Inverting Self-Triggered Control: Adversarial Reinforcement Learning for Sparse Denial-of-Service Attacks

Self-triggered reinforcement learning control (RL-STC) learns the sparsest control schedule that preserves Lyapunov-decreasing stability under a Run-Time Assurance (RTA) override. We invert this: an adversarial RL agent learns the sparsest jamming or Denial-of-Service (DoS) schedule that destabilizes the closed loop, with a Lyapunov-increase admissibility predicate mirroring the defender's safety certificate. We prove a plant-property lower bound on the minimum jam count required for an immediate hold-last medium-access-control adversary to force a crash against a self-triggered controller (STC) satisfying a Lyapunov contract, and recover a certificate-level analog of the consecutive-grouping optimality of prior count-budget DoS scheduling as a corollary. This extends the DoS-scheduling count-budget analysis from periodic and linear-time-invariant to STC controllers. Empirically, we train against four fixed defenders per plant (one Linear Quadratic Regulator (LQR) and three RL-STC) on Pendulum, CartPole, and Quadrotor2D. The learned adversary is the only adversary that crashes every defender on every plant at 100%: greedy misses Quadrotor2D LQR on 42% of episodes and periodic misses Pendulum LQR on 97%. On jam-time-per-failure it beats baselines by up to 2.8 times, and shows its widest absolute margin on Quadrotor2D LQR. Robustness ablations show that Gaussian observation noise exceeding the initial-state magnitude and position-only observation both preserve 100% failure rate and keep the learned adversary strictly ahead of both baselines on jam-time-per-failure.