Bounded Controller Synthesis for CGBF

This repository is an add-on to the paper:

Ding, J., Yuan, D. and Deka, S.A., 2025.
Backstepping Reach-avoid Controller Synthesis for Multi-input Multi-output Systems with Mixed Relative Degrees.
arXiv:2505.03612

It provides code and tools to enforce control bounds for the proposed reach-avoid controller via a Sum-of-Squares (SOS) programming approach.

Further documentation:
See Docs/Bounded_Controller_Synthesis_for_CGBF_Controller.pdf

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File Structure

• Docs/: Documentation of the proposed approach to enforce control bounds.
• cbf_with_constraints.py: Applies CBF to constrain dynamics within a defined safe $\psi$ region (Python).
• constrained_CBF_solver.jl: Julia script to solve the CBF SOS problem given system dynamics and safe region.
• constrained_HOCBF_solver.jl: Julia script to solve the High-Order CBF SOS problem.
• sos_solver.jl: Julia SOS solver providing:
  • sos_solver: Original SOS solver for the CGBF problem.
  • sos_solver2: Solver for control bounds with polynomial decision variable $\mu$.
  • sos_solver3: Solver for control bounds with scalar decision variable $\mu$.
• combined_controller.jl: CGBF controller with additional SOS constraints to enforce control bounds (depends on sos_solver.jl).
• utils.py: Python utility functions.
• utils.jl: Julia utility functions.

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References

1. Ding, J., Yuan, D. and Deka, S.A., 2025. Backstepping Reach-avoid Controller Synthesis for Multi-input Multi-output Systems with Mixed Relative Degrees. arXiv:2505.03612