Example gallery
A guide answers "how do I do X"; an example answers "what does a real problem look like". Each page here is a complete, self-contained problem worked end to end — a story with a result, not a feature demonstration.
Read them in order: each one uses something the previous introduced.
| Example | Story | Introduces |
|---|---|---|
| Energy minimisation | The double integrator, transferred at minimal energy. | @def, solve, plot, a Hamiltonian flow, shooting |
| Time minimisation (bang–bang) | The same wagon, transferred as fast as possible. | bang–bang control, flow concatenation, switching-time detection |
| Parameter estimation without a control | Fitting a growth rate and an oscillator's pulsation — no control anywhere. | control-free problems, variable_costate=true |
| Control and variable together | The same two systems, now with a control input to pay for. | estimating a parameter and a control at once |
| Singular control | A drift system whose optimal control has a singular arc. | Lift, @Lie Poisson brackets, the Geometry toolkit's payoff |
| State constraint | The double integrator again, this time with a velocity or position bound. | boundary arcs, costate jumps, constraint=/multiplier= |
See also
- Flows overview and Geometry overview — the tools these examples are built from.