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Please do not hesitate to send your comments, questions or bug reports ! 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.