The Direct Multiple Shooting Method for Optimal Control

2011 ◽  
pp. 13-29 ◽  
Author(s):  
Christian Kirches
Keyword(s):  
Optimal Control ◽  
Shooting Method ◽  
Multiple Shooting ◽  
Multiple Shooting Method

scholarly journals OPTIMAL CONTROL OF THE ATMOSPHERIC ARC OF A SPACE SHUTTLE AND NUMERICAL SIMULATIONS WITH MULTIPLE-SHOOTING METHOD

2005 ◽  
Vol 15 (01) ◽  
pp. 109-140 ◽  
Author(s):  
B. BONNARD ◽  
L. FAUBOURG ◽  
E. TRELAT
Keyword(s):  
Optimal Control ◽  
Shooting Method ◽  
Space Shuttle ◽  
Dynamic Pressure ◽  
Thermal Flux ◽  
Optimal Solution ◽  
Multiple Shooting ◽  
The Maximum Principle ◽  
Multiple Shooting Method ◽  
Geometric Optimal Control

This article, continuation of previous works,5,3 presents the applications of geometric optimal control theory to the analysis of the Earth re-entry problem for a space shuttle where the control is the angle of bank, the cost is the total amount of thermal flux, and the system is subject to state constraints on the thermal flux, the normal acceleration and the dynamic pressure. Our analysis is based on the evaluation of the reachable set using the maximum principle and direct computations with the boundary conditions according to the CNES research project. The optimal solution is approximated by a concatenation of bang and boundary arcs, and is numerically computed with a multiple-shooting method.

scholarly journals Block-structured quadratic programming for the direct multiple shooting method for optimal control

2011 ◽  
Vol 26 (2) ◽  
pp. 239-257 ◽  
Author(s):  
Christian Kirches ◽  
Hans Georg Bock ◽  
Johannes P. Schlöder ◽  
Sebastian Sager
Keyword(s):  
Optimal Control ◽  
Quadratic Programming ◽  
Shooting Method ◽  
Multiple Shooting ◽  
Multiple Shooting Method ◽  
Block Structured

scholarly journals Multiple shooting method in stability analysis of non-prismatic multi-segment columns

2013 ◽  
Vol 12 (4) ◽  
pp. 225-232
Author(s):  
Ryszard Hołubowski ◽  
Andrzej Merena
Keyword(s):  
Finite Element Method ◽  
Stability Analysis ◽  
Shooting Method ◽  
High Efficiency ◽  
Variable Coefficients ◽  
Multiple Shooting ◽  
System Of Differential Equations ◽  
The Finite Element Method ◽  
Concentrated Force ◽  
Multiple Shooting Method

The application of multiple shooting method in stability analysis of non-prismatic multi-segment columns with pinned ends loaded with a concentrated force applied to the upper node has been presented. Numerical analyses were carried out for an exemplary three-segment column by solving the system of differential equations with variable coefficients and parameter. The results were compared with the solution obtained by using SOFiSTiK software based on the finite element method. The analyses show that considering the stiffness changes along the length can have a significant influence on the values of critical loads and thus change the resistance of the column. The advantage of the proposed method is its high efficiency and easy description of stiffness changes.

Nonlinear Analysis of Rotor Systems Including a Bearing Clearance by the Multiple Shooting Method

2001 ◽  
Author(s):  
David Demailly ◽  
Fabrice Thouverez ◽  
Louis Jézéquel ◽  
Jérôme Bonini
Keyword(s):  
Contact Zone ◽  
Response Curve ◽  
Shooting Method ◽  
Simplified Model ◽  
Multiple Shooting ◽  
Frequency Response Curve ◽  
Rotor Systems ◽  
Transition Zones ◽  
Full Contact ◽  
Multiple Shooting Method

Abstract In this paper the Multiple Shooting Method is briefly exposed. This method is then applied to a simplified model of a rotor/stator system including a bearing with clearance under static and unbalance forces. With bearing having a small amount of clearance, it is pointed out that the orbits are no longer circular at certain frequencies as for linear systems. If the clearance is large, the frequency response curve can be divided into three zones: a non-contact zone, a zone with one or several gains and looses of contact per period and a full contact zone. For both cases we emphasize on the evolution of the orbits while passing through transition zones.

scholarly journals Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Amira Rachah ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Ebola Virus ◽  
World Health ◽  
Multiple Shooting ◽  
Multiple Shooting Method ◽  
Major Outbreak ◽  
Health Organization ◽  
Spread Of Infection ◽  
The Impact

The Ebola virus is currently one of the most virulent pathogens for humans. The latest major outbreak occurred in Guinea, Sierra Leone, and Liberia in 2014. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multiple shooting method.

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