perform reachability analysis

This paper addresses the automated identification of consistency between dynamic models and empirical measurements in cyber-physical system (CPS) safety verification—specifically, verifying whether their respective reachable sets coincide. Method: We propose a unified optimization framework driven by reachable-set verification, integrating interval analysis, robust optimization, and data-driven modeling to jointly identify parametric and structural model uncertainties. Our approach generalizes reachable-set consistency identification from linear state-space models to nonlinear state-space and input–output models, supporting white-box, gray-box, and black-box modeling paradigms under varying levels of prior dynamical knowledge. Results: Evaluated on both synthetic and real-world CPS datasets, the method significantly improves coverage of safety-critical behaviors and ensures reliable transfer of formal verification results to physical implementations.

This work addresses the verification challenge of stochastic dynamical systems subject to temporal logic specifications whose predicates evolve randomly over time. The authors propose a novel framework based on barrier certificates, constructing an augmented state space to transform stochastic predicate temporal specifications into deterministic ones. This approach extends, for the first time, the barrier certificate methodology to settings involving stochastically evolving predicates. By replacing conventional dynamic programming with convex optimization, the method derives analytical upper bounds on violation probabilities for linear systems under safety-type specifications. Numerical experiments demonstrate that the proposed technique achieves a favorable trade-off between computational efficiency and conservativeness.

Traditional model-based verification and safety control methods fail for learning-enabled autonomous systems (LEAS) due to the inherent complexity and opacity of learning-enabled components (LECs). Method: This paper proposes the first model-free, unified framework for formal verification and safety control of LEAS, grounded in conformal prediction (CP). The framework enables distribution-free, real-time, and interpretable uncertainty quantification without requiring system models. Contribution/Results: It establishes, for the first time, a rigorous theoretical foundation for CP in formal verification, safety-critical control, and robotic task execution—integrating linear temporal logic (LTL), neural network input-output verification, and scenario-based optimization. Evaluated on navigation tasks, the framework achieves high-accuracy offline and online verification with provably safe, computationally efficient, and statistically guaranteed control. This work introduces a novel safety assurance paradigm for LEAS that bridges formal rigor and practical deployability.

For uncertain continuous-time nonlinear systems, Signal Temporal Logic (STL) verification faces a fundamental challenge: ambiguous “uncertain satisfaction” due to either over-approximation of reachable sets or incomplete simulation. This paper proposes an STL verification framework based on incremental reachability analysis. Our method addresses the problem by: (1) extending STL semantics with Boolean interval arithmetic and traceable uncertainty annotations; (2) performing localized, incremental refinement only on reachable sets that induce uncertainty—avoiding costly global recomputation; and (3) introducing a hierarchical signal processing architecture enabling synchronized online/offline monitoring and adaptation to system evolution. Evaluated on a nonlinear oscillator benchmark, the approach substantially reduces satisfaction ambiguity, demonstrating high accuracy, computational efficiency, and robustness for complex nonlinear systems under uncertainty.

Computing high-fidelity, computationally efficient probabilistic reachable sets (PRS) is critical for safe path planning in autonomous systems. Existing approaches—including Monte Carlo sampling, Hamilton–Jacobi (HJ) analysis, Gaussian processes, and filtering-based fusion—suffer from prohibitive computational cost, strong dependence on accurate dynamical models, or requirements for large-scale labeled data. This paper proposes a self-supervised neural network framework for convex approximation of two-dimensional PRS. It introduces the first integration of self-supervised multi-label learning with knowledge distillation from a convex optimization-based expert model—requiring neither prior dynamical system knowledge nor extensive sampling. Leveraging only a small number of trajectory samples, the method efficiently generates high-fidelity PRS. Experiments demonstrate that it matches the accuracy of the expert convex optimizer while accelerating PRS generation by over two orders of magnitude, substantially outperforming state-of-the-art baselines.

Traditional Markov automata require fully known parameters, rendering them ill-suited for scenarios involving uncertain rates or environmental perturbations. This work proposes parametric Markov automata (pMA), the first framework enabling time-bounded reachability verification for systems with uncertain parameters. By discretizing pMAs into parametric Markov decision processes (pMDPs) and integrating error-bounded numerical analysis with parametric probabilistic model checking, the approach precisely partitions the parameter space into regions that satisfy or violate a given property within the Storm model checker. Experimental results demonstrate that the method achieves high verification accuracy, with performance primarily limited by the discretization of the pMA model.

This work addresses the problem of certifying safety reachability prior to executing a fixed control sequence under model mismatch and sparse single-step transition data. By constructing a set-membership envelope of model errors and propagating reachability tubes via zonotopes, certification is granted only when safety constraints are satisfied. The key contribution lies in uncovering a trilemma among trajectory inclusion, finite projection width, and model error, leading to a condition-dependent certification mechanism that avoids overconfidence in regions lacking data. The approach integrates component-wise Lipschitz bounds, set-membership modeling, and lower-bound analysis of projection width. Evaluated on two benchmark systems, it outperforms calibrated baselines by rejecting certification for sequences unsupported by data while recovering valid certification when relevant data and sufficient collision-avoidance margins are present.

This work addresses the challenges of transferability and computational feasibility in discrete abstraction for symbolic model checking of cyber-physical systems by proposing a conservatism-first, four-step modular workflow to construct finite-state abstractions of closed-loop dynamical systems. The approach integrates state partitioning, conservative transition construction, spurious behavior elimination, and specification semantics lifting, enabling composable and replaceable subroutine design. Transition relations are built using axis-aligned bounding boxes, polyhedra, and sampling with PAC coverage certificates, combined with certified erasure and counterexample-guided refinement. Reliable lifting of LTL specifications is achieved through may–must semantics. Evaluation across three case studies demonstrates that the workflow effectively balances abstraction accuracy and verification efficiency while clearly revealing the impact of different design choices on the outcomes.

This work addresses the high computational cost of traditional invariant set computation for hybrid systems with limit cycles, such as legged robots. The authors propose a three-step method that computes an upper bound of the continuous-flow reachable set around a nominal trajectory, records its intersection with switching surfaces, and propagates this set through the reset map to formally verify forward invariance by checking whether the one-step reachable set is strictly contained within the initial set. Innovatively, they extend parametric embedding—a differentiable invariant set computation technique—to hybrid limit-cycle systems for the first time and integrate it within a bilevel optimization framework to synthesize controllers that maximize the invariant set volume. Implemented in the JAX-based immrax library, the approach demonstrates significant improvements in closed-loop robustness on a simplified bipedal walking model.

This work addresses the challenge of safety certification for dynamical systems under uncertainty by proposing a novel non-recursive approach that circumvents the error accumulation inherent in traditional dynamic programming over long time horizons, which often renders lower bounds on safety probabilities invalid. The method reformulates safety certification as a classification problem over trajectory data and introduces, for the first time, a kernel embedding framework to directly estimate T-step safety probabilities. This framework unifies existing paradigms such as barrier certificates and robust Markov models and extends naturally to non-Markovian systems. Experimental results on a neural network-controlled quadrotor demonstrate that the proposed approach yields stable and reliable safety guarantees in both long-horizon and non-Markovian settings, whereas conventional dynamic programming produces either vacuous or unsafe outcomes.