Safe and Robust Domains of Attraction for Discrete-Time Systems: A Set-Based Characterization and Certifiable Neural Network Estimation
department of Applied Mathematics, University of Waterloo（应用数学系，滑铁卢大学）；Department of Mechanical and Mechatronics Engineering at the University of Waterloo（机械与机电工程系，滑铁卢大学）
Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizing DOAs for general nonlinear systems remains challenging due to both theoretical and computational limitations, particularly in the presence of uncertainties and state constraints. In this paper, we propose a novel framework for the accurate estimation of safe (state-constrained) and robust DOAs for discrete-time nonlinear uncertain systems with continuous dynamics, open safe sets, compact disturbance sets, and uniformly locally $\ell_p$-stable compact RISs. The notion of uniform $\ell_p$ stability is quite general and encompasses, as special cases, uniform exponential and polynomial stability. The DOAs are characterized via newly introduced value functions defined on metric spaces of compact sets. We establish their fundamental mathematical properties and derive the associated Bellman-type (Zubov-type) functional equations. Building on this characterization, we develop a physics-informed neural network (NN) framework to learn the corresponding value functions by embedding the derived Bellman-type equations directly into the training process. To obtain certifiable estimates of the safe robust DOAs from the learned neural approximations, we further introduce a verification procedure that leverages existing formal verification tools. The effectiveness and applicability of the proposed methodology are demonstrated through four numerical examples involving nonlinear uncertain systems subject to state constraints, and its performance is compared with existing methods from the literature.
Certifiable Safe RLHF: Semantic Grounding and Fixed Penalty Constraint Optimization for Safer LLM Alignment
Department of Electrical and Computer Engineering（电气与计算机工程系）；New Jersey Institute of Technology（新泽西理工学院）；Department of Computer Engineering（计算机工程系）；Heritage Institute of Technology（遗产理工学院）
Safe Domains of Attraction for Discrete-Time Nonlinear Systems: Characterization and Verifiable Neural Network Estimation
Department of Applied Mathematics, University of Waterloo（应用数学系，滑铁卢大学）；Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign（电气与计算机工程系，伊利诺伊大学厄巴纳-香槟分校）
Barrier-Riccati Synthesis for Nonlinear Safe Control with Expanded Region of Attraction
Control & Instrumentation Engineering Department, King Fahd University of Petroleum and Minerals（国王法赫德石油和矿物大学控制与仪器工程系）；Department of Electrical & Computer Engineering（电气与计算机工程系）；Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）；Daniel Guggenheim School of Aerospace Engineering（丹尼尔·古根海姆航空航天工程学院）；George W. Woodruff School of Mechanical Engineering（乔治·W·伍德鲁夫机械工程学院）
Robust Co-Design of Canonical Underactuated Systems for Increased Certifiable Stability
German Research Center for Artificial Intelligence (DFKI GmbH)（德国人工智能研究中心）；University of Padova（帕多瓦大学）；Chalmers University of Technology（查尔姆斯理工大学）；University of Bremen（不来梅大学）
