scholarly journals Pontryagin’s Maximum Principle for the Loewner Equation in Higher Dimensions

2015 ◽  
Vol 67 (4) ◽  
pp. 942-960 ◽  
Author(s):  
Oliver Roth
Keyword(s):  
Maximum Principle ◽  
Optimal Control Theory ◽  
Necessary Conditions ◽  
Higher Dimensions ◽  
Pontryagin’S Maximum Principle ◽  
Extremal Problems ◽  
Pontryagin's Maximum Principle ◽  
Loewner Equation ◽  
First Order ◽  
The Pontryagin Maximum Principle

AbstractIn this paper we develop a variational method for the Loewner equation in higher dimensions. As a result we obtain a version of Pontryagin’s maximum principle from optimal control theory for the Loewner equation in several complex variables. Based on recent work of Arosio, Bracci, and Wold, we then apply our version of the Pontryagin maximum principle to obtain first-order necessary conditions for the extremal mappings for a wide class of extremal problems over the set of normalized biholomorphic mappings on the unit ball in ℂn.

scholarly journals KONTROL OPTIMAL PADA PEYEBARAN TUBERKULOSIS DENGAN EXOGENOUS REINFECTION

2019 ◽  
Vol 16 (1) ◽  
pp. 42-50
Author(s):  
J Nainggolan ◽  
F J Iswar ◽  
Abraham Abraham
Keyword(s):  
Numerical Simulation ◽  
Optimal Control ◽  
Mycobacterium Tuberculosis ◽  
Maximum Principle ◽  
Pontryagin Maximum Principle ◽  
Pontryagin’S Maximum Principle ◽  
Pontryagin's Maximum Principle ◽  
Simulation Results ◽  
The Pontryagin Maximum Principle ◽  
Exogenous Reinfection

Tuberculosis is a disease caused by Mycobacterium tuberculosis. Tuberculosis can be controlled through treatment, chemoprophylaxis and vaccination. Optimal control of treatment in the exposed compartment can be done in an effort to reduce the number of exposed compartments individual into the active compartment of tuberculosis. Optimal control can be completed by the Pontryagin Maximum Principle Method. Based on numerical simulation results, optimal control of treatment in the exposed compartment can reduce the number of infected compartments individual with active TB.Keywords : Exogenous Reinfection, Optimal Control, Pontryagin's Maximum Principle, Spread Of Tuberculosis.

scholarly journals An elementary derivation of Pontrayagin's maximum principle of optimal control theory

1977 ◽  
Vol 20 (2) ◽  
pp. 142-156 ◽  
Author(s):  
J. M. Blatt ◽  
J. D. Gray
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Pontryagin’S Maximum Principle ◽  
Time Variable ◽  
Pontryagin's Maximum Principle ◽  
Elementary Derivation ◽  
Mathematical Techniques

AbstractPontryagin's maximum principle is derived by elementary mathematical techniques. The conditions on the functions which enter are generally somewhat more stringent than in Pontryagin's derivation, but one (practically very awkward) condition of Pontryagin can be relaxed: continuity in the time variable can be replaced by a much weaker condition.

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.

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