Application of Pontryagin’s Principle to a Minimum Weight Design Problem

1970 ◽  
Vol 92 (2) ◽  
pp. 245-250 ◽  
Author(s):  
B. M. E. de Silva
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Theory ◽  
Design Problem ◽  
Minimum Weight ◽  
Inequality Constraints ◽  
Minimum Weight Design ◽  
The Maximum Principle ◽  
Weight Design ◽  
And Control

A minimum weight design problem has been formulated as a general problem in optimal-control theory with the addition of state and control inequality constraints. Complete analytical solutions have been derived using the maximum principle of Pontryagin.

Optimum Design of Bridge Girders for Electric Overhead Traveling Cranes

1978 ◽  
Vol 100 (3) ◽  
pp. 375-382
Author(s):  
S. S. Rao
Keyword(s):  
Design Problem ◽  
Function Method ◽  
Minimum Weight ◽  
Inequality Constraints ◽  
Bridge Girders ◽  
Penalty Function Method ◽  
Minimum Weight Design ◽  
Overall Stability ◽  
Weight Design ◽  
Load Conditions

The problem of the design of box-type bridge girders for electric overhead traveling cranes is formulated as a minimum weight design problem with inequality constraints. The restrictions placed on the design problem include limitations on the maximum allowable deflections and stresses as well as on the shock absorbing capacity during accidental collision. The overall stability and rigidity considerations are also taken into account. Several load conditions, as per the code specifications, are considered in the design problem. The resulting nonlinear programming problem is solved by using an interior penalty function method. Numerical examples are given to illustrate the effectiveness of the approach. The resulting computer program is used to make a sensitivity analysis of the problem.

scholarly journals Sub-Riemannian geometry and swimming at low Reynolds number: the Copepod case

2019 ◽  
Vol 25 ◽  
pp. 9 ◽  
Author(s):  
P. Bettiol ◽  
B. Bonnard ◽  
A. Nolot ◽  
J. Rouot
Keyword(s):  
Optimal Control ◽  
Reynolds Number ◽  
Maximum Principle ◽  
Numerical Simulations ◽  
Riemannian Geometry ◽  
Optimal Control Theory ◽  
Geometric Analysis ◽  
Optimal Solutions ◽  
The Maximum Principle ◽  
Recovery Stroke

In Takagi [Phys. Rev. E 92 (2015) 023020], based on copepod observations, Takagi proposed a model to interpret the swimming behaviour of these microorganisms using sinusoidal paddling or sequential paddling followed by a recovery stroke in unison, and compares them invoking the concept of efficiency. Our aim is to provide an interpretation of Takagi’s results in the frame of optimal control theory and sub-Riemannian geometry. The maximum principle is used to select two types of periodic control candidates as minimizers: sinusoidal up to time reparameterization and the sequential paddling, interpreted as an abnormal stroke in sub-Riemannian geometry. Geometric analysis combined with numerical simulations are decisive tools to compute the optimal solutions, refining Takagi computations. A family of simple strokes with small amplitudes emanating from a center is characterized as an invariant of SR-geometry and allows to identify the metric used by the swimmer. The notion of efficiency is discussed in detail and related with normality properties of minimizers.

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