scholarly journals How to build a new athletic track to break records

2020 ◽  
Vol 7 (3) ◽  
pp. 200007
Author(s):  
Amandine Aftalion ◽  
Emmanuel Trélat
Keyword(s):  
Optimal Control ◽  
Optimal Path ◽  
Control Model ◽  
Neural Drive ◽  
Record Times ◽  
Control Effort ◽  
Fixed Distance ◽  
Dubins Path ◽  
Different Types ◽  
Economic Decision Theory

We introduce a new optimal control model which encompasses pace optimization and motor control effort for a runner on a fixed distance. The system couples mechanics, energetics, neural drive to an economic decision theory of cost and benefit. We find how effort is minimized to produce the best running strategy, in particular, in the bend. This allows us to discriminate between different types of tracks and estimate the discrepancy between lanes. Relating this model to the optimal path problem called the Dubins path, we are able to determine the geometry of the optimal track and estimate record times.

scholarly journals Environmental and population externalities

2009 ◽  
Vol 15 (1) ◽  
pp. 1-19 ◽  
Author(s):  
FRANK JÖST ◽  
MARTIN F. QUAAS
Keyword(s):  
Optimal Control ◽  
Population Policy ◽  
Control Model ◽  
Household Size ◽  
Economic Capital ◽  
External Effects ◽  
The Family ◽  
Different Types ◽  
Polluting Emissions ◽  
Number Of Births

ABSTRACTWe analyze the external effects that arise in the decisions of firms on polluting emissions and in the decisions of parents on the number of births in an optimal control model with three stock variables representing population, economic capital, and pollution. We distinguish two different types of households, which represent opposite ends of a spectrum of potential familial structures: ‘dynastic households’, in which the family sticks together forever and ‘micro-households’, in which children leave their parent's household immediately after birth. We show that the decision of parents on the number of births involves an externality that is qualitatively different for both types of familial structure. Hence, population policy should be different, according to the type of household. A first best result may be obtained in the case of dynastic households if an appropriate tax on the household size is applied, or, in the case of micro-households, if an appropriate tax on children is applied.

An LQ Approach to Active Control of Vibrations in Helicopters

1996 ◽  
Vol 118 (3) ◽  
pp. 482-488 ◽  
Author(s):  
Sergio Bittanti ◽  
Fabrizio Lorito ◽  
Silvia Strada
Keyword(s):  
Optimal Control ◽  
Active Control ◽  
Linear Quadratic ◽  
Control Effort ◽  
Vibration Effect ◽  
Suitable Definition ◽  
Lq Optimal Control ◽  
The One ◽  
Definition Of ◽  
And Control

In this paper, Linear Quadratic (LQ) optimal control concepts are applied for the active control of vibrations in helicopters. The study is based on an identified dynamic model of the rotor. The vibration effect is captured by suitably augmenting the state vector of the rotor model. Then, Kalman filtering concepts can be used to obtain a real-time estimate of the vibration, which is then fed back to form a suitable compensation signal. This design rationale is derived here starting from a rigorous problem position in an optimal control context. Among other things, this calls for a suitable definition of the performance index, of nonstandard type. The application of these ideas to a test helicopter, by means of computer simulations, shows good performances both in terms of disturbance rejection effectiveness and control effort limitation. The performance of the obtained controller is compared with the one achievable by the so called Higher Harmonic Control (HHC) approach, well known within the helicopter community.

Air Suspension Optimal Control Based on the Genetic Algorithm

2011 ◽  
Vol 467-469 ◽  
pp. 1066-1071
Author(s):  
Zhong Xin Li ◽  
Ji Wei Guo ◽  
Ming Hong Gao ◽  
Hong Jiang
Keyword(s):  
Genetic Algorithm ◽  
Optimal Control ◽  
Dynamic Model ◽  
Control Method ◽  
Control Model ◽  
Weight Matrix ◽  
Object A ◽  
Full Vehicle ◽  
Air Suspension ◽  
Optimal Control Method

Taking the full-vehicle eight-freedom dynamic model of a type of bus as the simulation object , a new optimal control method is introduced. This method is based on the genetic algorithm, and the full-vehicle optimal control model is built in the MatLab. The weight matrix of the optimal control is optimized through the genetic algorithm; then the outcome is compared with the artificially-set optimal control simulation, which shows that the genetic-algorithm based optimal control presents better performance, thereby creating a smoother ride and improving the steering stability of the vehicle.

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