SMC-ES: Automated synthesis of formally verified control policies

Reinforcement learning (RL) enables the synthesis of control policies directly from data, making it highly appealing for complex cyber-physical systems (CPSs) and robotics. A persistent challenge, however, is ensuring strict, hard safety constraints during the active learning phase. In real-world physical systems, violating mechanical limits can cause irreversible damage, necessitating that exploration remains strictly within safe operational regions. We propose a generalized framework that combines the adaptive, high-performance nature of deep reinforcement learning (DRL) with the formal safety guarantees of model predictive control (MPC). Using a mathematical model of the system dynamics, offline MPC computations define a feasible state-action space, representing all safe combinations of system states and control inputs that guarantee constraint satisfaction. During training and deployment, the RL agent's instantaneous actions are projected onto this globally verified feasible set via a safety filter. We systematically evaluate our generalized approach on a non-linear 1-DoF laboratory testbed, demonstrating successful exploration and stable policy convergence on physical hardware.

Training controllers that are safe and robust in simulation, and systematically assessing their readiness for real-world deployment, remain key challenges in sim-to-real transfer. To address this, we propose LyEvO, a physics-grounded framework that combines constrained Evolutionary Optimization and Statistical Model Checking (SMC)-based verification with Lyapunov-based stability analysis. Leveraging prior knowledge of the system dynamics, LyEvO uses Lyapunov analysis to compute an initial candidate stability region. An iterative loop then uses operational scenarios drawn from this region to jointly optimize and statistically verify a policy, and subsequently expands the region's boundaries based on the verification outcome. This integrated procedure provides a practical criterion for assessing deployment readiness. We evaluate LyEvO on Cartpole and 3D Quadrotor benchmarks through extensive simulations and targeted real-world experiments, demonstrating safe and robust sim-to-real transfer.

Autonomous agents, whether LLM-driven software agents or robotic physical agents, face a common class of failure modes when operating without continuous human oversight: safety violations from unverified actions, behavioral instability from unconstrained loops, and continuity loss from unhandled error states. We develop \system{}, a discrete-time control system that combines five execution gears (\Gobs{}, \Gsug{}, \Gplan{}, \Gexec{}, \Gint{}) with utility-gated dispatch and event-driven fallback. For the single-agent case, we prove monotonic stability, execution safety, eventual stabilization, fallback completeness, and equivalence to a gear-constrained Markov decision process. For multi-agent cyber-physical systems (CPS), we apply the established \smart{} managed-autonomy lifecycle and map runtime evidence into its four governance states (\Stable{}/\Meta{}/\Assisted{}/\Regulated{}). Consensus gating, swarm-level Lyapunov analysis, per-agent gear authority, and rendezvous control provide distributed safety and stability guarantees, including zero collision under the stated assumptions. We evaluate the resulting runtime on a three-agent UR5 robotic assembly cell using fault magnitudes calibrated from the NIST \emph{Degradation Measurement of Robot Arm Position Accuracy} dataset across 10,000 Monte Carlo episodes. It achieves a 99.6% anomaly detection rate versus 2.1% for the single-agent baseline, reduces detection latency by $3.5\times$, and supplies a formal physical-workspace safety certificate. The execution gears act as micro-level permissions beneath the \smart{} runtime governance states, separating action control from autonomy governance.