feat(gds-control): backward reachable set computation #127
Description
Problem
gds-control models control system structure (states, inputs, sensors, controllers) but does not compute reachable sets. Backward reachability is a key analysis tool for safety verification and differential games.
Proposed Solution
Add reachability analysis to gds-control:
- Backward reachable set computation from target sets
- Isochrone extraction (level sets of the value function)
- Compatible with continuous-time models (feat(gds-sim): continuous-time ODE integration support #122)
- Visualization support (feat(gds-viz): dynamical systems visualization (phase portraits, trajectories) #126)
Motivation
The Homicidal Chauffeur notebook computes backward reachable sets by integrating 80 dense trajectories backward from the capture circle, then extracting isochrones at T=1,2,4,6,8,12.
Dependencies
- feat(gds-sim): continuous-time ODE integration support #122 (continuous-time ODE integration — backward integration)
- feat(gds-viz): dynamical systems visualization (phase portraits, trajectories) #126 (dynamical visualization — isochrone plots)