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Optimization Two Point BVPs

  1. Jul 11, 2006 #1
    Hey everyone, I'm working on a project here to develop a two point BVP solver. As we all know optimizing a TPBVP is not the easiest thing in the world. Let me first start by giving you an example of what I'm doing. We wish to optimize the launch trajectory of a rocket assuming the only forces are inertial forces and inverse squared gravitation. (Neglect aerodynamic forces - at least for now). The result is a TPBVP in which 3 initial conditions are unkown. The way I'm approaching this optimization problem is using the Euler- Lagrange method. In the end im summing up the error of each simulation. The error is the difference between the specificed terminal conditions and the actual simualted conditions. By modified the three initial conditions of the cofactos it becomes possible to eliminate the error. Since there are 3 IC's we must choose perfectly its like finding a point in the box. My current method is to evaluate the error in planes where 1 IC is held constant and the other two may vary. The find the minimum constraint violation and search 1 plane higher in the same "neighborhood" and 1 plane lower and determine which one is tending towards the minimum to choose the appropriate direction. This method is called the shooting method and is a very long iteration process. Is there any other way to solve these TPBVPS. I know this topic is fairly advanced and not many people know of the method but im just looking for some decent input as this is taking FOREVER to simualte, i need a better computer :(
  2. jcsd
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