robust conformal controller synthesis

This work addresses the challenge that existing conformal prediction–based CLF/CBF controllers struggle to guarantee system stability and safety due to distribution shifts induced by closed-loop policy updates. To overcome this limitation, the paper proposes a phased iterative update strategy that integrates adversarially robust conformal prediction with a distribution shift budget during each policy optimization step. Notably, it provides the first theoretical guarantees of cross-iteration stability and safety for robust conformal CLF/CBF methods. Leveraging trajectory sensitivity analysis, the authors design both explicit and implicit update rules for conformal prediction boundaries. Empirical validation across three case studies demonstrates that the proposed approach achieves safe and stable control performance with rigorous theoretical assurances.

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.

This work addresses the challenge of verifying neural control barrier functions (NCBFs) for nonlinear dynamical systems, where learning errors lead to both verification intractability and excessive conservatism. We propose CP-NCBF—the first framework integrating conformal prediction with NCBFs—abandoning restrictive Lipschitz continuity assumptions and instead employing quantile calibration for probabilistic safety certification. CP-NCBF guarantees that the safety set containment probability is rigorously controlled at a user-specified confidence level. Compared to existing approaches, CP-NCBF achieves sample efficiency, scalability, and relaxed safety set constraints. In autonomous driving obstacle avoidance and UAV geofencing tasks, it significantly expands the feasible safe region while reducing conservatism, all while strictly bounding the safety verification error rate within a pre-specified threshold.

Addressing the challenge of achieving both high performance and formal safety guarantees for high-dimensional autonomous systems in real-world environments, this paper proposes a two-stage co-optimization framework. In the first stage, state constraints are relaxed into penalty terms within a gradient-based model predictive control (MPC) formulation, enhancing computational efficiency and scalability. In the second stage, a safety-critical control barrier function (CBF)-based filter is constructed and implemented via quadratic programming (QP) to minimally modify a reference controller while strictly enforcing hard safety constraints. The method innovatively integrates gradient optimization, relaxed safety-constrained optimal control problems (SC-OCPs), and CBF-QP filtering—thereby reconciling high-performance control with formal safety certification, while avoiding the excessive conservatism and computational infeasibility common in conventional safety filters. The approach is validated on two high-dimensional, complex dynamical systems.

Ensuring safety for nonlinear affine systems under complex, uncertain disturbances remains challenging. Method: This paper proposes a robust safety controller that integrates uncertainty estimation with high-order control barrier functions (HOCBFs). It innovatively embeds bounds on estimation errors directly into the CBF constraints and extends the formulation to a second-order cone programming (SOCP) framework. The approach unifies elastic actuator modeling, HOCBF-based safety constraints, and quadratic-programming (QP) feedback control. Contribution/Results: It is the first method to provide rigorous robust safety guarantees against both matched and mismatched disturbances. Evaluations in simulation and on a tracked robot navigating inclined terrain demonstrate 100% safety constraint satisfaction, a 42% improvement in disturbance rejection, and significantly enhanced motion robustness and real-time safety under dynamic uncertainties.

Existing control barrier function (CBF) approaches rely on explicit structural knowledge of system dynamics and uncertainty models, limiting their applicability to general nonlinear systems and often yielding overly conservative safe sets. This work proposes a model-free robust Q-CBF framework that, for the first time, integrates the safety value function with the Q-function to formulate robust safety constraints directly in the state-action space. By leveraging adversarial reinforcement learning and solving the associated Hamilton–Jacobi–Isaacs equation, the method computes the largest possible robustly safe set. Evaluations on an inverted pendulum and a 36-dimensional quadrupedal robot demonstrate that the proposed approach significantly reduces conservatism and achieves more reliable safe control under unknown disturbances.

本文提出一种基于自适应保形分位数预测区间的安全控制框架，以解决不确定性条件下的安全关键控制问题，提高控制性能并确保高概率安全性。

This work addresses the lack of statistical guarantees on tracking error and safety in data-driven nonlinear control arising from modeling uncertainties in Koopman operator-based approaches. To this end, the paper proposes a closed-loop control framework that integrates Koopman operators, contraction theory, and conformal prediction. Notably, it introduces distribution-free conformal prediction into Koopman-based control for the first time, explicitly characterizing both forward and inverse modeling errors. This integration yields quantifiable probabilistic bounds on tracking error, thereby enabling high-precision control with statistically robust safety assurances. The effectiveness of the proposed method is validated through simulations on a Dubins car and real-world experiments on a flapping-wing unmanned aerial vehicle, demonstrating its ability to simultaneously ensure safety and tracking performance under significant modeling uncertainty.

This work addresses the excessive conservatism of traditional control methods in safety-critical systems, which often compromises optimal performance and feasibility. To overcome this limitation, the authors propose a novel framework that embeds Control Barrier Functions (CBFs) as terminal constraints within Model Predictive Control (MPC), thereby rigorously guaranteeing safety while significantly reducing conservatism and enlarging the set of reachable states. The approach enables warm-starting of the underlying nonlinear optimization problem to accelerate convergence and is supported by constructive theoretical proofs ensuring formal correctness. Simulation results demonstrate a 1.7–2.7× reduction in infeasible regions and successful tracking of reference trajectories entirely residing within regions deemed unsafe by conventional CBF formulations, thereby validating the method’s superiority and effectiveness.

This work addresses the challenge of providing reliable safety guarantees in high-dimensional systems, where learning-based safety filters often fail due to prediction errors. To overcome this limitation, the paper proposes Adaptive Conformal Filtering (ACoFi), a novel framework that integrates Hamilton-Jacobi reachability analysis with adaptive conformal inference to dynamically adjust the policy switching threshold in response to prediction uncertainty. ACoFi offers an asymptotically valid, user-specified upper bound on the miscoverage rate of safety predictions, thereby delivering a soft yet theoretically grounded safety guarantee. Experimental evaluations on Dubins car and Safety Gymnasium benchmarks demonstrate that ACoFi significantly outperforms fixed-threshold baselines, achieving higher safety performance and fewer constraint violations—particularly in out-of-distribution scenarios.