimality condition.

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.

Optimal Control of a Hydrostatic Wind Turbine Drivetrain for Efficiency Improvements

2017 ◽  
Author(s):  
Majid Deldar ◽  
Sohel Anwar
Keyword(s):  
Optimal Control ◽  
Wind Speed ◽  
Wind Turbine ◽  
Wind Power ◽  
Minimum Principle ◽  
Maximum Output Power ◽  
Maximum Efficiency ◽  
Control Law ◽  
Maximum Output ◽  
Pontryagin Minimum Principle

To increase productivity of a wind power plant, the overall loss of its drivetrain should be minimized. For hydrostatic transmission wind turbine (HTSWT), aerodynamic efficiency of the rotor and the hydrostatic efficiency of pump and motor determine the overall loss. In this study, optimal control theory is utilized to develop a control law that minimizes the overall loss. A nonlinear model is considered for the drivetrain and a performance index (PI) is defined for the overall loss subject to system constraints which were then used to derive the optimal control law based on Pontryagin Minimum Principle (PMP),. Simulation results verified that the controller was able to maximize the drive-train efficiency. At very low wind speed, a trade-off is observed between aerodynamic and hydrostatic efficiency. For higher wind speed where the hydrostatic efficiency asymptotically reaches its maximum efficiency maximum output power coincided with maximum power point tracking of input wind power.

scholarly journals APPLICATION OF THE PONTRYAGIN MAXIMUM PRINCIPLE TO CONTROL TUMOR ANGIOGENESIS

2021 ◽  
Vol 6 (12(62)) ◽  
pp. 51-55
Author(s):  
Cherif Abdelillah Otmane
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Tumor Angiogenesis ◽  
Pontryagin Maximum Principle ◽  
Optimal Trajectory ◽  
Minimum Principle ◽  
Pontryagin Minimum Principle ◽  
Sample Application ◽  
Control Tumor ◽  
The Pontryagin Maximum Principle

We present a sample application covering several cases using an extension of the Pontryagin Minimum Principle (PMP) [3]. We are interested in the management of tumor angiogenesis, that is, the therapeutic management of the proliferation of cancer cells that develop new blood vessels. Let us formulate the problem and derive the optimal control and apply the Pontryagin maximum principle to our optimal trajectory, and we derive the theorem and check it with an example. Then we will study stabilization.

Optimal Control

2018 ◽  
pp. 348-390
Author(s):  
David J. N. Limebeer ◽  
Matteo Massaro
Keyword(s):  
Optimal Control ◽  
Large Scale ◽  
Minimum Principle ◽  
Pontryagin Minimum Principle ◽  
Singular Arcs ◽  
Curvature Estimate ◽  
Global Positioning ◽  
Hamilton Jacobi Bellman Equation ◽  
Problem Formulations ◽  
Hamilton Jacobi Bellman

Chapter 8 focuses on nonlinear optimal control and its applications. The chapter begins by introducing the fundamentals of optimal control and prototypical problem formulations. This is followed by the treatment of first-order necessary conditions including the Pontryagin minimum principle, dynamic programming, and the Hamilton–Jacobi–Bellman equation. Singular arcs and bang–bang controls are relevant in the solution of many minimum-time and minimum-fuel problems and so these issues are discussed with the help of examples that have been worked out in detail.This chapter then turns towards direct and indirect numericalmethods suitable for solving large-scale optimal control problems numerically.The chapter concludes with an example relating to the calculation of an optimal track curvature estimate from global positioning system (GPS) data.

Sign in / Sign up

Export Citation Format

Share Document