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An evolution of the Simplicial package below, more focused
on the shooting method and Boundary Value Problem solving.
Sample problems included in the package:
- Low thrust orbital transfer with minimal fuel consumption
Changelog:
- 2.1: [11/10/2010] Rewrite of multi-arcs and mixed constraints, and numerical minimization of the Hamiltonian for
problems with non-analytic models.
- 2.0: [27/09/2010] Complete rewrite from scratch of the Shoot1.x package
. Parallel (OpenMP) grid shooting for an easier
initialization.
A
Piecewise Linear ("simplicial") continuation method to solve
optimal control problems via indirect methods.
The Simplicial package implements a
PL
continuation method, whose
objective is to follow the
zero
path
of an
homotopy
connecting two
problems. This is typically done by building a piecewise linear
approximation of the path over a triangulation of the research space in
simplices (hence the name "simplicial methods").
This code was designed more specifically for the resolution of
optimal control
problems via
indirect
methods (necessary
conditions, Pontriagyn's Maximum Principle). Such methods transform the
original problem into finding a zero of a certain
shooting function,
whereas direct
methods involve complete (state-control) or partial (control only)
discretization of the problem.
The package is written mostly in standard Fortran 9x, and includes
several
F77 third party codes (mostly integrators). Main features
include
several choices of triangulations (uniform or refining), with
fixed or adaptive meshsize, and generation of various output
files
related to the zero path,
with associated Matlab scripts for visualization.
The shooting method part offers several choices of integrators (fixed
or variable step), and can handle control discontinuities and singular
arcs. The use of variational equations to compute the Jacobian of the
shooting function (with smooth or discontinuous control).
Download the Simplicial
package v1.3 (10/07/2006) (sources
+ problem files + user guide)
Sample problems included in the package:
- Demo Problem (simple dim 2 optimal control problem)
- Low thrust orbital transfer with minimal fuel consumption
- Two singular arcs problems
Changelog:
- 1.3
(10/07/2006):
variational equations for Jacobian evaluation.
- 1.2
(17/01/2006):
discontinuous control specific handling.
- 1.1
(21/07/2005): some
internal rewriting and cleaning, singular arcs problem files.
- 1.0
(25/03/2005): first
version, with demonstration and orbital transfer problem files.