Robust Optimal Control of Arbitrarily Switched Systems: A Path-Complete Framework

What the math gives to ML

The paper supplies a constructive way to handle arbitrary discrete switching by assigning separate value or Lyapunov-like functions to nodes of a labeled path-complete graph, then combining them through a reachability-aware min-max operation. This is transferable to robust reinforcement learning and recurrent architectures exposed to unknown sequences of dynamics, corruptions, or update operators: instead of one critic or one stability certificate, train a structured family whose graph edges cover every possible mode transition. The key engineering asset is not merely multiple critics, but the reachability condition that makes a pointwise min-max envelope valid under arbitrary switching. A practical first implementation is a neural robust critic trained with sampled Bellman-inequality violations, followed by interval or Lipschitz verification on a bounded state region if formal certification is required.