Trajectory and Control

This page highlights the externally facing APIs for trajectory sheaves and control-oriented examples.

When to use this page

Use this guide when you want to:

• Encode a discrete-time dynamical system as a sheaf.
• Solve boundary-value trajectory problems via sheaf methods.
• Work with controlled trajectory models and platoon-style examples.

Trajectory Sheaf Construction

• Main APIs: TrajectorySheaf, build_trajectory_sheaf, colocation_trajectory.
• See: Trajectory Sheaves.

Controlled Dynamics

• Main APIs: ControlledTrajectorySheaf, controlled_vehicle_platoon_with_herding.
• See: Trajectory Sheaves and Herding Platoon Utilities.

# Sketch: discrete-time trajectory sheaf from x_{t+1} = A * x_t
S = TrajectorySheaf(A, horizon)

# Colocation solve for endpoint constraints
traj = colocation_trajectory(S, x0, xT)

For end-to-end worked examples, start in:

• generated/trajectory_sheaf.md
• generated/control/controlled_vehicle_platoon.md
• generated/control/controlled_mass_spring_damper_chain.md