Optimal control of electrical machines using Pontryagin’s maximum principle

2020 ◽  
pp. 1-15
Author(s):  
Wissem Bekir ◽  
Lilia EL Amraoui ◽  
Frédéric Gillon
Keyword(s):  
Optimal Control ◽  
Energy Consumption ◽  
Maximum Principle ◽  
Optimal Solution ◽  
Optimization Method ◽  
Pontryagin’S Maximum Principle ◽  
Electrical Machines ◽  
Stepper Motor ◽  
Control Techniques ◽  
Numerical Resolution

This paper presents an optimization method that deal with control techniques for electrical machines, in order to impose a displacement with a minimum of energy consumption. It’s a generic method; However, its application to electrical machines is complex for implementation. The present work provides the shape of the optimal solution. Moreover, a resolution technique related to the nature of the model is proposed, which facilitate the numerical resolution of costate problem. The method is applied to hybrid stepper motor and the obtained results are then analyzed.

scholarly journals Optimal Speed Profile Determination with Fixed Trip Time in the Electric Train Operation of the Cat Linh-Ha Dong Metro Line based on Pontryagin's Maximum Principle

2020 ◽  
Vol 10 (6) ◽  
pp. 6488-6493
Author(s):  
T. T. T. A. Anh ◽  
N. V. Quyen
Keyword(s):  
Energy Consumption ◽  
Maximum Principle ◽  
Pontryagin’S Maximum Principle ◽  
Speed Profile ◽  
Saving Energy ◽  
Pontryagin's Maximum Principle ◽  
Improve Energy Efficiency ◽  
Optimal Speed ◽  
Trip Time ◽  
Train Operation

The significant energy consumption for railway electric transportation operation poses a great challenge in outlining saving energy solutions. Speed profile optimization based on optimal control theory is one of the most common methods to improve energy efficiency without the railway infrastructure investment costs. The paper proposes an optimization method based on Pontryagin's Maximum Principle (PMP), not only to find optimal switching points in three operation phases: accelerating, coasting, braking, and from these switching points being able to determine the optimal speed profile, but also to ensure fixed-trip time. In order to determine trip time abiding by the scheduled timetables by applying nonlinear programming puts the Lagrange multiplier λ in the objective function regarded as a time constraint condition. The correctness and energy effectiveness of this method have been verified by the simulation results with data collected from the electrified trains of the Cat Linh-Ha Dong metro line in Vietnam. The saving energy levels are compared in three scenarios: electrified train operation tracking the original speed profile (energy consumption of the route: 144.64kWh), train operation tracking the optimal speed profile without fixed-trip time (energy consumption of the route: 129.18kWh), and train operation tracking the optimal speed profile and fixed trip time (energy consumption of the route: 132.99kWh) in an effort to give some useful choices for operating metro lines.

A hamiltonian approach to optimal stochastic resource allocation

1977 ◽  
Vol 9 (01) ◽  
pp. 55-68 ◽  
Author(s):  
P. Nash ◽  
J. C. Gittins
Keyword(s):  
Optimal Control ◽  
Resource Allocation ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Schedule ◽  
Pontryagin’S Maximum Principle ◽  
Hamiltonian Approach ◽  
Stochastic Resource Allocation ◽  
Service Times

The problem of scheduling items for service with random service times is formulated as an optimal control problem. Pontryagin's maximum principle is used to determine the optimal schedule in certain cases.

scholarly journals Optimal Control Strategies in an Alcoholism Model

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Xun-Yang Wang ◽  
Hai-Feng Huo ◽  
Qing-Kai Kong ◽  
Wei-Xuan Shi
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Maximum Principle ◽  
Numerical Simulations ◽  
Control Strategies ◽  
Pontryagin’S Maximum Principle ◽  
Social Phenomenon ◽  
Pontryagin's Maximum Principle ◽  
Existence And Stability ◽  
Objective Functional

This paper presents a deterministic SATQ-type mathematical model (including susceptible, alcoholism, treating, and quitting compartments) for the spread of alcoholism with two control strategies to gain insights into this increasingly concerned about health and social phenomenon. Some properties of the solutions to the model including positivity, existence and stability are analyzed. The optimal control strategies are derived by proposing an objective functional and using Pontryagin’s Maximum Principle. Numerical simulations are also conducted in the analytic results.

scholarly journals OPTIMIZING THE QUARANTINE COST FOR SUPPRESSION OF THE COVID-19 EPIDEMIC IN MEXICO

2020 ◽  
Vol 28 (1) ◽  
pp. 55-78
Author(s):  
ABDON E. CHOQUE RIVERO ◽  
EVGENII N. KHAILOV ◽  
ELLINA V. GRIGORIEVA
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Function ◽  
Optimal Solution ◽  
Weighted Sum ◽  
Bounded Control ◽  
Infection Level ◽  
Total Cost ◽  
The Maximum Principle ◽  
The Pontryagin Maximum Principle

This paper is one of the few attempts to use the optimal control theory to find optimal quarantine strategies for eradication of the spread of the COVID-19 infection in the Mexican human population. This is achieved by introducing into the SEIR model a bounded control function of time that reflects these quarantine measures. The objective function to be minimized is the weighted sum of the total infection level in the population and the total cost of the quarantine. An optimal control problem reflecting the search for an effective quarantine strategy is stated and solved analytically and numerically. The properties of the corresponding optimal control are established analytically by applying the Pontryagin maximum principle. The optimal solution is obtained numerically by solving the two-point boundary value problem for the maximum principle using MATLAB software. A detailed discussion of the results and the corresponding practical conclusions are presented.

Train Optimal Control Strategy on Continuous Change Gradient Steep Downgrades

2011 ◽  
Vol 267 ◽  
pp. 211-216 ◽  
Author(s):  
Peng Zhou ◽  
Hong Ze Xu ◽  
Meng Nan Zhang
Keyword(s):  
Optimal Control ◽  
Energy Consumption ◽  
Energy Saving ◽  
Control Strategy ◽  
Operation Time ◽  
Optimization Method ◽  
Continuous Change ◽  
Optimal Control Strategy ◽  
Energy Feedback ◽  
Time And Energy

Reducing the traction energy consumption plays an important role in railway energy saving. Viewed from the present research situation--the models were all based on the train without energy-feedback, moreover the line condition is the fixed steep down or steep up grades, the train group energy control strategy on continuous change gradient steep downgrades with the energy-feedback is proposed. The advantage for energy-saving of the strategy is proved through the traction calculation in theory. On that basis the optimization method is applied to get the optimal strategy balancing the operation time and energy consumption. By comparing the traditional control strategy with the optimal control strategy, the experiments show that the optimal overall target index of the operation time and energy consumption is much better.

scholarly journals Optimal control with a cost of switching control

1976 ◽  
Vol 19 (3) ◽  
pp. 316-332 ◽  
Author(s):  
John M. Blatt
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Existence Theorem ◽  
Switching Control ◽  
Pontryagin’S Maximum Principle ◽  
Pontryagin's Maximum Principle ◽  
Theory Of Optimal Control ◽  
General Existence

AbstractThe Pontryagin theory of optimal control is modified by assuming a positive cost associated with switching control from one discrete value to another. The resulting new theory permits a general existence theorem. Pontryagin's maximum principle is replaced by an “indifference principle”.

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