a post with bibliography

Deep reinforcement learning (RL) has achieved impressive empirical success in complex control tasks, many of which are fundamentally set-stabilization problems. To safely deploy learned policies, existing methods often modify RL algorithms to enforce formal stability guarantees. However, these algorithmic modifications alter the core RL objective, which can restrict natural exploration and complicate training. This paper offers a complementary perspective: while such algorithmic modifications are valuable for training-time safety during exploration, modifying the core RL objective is often unnecessary to guarantee the stability of the deployed policy. We prove that the unmodified discounted RL objective intrinsically guarantees closed-loop practical asymptotic stability in deterministic continuous control settings. By adapting the discrete-time input-to-state stability (ISS) framework and drawing inspiration from discounted model predictive control (MPC), we model the suboptimality induced by the discount factor and the neural network approximation error as bounded disturbances. We establish that near-optimal parameterized feedback laws steer the closed-loop system into a bounded neighborhood of the target set. The size of this neighborhood vanishes in the limit as the approximation error approaches zero and, subsequently, the discount factor approaches one.

We address the challenge of switching among multiple learned policies in reinforcement learning control systems, where conventional value function-based methods can lead to chattering in the presence of small measurement noise. Our goal is to design a switching logic that assures asymptotic stability and maintains a robustness margin so that rapid switching is prevented under bounded measurement noise. To this end, we propose a timer-based hybrid supervisor that integrates a resettable timer that enforces a minimum dwell time on the active policy. This dwell time is adaptively adjusted by predicting the evolution of the state of the system, ensuring that a switch occurs only when a significantly better alternative is predicted. We derive sufficient conditions under which the hybrid supervisor is guaranteed to exhibit non-Zeno behavior and render a compact set robustly globally asymptotically stable in the presence of bounded measurement noise. Simulation results on representative decision-making problems demonstrate that our hybrid supervisor is robust under noisy conditions where a conventional switching strategy fails.

Combines hybrid control theory with reinforcement learning by embedding hysteresis-based switching logic across overlapping state-space regions, eliminating chattering vulnerabilities in obstacle avoidance tasks.