simulatetraj documentation

Simulatetraj solves initial value problems of the form \(\dot{x}=f(x,u,t,p)\). The definition of the variables are provided in the table.

Symbol	Description	Dimensions
\(x(t)\)	State vector	\(\mathbb{R}^{n_x}\)
\(u(t)\)	Control vector	\(\mathbb{R}^{n_u}\)
\(p\)	Parameter vector	\(\mathbb{R}^{n_p}\)
\(t\)	time	\(\mathbb{R}^{1}\)

Backend Implementation

The simulatetraj function utilizes a CasADi integrator backend, supporting various numerical methods such as explicit RK4, IRK, and solvers from the CVODES suite. The framework supports symbolic objects, allowing for the construction of symbolic state trajectories that can be embedded into expression graphs for nonlinear optimization within CasADi.

Numerical Transformation and Efficiency

Internally, the differential equation is transformed from the time interval \([t_0, t_f]\) to a normalized domain \([0, 1]\) .

\[\begin{split}\dot{x}=f(t,x,u)\\ \dot{x}=(t_f-t_0) f(t_0+(t_f-t_0)\tau,x,u)\end{split}\]

This approach offers significant advantages.

• Numerical Conditioning - It improves stability and facilitates parametric studies.

• Resource Optimization - Most importantly, it allows the integrator object to be reused within the context of multiple shooting. This eliminates the overhead of repeated object creation, saving valuable computational time.

Installation:

• Installation instructions

Differential equation:

• ODE 1
  • Elimination
  • without control elimination
• ODE 2
• Lotka voltera/prey-predator model

Trajectory optimization:

• Symbolic integrator for OCPs
• Optimal control problem 1
• Optimal control problem 2

API:

• API

Indices and tables

• Index

• Module Index

• Search Page